ECO 3104 - Examples
ECO 3104 - Examples This Version: September 26, 2013
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Supply and Demand Problem 1: The demand for books is: QD = 120 − P The supply of books is: QS = 5P
(a) What is the equilibrium price of books? (b) What is the equilibrium quantity of books sold? (c) If P = $15, do we observe a shortage or excess supply? How big is it? (d) If P = $25, do we observe a shortage or excess supply? How big is it? Problem 2: The inverse demand curve for product X is given by: PX = 25 − 0.005Q + 0.15PY , where PX represents price in dollars per unit, Q represents rate of sales in pounds per week, and PY represents selling price of another product Y in dollars per unit. The inverse supply curve of product X is given by: PX = 5 + 0.004Q. Determine the equilibrium price and sales of X when the price of product Y is PY = $10. Problem 3: The daily demand for hotel rooms on Manhattan Island in New York is given by the equation QD = 250, 000 − 375P. The daily supply of hotel rooms on Manhattan Island is given by the equation QS = 15, 000 + 212.5P. 2
What is the equilibrium price and quantity of hotel rooms on Manhattan Island? Problem 4: For U.S. consumers, the income elasticity of demand for fruit juice is 1.1. The economy enters a recession and consumer income declines by 2.5%. What is the expected percentage change in the quantity of fruit juice demanded? Problem 5: The cross-price elasticity of demand for peanut butter with respect to the price of jelly is -0.3. The price of jelly declines by 15%.What is the expected percentage change in the quantity demanded for peanut butter? Problem 6: Harding Enterprises has developed a new product called the Gillooly Shillelagh. The market demand for this product is given as follows: Q = 240 − 4P (a) At what price is the price elasticity of demand equal to zero? (b) At what price is demand infinitely elastic? (c) At what price is the price elasticity of demand equal to minus one? (d) If the shillelagh is priced at $40, what is the point price elasticity of demand? Problem 7: The demand for a bushel of wheat in 1981 was given by the equation QD = 3550 − 266P. (a) What is the price elasticity of demand at a price of $3.46? (b) If the price of wheat falls to $3.27 per bushel, what happens to the revenue generated from the sale of wheat? 3
Consumer Behavior Problem 8: Consider Gary’s utility function: U (X, Y ) = 5XY , where X and Y are two goods. (a) If Gary consumed 10 units of X and received 250 units of utility, how many units of Y must he have consumed? (b) Would a market basket of X = 15 and Y = 3 be preferred to the above combination? Problem 9: A consumer has $100 per day to spend on product A, which has a unit price of $7, and product B, which has a unit price of $15. What is the slope of the budget line if good A is on the horizontal axis and good B is on the vertical axis? Problem 10: If the quantity of good A (QA ) is plotted along the horizontal axis, the quantity of good B (QB ) is plotted along the vertical axis, the price of good A is PA , the price of good B is PB and the consumer’s income is I, then the . slope of the consumer’s budget constraint is Problem 11: The budget constraint for a consumer who only buys apples (A) and bananas (B) is PA A + PB B = I where consumer income is I, the price of apples is PA , and the price of bananas is PB . To plot this budget constraint in a figure with apples on the horizontal axis, we should use a budget line represented by which equation?
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Problem 12: Sally consumes two goods, X and Y . Her utility function is given by the expression U = 3XY 2 . The current market price for X is $10, while the market price for Y is $5. Sally’s current income is $500. (a) Write the expression for Sally’s budget constraint. (b) Determine the X, Y combination which maximizes Sally’s utility, given her budget constraint. (c) Calculate the impact on Sally’s optimum market basket of an increase in the price of X to $15. What would happen to her utility as a result of the price increase? Problem 13: Jane lives in a dormitory that offers soft drinks and chips for sale in vending machines. Her utility function is U = 3SC (where S is the number of soft drinks per week and C the number of bags of chips per week), so her marginal utility of S is 3C and her marginal utility of C is 3S. Soft drinks are priced at $0.50 each, chips $0.25 per bag. (a) Write an expression for Jane’s marginal rate of substitution between soft drinks and chips. (b) Use the expression generated in part (a) to determine Jane’s optimal mix of soft drinks and chips. (c) If Jane has $5.00 per week to spend on chips and soft drinks, how many of each should she purchase per week? Problem 14: An individual consumes products X and Y and spends $25 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y . The consumer in this case has a utility function expressed as: U (X, Y ) = 0.5XY 5
(a) Express the budget equation mathematically. (b) Determine the amount of consumption of X and Y that will maximize utility. (c) Determine the total utility that will be generated from the consumption bundle you calculated in part (b). Problem 15: Janice Doe consumes two goods, X and Y . Janice has a utility function given by the expression: U = 4X 0.5 Y 0.5 . The current prices of X and Y are 25 and 50, respectively. Janice currently has an income of 750 per time period. (a) Calculate the Marginal Utility of X and Y (b) Write an expression for Janice’s budget constraint. (c) Calculate the optimal quantities of X and Y that Janice should choose, given her budget constraint. (d) Suppose that the government rations purchases of good X such that Janice is limited to 10 units of X per time period. Assuming that Janice chooses to spend her entire income, how much Y will Janice consume? (e) Calculate the impact of the ration restriction on Janice’s utility. Problem 16: John consumes two goods, X and Y . The marginal utility of X and the marginal utility of Y satisfy the following equations: M UX = Y and M UY = X. The price of X is $9, and the price of Y is $12. (a) Write an expression for John’s MRS. (b) What is the optimal mix between X and Y in John’s market basket? 6
(c) John is currently consuming 15 X and 10 Y per time period. Is he consuming an optimal mix of X and Y ? Problem 17: Natasha derives utility from attending rock concerts (r) and from drinking colas (c) as follows: U (c, r) = c0.9 r0.1 (a) Calculate the marginal utility of cola (M Uc ) and the marginal utility of rock concerts (M Ur ) (b) If the price of cola (Pc ) is $1 and the price of concert tickets (Pr ) is $30 and Natasha’s income is $300, how many colas and tickets should Natasha buy to maximize utility? (c) Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the above prices and income, how many colas and tickets should Natasha buy to maximize utility? (d) Is Natasha better off with or without the constraint?
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Individual and Market Demand Problem 18: Donald derives utility from only two goods, carrots (Qc ) and donuts (Qd ). His utility function is as follows: U (Qc , Qd ) = Qc Qd The marginal utility that Donald receives from carrots (M Uc ) and donuts (M Ud ) are given as follows: M Uc = Qd and M Ud = Qc Donald has an income (I) of $120 and the price of carrots (Pc ) and donuts (Pd ) are both $1. (a) What is Donald’s budget line? (b) What is the optimal ratio of Qc and Qd ? (c) What quantities of Qc and Qd will maximize Donald’s utility? (d) Holding Donald’s income and Pd constant at $120 and $1 respectively, what is Donald’s demand curve for carrots? (e) Suppose that a tax of $1 per unit is levied on donuts. How will this alter Donald’s utility maximizing market basket of goods? Problem 19: The following data pertain to products A and B, both of which are purchased by Madame X. Initially, the prices of the products and quantities consumed are: PA = $10, QA = 3, PB = $10, QB = 7. Madame X has $100 to spend per time period. After a reduction in price of B, the prices and quantities consumed are: PA = $10, QA = 2.5, PB = $5, QB = 15. 8
Assume that Madame X maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Madame X to put her back on the original indifference curve, she would consume this combination of A and B: QA = 1.5, QB = 9 (a) Determine the change in consumption rate of good B due to (1) the substitution effect and (2) the income effect. (b) Determine if product B is a normal, inferior, or Giffen good. Explain. Problem 20: A local retailer has decided to carry a well-known brand of shampoo. The marketing department tells them that the quarterly demand by an average man is: QM d = 3 − 0.25P and the quarterly demand by an average woman is: QW d = 4 − 0.5P The market consists of 10,000 men and 10,000 women. How may bottles of shampoo can they expect to sell if they charge $6 per bottle? Problem 21: The price elasticity of demand for red herring is -4. The demand curve for red herring is: Q = 120 − P . What is the price of red herring? Problem 22: Harding Enterprises has developed a new product called the Gillooly shillelagh. The market demand for this product is given as follows: Q = 240 − 4P (a) If the shillelagh is priced at $40, what is the price elasticity of demand? Is demand elastic or inelastic? 9
(b) If the shillelagh price is increased slightly from $40, what will happen to the total expenditure on the Gillooly shillelagh? Problem 23: The demand for telephone wire can be expressed as: Q = 6000 − 1, 500P, where Q represents units, in pounds per day, and P represents price, in dollars per pound. Determine the price elasticity of demand at P = $2.00 per pound. Problem 24: The total world demand for power transmission wire is made up of both domestic and foreign demands. Thus, the total demand is the sum of the two sub-demands, which are given as: Domestic demand:Pd = 5 − 0.005Qd Foreign demand:Pf = 3 − 0.00075Qf , where Pd and Pf are in dollars per pound, and Qd and Qf are in pounds per day. (a) Determine the total world demand for power transmission wire. (b) Determine the prices at which domestic and foreign buyers would enter the market. (c) Determine the domestic and foreign quantities at P = $2.50 per pound. Check to see if the sum of Qd and Qf equals Q. (d) Determine total quantity sold at P = $4.00 per pound. Problem 25: Suppose that the demand for artichokes (Qa ) is given as: Qa = 120 − 4P 10
(a) What is the price elasticity of demand if the price of artichokes is $10? (b) Suppose that the price of artichokes increases to $12. What will happen to the number of artichokes sold and the total expenditure by consumers on artichokes? (c) At what price if any is the demand for artichokes infinitely elastic? Problem 26: Ronald’s monthly demand for Cap Rock Chardonnay is given by Q=6+
1 1 (I − T ) − P, 5, 000 10
where I is Ronald’s monthly income, T is his tax expense and P is the price of Cap Rock Chardonnay. Suppose the price of Cap Rock Chardonnay is $10, Ronald’s monthly income is $15,000, and his tax expense is $5,000. (a) How much does Ronald change his Chardonnay consumption if his taxes are increased by 20%. (b) Calculate Ronald’s Consumer Surplus from consuming Cap Rock Chardonnay before and after the increase in taxes. Problem 27: The wheat market is perfectly competitive, and the market supply and demand curves are given by the following equations: QD = 20, 000, 000 − 4, 000, 000P , and QS = 7, 000, 000 + 2, 500, 000P, where QD and QS are quantity demanded and quantity supplied measured in bushels, and P = price per bushel. (a) Determine consumer surplus at the equilibrium price and quantity. (b) Assume that the government has imposed a price floor at $2.25 per bushel and agrees to buy any resulting excess supply. How many bushels of wheat will the government be forced to buy? Determine consumer surplus with the price floor. 11
Problem 28: The market supply curve of rubber erasers is given by QS = 35, 000+2, 000P . The demand for rubber erasers can be segmented into two components. The first component is the demand for rubber erasers by art students. This demand is given by qA = 17, 000 − 250P . The second component is the demand for rubber erasers by all others. This demand is given by qO = 25, 000 − 2000P . (a) Derive the total market demand curve for rubber erasers. (b) Find the equilibrium market price and quantity. (c) Determine the consumer surplus for each component of demand.
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Production and the Cost of Production Problem 29: Joe owns a coffee house and produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). What is the average product of labor? Problem 30: The total cost (TC) of producing computer software dvds (Q) is given as: T C = 200 + 5Q. What is the marginal cost? Problem 31: A firm’s total cost function is given by the equation: T C = 4000 + 5Q + 10Q2 . (a) Write an expression for each of the following cost concepts: (i) Total Fixed Cost (ii) Average Fixed Cost (iii) Total Variable Cost (iv) Average Variable Cost (v) Marginal Cost (b) Determine the quantity that minimizes average total cost. Problem 32: Acme Container Corporation produces egg cartons that are sold to egg distributors. Acme has estimated this production function for its egg carton division: Q = 25L0.6 K 0.4 , 13
where Q = output measured in one thousand carton lots, L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $10 per hour and considers the relevant rental price for capital to be $25 per hour. Determine the optimal capital-labor ratio that Acme should use in the egg carton division. Problem 33: Davy Metal Company produces brass fittings. Davy’s engineers estimate the production function represented below as relevant for their long-run capitallabor decisions. Q = 500L0.6 K 0.8 , where Q = annual output measured in pounds, L =labor measured in person hours, K = capital measured in machine hours. The marginal products of labor and capital are: M PL = 300L−0.4 K 0.8 , and M PK = 400L0.6 K −0.2 Davy’s employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars. (a) Determine the firm’s optimal capital-labor ratio, given the information above. (b) How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm’s output. (c) Davy is currently negotiating with a newly organized union. The firm’s personnel manager indicates that the wage may rise to $22.50 under the proposed union contract. Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm’s employment of capital and labor. What will happen to the firm’s output?
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Problem 34: The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q = 0.25K 0.25 L0.75 , where Q represents memo pads (boxes per hour), K denotes capital input (units per hour), and L denotes labor input (units of worker time per hour). The marginal products of labor and capital are as follows: M PL = (0.75)(0.25)K 0.25 L−0.25 , and M PK = (0.25)(0.25)K −0.75 L0.75 (a) Construct the isocost equation. (b) Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute the level of output. Problem 35: A paper company dumps nondegradable waste into a river that flows by the firm’s plant. The firm estimates its production function to be: Q = 6KW, where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year. The marginal products of capital and waste generation are given as follows: M PK = 6W , and M PW = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. 15
(a) Determine the firm’s optimal ratio of waste water to capital. (b) Given the firm’s $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? (c) The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm’s cost as a result of the effluent fee?
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Profit Maximization and Competitive Supply Problem 36: Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for $100 per thousand. Conigan’s total cost curve is: T C = 3, 000, 000 + 0.001Q2 where Q is measured in thousand box bundles per year. (a) Calculate the marginal costs (b) Calculate Conigan’s profit maximizing quantity. Is the firm earning a profit? (c) Analyze Conigan’s position in terms of the shutdown condition. Should Conigan operate or shut down in the shortrun? Problem 37: Spacely Sprockets’ short-run cost curve is: C(q, K) =
25q 2 + 15K, K
where q is the number of Sprockets produced and K is the number of robot hours Spacely hires. Currently, Spacely hires 10 robot hours per period. The short-run marginal cost curve is: M C(q, K) = 50
q . K
Suppose the market is perfectly competitive. If Spacely receives $250 for every sprocket he produces, what is his profit maximizing output level? Calculate Spacely’s profits.
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Problem 38: Laura’s internet services has the following short-run cost curve: C(q, K) =
25q 2 + rK K 2/3
where q is Laura’s output level, K is the number of servers she leases and r is the lease rate of servers. Laura’s short-run marginal cost function is: M C(q, K) =
50q . K 2/3
Currently, Laura leases 8 servers, the lease rate of servers is $15, and since the market is perfectly competitive, Laura can sell all the output she produces for $500 per unit. (a) Find Laura’s short-run profit maximizing level of output. Calculate Laura’s profits. (b) If the lease rate of internet servers rise to $20, how does Laura’s optimal output and profits change? Problem 39: Homer’s Boat Manufacturing cost function is: C(q) = can sell all the boats he produces for $1,200.
75 4 q +10, 240. 128
Homer
(a) What is the marginal cost function? (b) What is his optimal output? Calculate Homer’s profit or loss. Problem 40: A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are: T C = 5 − 0.05Q + 0.001Q2 M C = −0.05 + 0.002Q, where T C is total cost and Q is output rate (units per time period). 18
(a) Determine the output rate that maximizes profit or minimizes losses in the shortterm. (b) If input prices increase and cause the cost functions to become T C = 5 − 0.10Q + 0.002Q2 M C = −0.10 + 0.004Q, what will the new equilibrium output rate be? Problem 41: Sarah’s Pretzel plant has the following short-run cost function: C(q, K) =
wq 3 + 50K 1000K 3/2
where q is Sarah’s output level, w is the cost of a labor hour, and K is the number of pretzel machines Sarah leases. Sarah’s short-run marginal cost curve is 3wq 2 M C(q, K) = . 1000K 3/2 At the moment, Sarah leases 10 pretzel machines, the cost of a labor hour is $6.85, and she can sell all the output she produces at $35 per unit. (a) Determine Sarah’s optimal output and profits. (b) The cost per labor hour rises to $7.50, what happens to Sarah’s optimal level of output and profits?
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Problem 42: The market demand for a type of carpet known as KP-7 has been estimated as: P = 40 − 0.25Q, where P is price ($/yard) and Q is rate of sales (hundreds of yards per month). The market supply is expressed as: P = 5.0 + 0.05Q. A typical firm in this market has a total cost function given as: C = 100 − 20.0q + 2.0q 2 . where q is the output produced by the typical firm. (a) Determine the equilibrium market output rate and price. (b) Determine the output rate for a typical firm. (c) Determine the rate of profit (or loss) earned by the typical firm. Problem 43: The market for wheat consists of 500 identical firms, each with the total and marginal cost functions shown: T C = 90, 000 + 0.00001q 2 M C = 0.00002q, where q is measured in bushels per year. The market demand curve for wheat is Q = 90, 000, 000 − 20, 000, 000P , where Q is the market quantity demanded, again measured in bushels, and P is the price per bushel. (a) Determine the short-run equilibrium price and quantity that would exist in the market. (b) Calculate the profit maximizing quantity for the individual firm. Calculate the firm’s short-run profit (loss) at that quantity. 20
(c) Assume that the short-run profit or loss is representative of the current long-run prospects in this market. You may further assume that there are no barriers to entry or exit in the market. Describe the expected long-run response to the conditions described in part b. Problem 44: Assume the market for tortillas is perfectly competitive. The market supply and demand curves for tortillas are given as follows: supply curve: P = .000002Q, demand curve: P = 11 − .00002Q The short run marginal cost curve for a typical tortilla factory is: M C = .1 + .0009q where q is the output for an individual firm, and Q is the market output. (a) Determine the equilibrium price for tortillas. (b) Determine the profit maximizing short run equilibrium level of output for a tortilla factory. (c) Assuming that all of the tortilla factories are identical, how many tortilla factories are producing tortillas?
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The Analysis of Competitive Markets Problem 45: The utilities commission in a city is currently examining pay telephone service in the city. The commission has been asked to evaluate a proposal by a city council member to place a $0.10 price ceiling on local pay phone service. The staff economist at the utilities commission estimates the demand and supply curves for pay telephone service as follows: QD = 1600 − 2400P , and QS = 200 + 3200P, where P = price of a pay telephone call, and Q = number of pay telephone calls per month. (a) Determine the equilibrium price and quantity that will prevail without the price ceiling. (b) Analyze the quantity that will be available with the price ceiling. Problem 46: In a competitive market, the following supply and demand equations are given: Supply P = 5 + 0.036Q, and Demand P = 100 − 0.04Q, where P represents price per unit in dollars, and Q represents rate of sales in units per year. (a) Determine the equilibrium price and sales rate. (b) Determine the deadweight loss that would result if the government were to impose a price ceiling of 40 dollars per unit.
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Problem 47: The demand and supply functions for basic cable TV in the local market are given as: QD = 200, 000 − 4, 000P and QS = 20, 000 + 2, 000P. (a) Calculate the consumer and producer surplus in this market. (b) If the government implements a price ceiling of $15 on the price of basic cable service, calculate the new levels of consumer and producer surplus. Are all consumers better off? Are producers better off? Problem 48: The market demand and supply functions for pork are: QD = 2, 000 − 500P and QS = 800 + 100P. To help pork producers, the U.S. Congress is considering legislation that would put a price floor at $2.25 per unit. To achieve this price floor the government wants to buy enough units of pork to keep the price at $2.25 per unit. (a) How many units of pork will the government be forced to buy to keep the price at $2.25? (b) How much will the government spend in total? (c) How much does producer surplus increase? Problem 49: The market demand and supply functions for milk are: QD = 58 − 30.4P and QS = 16 + 3.2P. To help milk producers the government considers implementing a price floor of $1.75 and the government will purchase all the excess units at $1.75. 23
(a) How does the price floor affect the producer surplus? Calculate the change in producer surplus. (b) How many surplus units of milk are being produced? (c) What are the milk expenditures of the government? (d) Does the increase in producer surplus due to the price floor exceed government spending on excess milk? Problem 50: The market for semiskilled labor can be represented by the following supply and demand curves: LD = 32000 − 4000W and LS = −8000 + 6000W, where L = millions of person hours per year, and W = the wage in dollars per hour. (a) Calculate the equilibrium price and quantity that would exist under a free market. (b) What impact does a minimum wage of $3.35 per hour have on the market? (c) The government is contemplating an increase in the minimum wage to $5.00 per hour. Calculate the impact of the new minimum wage on the quantity of labor supplied and demanded. (d) Calculate producer surplus (laborers’ surplus) before and after the proposed change. Problem 51: The supply and demand curves for corn are as follows: QD = 3, 750 − 725P and QS = 920 + 690P, where Q = millions of bushels and P = price per bushel. 24
(a) Calculate the equilibrium price and quantity that would prevail in the free market. (b) The government has imposed a $2.50 per bushel support price. How much corn will the government be forced to purchase? (c) Calculate the loss in consumer surplus that would occur under the support program. Problem 52: The market for all-leather men’s shoes is served by both domestic (U.S.) and foreign (F) producers. The domestic producers have been complaining that foreign producers are dumping shoes onto the U.S. market. As a result, Congress is very close to enacting a policy that would completely prohibit sales by foreign manufacturers of leather shoes in the U.S. market. The demand curve and relevant supply curves for the leather shoe market are as follows: QD = 50, 000 − 500P QSU S = 6000 + 150P QSF = 2000 + 50P, where Q = thousands of pairs of shoes per year, and P = price per pair. (a) Currently there are no restrictions covering all-leather men’s shoes. What are the current equilibrium values? (b) Calculate the price and quantity that would prevail if the proposed policy is enacted. Problem 53: The market demand and supply functions for imported cars are: 1 QD = 800, 000 − 5P and QS = (14 + )P + 225, 000. 6 The legislature is considering a tariff (a tax on imported goods) equal to $2,000 per unit to aid domestic car manufacturers. 25
(a) What is the producer surplus if the tariff is implemented? (b) How many cars are imported? (c) Suppose that instead of a tariff, importers agree to voluntarily restrict their imports to this level. If they do and no tariff is implemented, calculate producer surplus in this scenario. (d) Do you expect importers will be more in favor of a tariff or a voluntary quota? Problem 54: A country which does not tax cigarettes is considering the introduction of a $0.40 per pack tax. The economic advisors to the country estimate the supply and demand curves for cigarettes as: QD = 140, 000 − 25, 000P and QS = 20, 000 + 75, 000P, where Q = daily sales in packs of cigarettes, and P = price per pack. The country has hired you to provide the following information regarding the cigarette market and the proposed tax. (a) What are the equilibrium values in the current environment with no tax? (b) What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively? (c) Calculate the deadweight loss from the tax. What is the revenue from the tax? Problem 55: The market demand and supply functions for cotton are: QD = 10 − 0.04P and QS = 38P − 20. (a) Calculate the consumer and producer surplus. 26
(b) To assist cotton farmers, suppose a subsidy of $0.10 a unit is implemented. Calculate the new level of consumer and producer surplus. (c) Did the increase in consumer and producer surplus exceed the increased government spending necessary to finance the subsidy?
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Market Power: Monopoly Problem 56: Barbara is a producer in a monopoly industry. Her demand curve, total revenue curve, marginal revenue curve and total cost curve are given as follows: Q = 160 − 4P ; T R = 40Q − 0.25Q2 M R = 40 − 0.5Q; T C = 4Q; M C = 4 (a) How much output will Barbara produce? (b) What is the price of her product? (c) How much profit will she make? Problem 57: A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q = 200 − 2P ; M R = 100 − Q T C = 5Q; M C = 5 (a) What level of output maximizes total revenue? (b) What is the profit maximizing level of output? (c) What is the profit maximizing price? (d) How much profit does the monopolist earn? Problem 58: The marginal revenue of green ink pads is given as follows: M R = 2500 − 5Q The marginal cost of green ink pads is 5Q. 28
(a) How many ink pads will be produced to maximize revenue? (b) How many ink pads will be produced to maximize profit? Problem 59: The marginal cost of a monopolist is constant and is $10. The marginal revenue curve is given as follows: M R = 100 − 2Q What is the profit maximizing price? Problem 60: A firm’s demand curve is given by P = 500 − 2Q. The firm’s current price is $300 and the firm sells 100 units of output per week. (a) Calculate the firm’s marginal revenue at the current price and quantity using the expression for marginal revenue that utilizes the price elasticity of demand. (b) Assuming that the firm’s marginal cost is zero, is the firm maximizing profit? Problem 61: The marginal cost of a monopolist is constant and is $10. The demand curve and marginal revenue curves are given as follows: Q = 100 − P ; M R = 100 − 2Q What is the deadweight loss from monopoly power?
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Problem 62: Determine the rule-of-thumb price, when the monopolist has a marginal cost of $25 and the price elasticity of demand is -3.0 Problem 63: Maui Macadamia Inc. has a monopoly in the macadamia nut industry. The demand curve, marginal revenue and marginal cost curve for macadamia nuts are given as follows: P = 360 − 4Q; M R = 360 − 8Q; M C = 4Q (a) What level of output maximizes the sum of consumer surplus and producer surplus? (b) What is the profit maximizing level of output? (c) At the profit maximizing level of output, what is the level of consumer surplus? (d) At the profit maximizing level of output, what is the level of producer surplus? (e) At the profit maximizing level of output, what is the deadweight loss?
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Problem 64: John Gardner is the city planner in a medium-sized southeastern city. The city is considering a proposal to award an exclusive contract to Clear Vision, Inc., a cable television carrier. Mr. Gardner has discovered that an economic planner hired a year before has generated the demand, marginal revenue, and marginal cost functions given below: P = 28 − 0.0008Q; M R = 28 − 0.0016Q M C = 0.0012Q, where Q = the number of cable subscribers and P = the price of basic monthly cable service. Conditions change very slowly in the community so that Mr. Gardner considers the cost and demand functions to be reasonably valid for present conditions. Mr. Gardner knows relatively little economics and has hired you to answer the questions listed below. (a) What price and quantity would be expected if the firm is allowed to operate completely unregulated? (b) Mr. Gardner has asked you to recommend a price and quantity that would be socially efficient. Recommend a price and quantity to Mr. Gardner using economic theory to justify your answer. (c) Compare the economic efficiency implications of (a) and (b) above.
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Pricing with Market Power Problem 65: A firm sells an identical product to two groups of consumers, A and B. The firm has decided that third-degree price discrimination is feasible and wishes to set prices that maximize profits. Which price and output strategy will maximize profits? Problem 66: Calloway Shirt Manufacturers sells knit shirts in two sub-markets. In one sub-market, the shirts carry Calloway’s popular label and breast logo and receive a substantial price premium. The other sub-market is targeted toward more price conscious consumers who buy the shirts without a breast logo, and the shirts are labeled with the name Archwood. The retail price of the shirts carrying the Calloway label is $42.00 while the Archwood shirts sell for $25. Calloway’s market research indicates a price elasticity of demand for the higher priced shirt of -2.0, and the elasticity of demand for the Archwood shirts is -4.0. Moreover, the research suggests that both elasticities are constant over broad ranges of output. (a) Are Calloway’s current prices optimal? (b) Management considers the $25 price to be optimal and necessary to meet the competition. What price should the firm set for the Calloway label to achieve an optimal price ratio? Problem 67: American Tire and Rubber Company sells identical radial tires under the firm’s own brand name and private label tires to discount stores. The radial tires sold in both sub-markets are identical, and the marginal cost is constant at $10 per tire for both types. The firm has estimated the following demand curves for each of the markets. P B = 70 − 0.0005QB (brand name) 32
P P = 20 − 0.0002QP (private label). Quantities are measured in thousands per month and price refers to the wholesale price. American currently sells brand name tires at a wholesale price of $28.50 and private label tires for a price of $17. Are these prices optimal for the firm? Problem 68: A lower east-side cinema charges $3.00 per ticket for children under 12 years of age and $5.00 per ticket for anyone 12 years of age or older. The firm has estimated that the price elasticity of demand for tickets purchased by those 12 years of age or older is -1.5. Calculate the elasticity of demand for tickets purchased for children under 12 years of age if prices are optimal. Problem 69: The local zoo has hired you to assist them in setting admission prices. The zoo’s managers recognize that there are two distinct demand curves for zoo admission. One demand curve applies to those ages 12 to 64, while the other is for children and senior citizens. The two demand and marginal revenue curves are: PA = 9.6 − 0.08QA ; M RA = 9.6 − 0.16QA PC/S = 4 − 0.05QCS ; M RC/S = 4 − 0.10QCS where PA = adult price, PC/S = children’s/senior citizen’s price, QA = daily quantity of adults, and QC/S = daily quantity of children and senior citizens. Crowding is not a problem at the zoo, so that the managers consider marginal cost to be zero. If the zoo decides to price discriminate, what are the profit maximizing price and quantity in each market? Calculate total revenue in each sub-market.
33
Problem 70: The BCY Corporation provides accounting services to a wide variety of customers, most of whom have had a business association with BCY for more than five years. BCY’s demand and marginal revenue curves are: P = 10, 000 − 10Q; M R = 10, 000 − 20Q. BCY’s marginal cost of service is: M C = 5Q. (a) If BCY charges a uniform price for a unit of accounting service, Q, what price must it charge per unit, and how many units must it produce per time period in order to maximize profit? Calculate the consumer surplus. (b) If BCY could enforce first-degree price discrimination, what would be the lowest price that it would charge and how many units would it produce per time period? (c) With perfect price discrimination and ignoring any fixed cost, what is total profit? How much additional consumer surplus is captured by switching from a uniform price to first-degree price discrimination? Problem 71: The industry demand curve for a particular market is: Q = 1800 − 200P. The industry exhibits constant long-run average cost at all levels of output, regardless of the market structure. Long-run average cost is a constant $1.50 per unit of output. Compare the economic efficiency of each possibility. (a) Calculate market output, price (if applicable), consumer surplus, and producer surplus (profit) for each of the scenarios below. (i) Perfect Competition (ii) Pure Monopoly (Hint: M R = 9 − 0.01Q) (iii) First Degree Price Discrimination (b) Compare the economic efficiency of each scenario. 34
Monopolistic Competition & Oligopoly Problem 72: A firm operating in a monopolistically competitive market faces the following demand curve: P = 10 − 0.1Q The firm’s total and marginal cost curves are: C = −10Q + 0.15Q2 + 130
and
M C = −10 + 0.3Q,
where P is in dollars per unit, output rate Q is in units per time period, and total cost C is in dollars. (a) From the demand curve facing the firm, determine the firm’s Marginal Revenue equation. (b) Determine the price and output rate that will allow the firm to maximize profit or minimize losses. (c) Compute a Lerner index for the firm. Problem 73: The local pizza market is monopolistically competitive. One of the local producers in the market is a pizza place called One Guy’s Pizza. The demand equation facing One Guy’s Pizza is given by Qd = 225 − 10P or equivalently, P = 22.5 − 0.1Qd . One Guy’s Pizza has a cost function equal to: C(Q) = 0.15Q2 (a) What is the marginal revenue curve for One Guy’s Pizza? 35
(b) What is the marginal cost for One Guy’s Pizza? (c) Determine the profit maximizing level of output and the price charged to customers by One Guy’s Pizza. (d) Would you expect the price and output to be the same in a long-run equilibrium? Problem 74: Suppose that the market demand for mountain spring water is given as follows: P = 1200 − Q Mountain spring water can be produced at no cost (i.e. T C = M C = 0). (a) What is the profit maximizing level of output and price of a monopolist? (b) What level of output would be produced by each firm in a Cournot duopoly equilibrium? What will be the equilibrium price? (c) What would be the equilibrium level of output and price in the long run if the industry was perfectly competitive? Problem 75: Two large diversified consumer products firms are about to enter the market for a new pain reliever. The two firms (Firm A and Firm B) are very similar in terms of their costs, strategic approach, and market outlook. Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price. The market demand curve for the pain reliever is given as: Q = 2600 − 400P. Both firms have constant long-run average costs of $2.00 per bottle. Patent protection insures that the two firms will operate as a duopoly for the foreseeable future. Price and quantity values are stated in per-bottle terms. If the firms act as Cournot duopolists, solve for 36
(a) Firm A’s reaction curve; (b) Firm B’s reaction curve; (c) The Cournot equilibrium quantities and price. Problem 76: Consider two identical firms (Firm 1 and Firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 50 − 0.5Q, where Q = Q1 + Q2 . (a) Find the Cournot equilibrium Q1 , Q2 and P . (b) Find the equilibrium Q and P for each firm assuming that the firms collude and share the profit equally. (c) Compare the efficiency of the equilibrium outcomes derived in (a) and (b) above. Problem 77: The Grand River Brick Corporation (Firm G) uses Business-to-Business internet technology to set output before Bernard’s Bricks (Firm B). This gives the Grand River Brick Corporation ”first-move” ability. The market demand for bricks is Q = 1, 000 − 100P or P = 10 − 0.01Q. Total output is Q = (qB + qG ), where qB is the output produced by Bernard’s Bricks and qG is the output produced by Grand River Brick Corporation. The marginal cost of producing an additional unit of bricks is constant at $2.00 for each firm. (a) Determine the reaction curve for Bernard’s Bricks. (b) Given that the Grand River Brick Corporation has this information and moves first, determine the optimal output decision for Grand River Brick Corporation. 37
(c) Does the ”first-move” ability of the Grand River Brick Corporation allow them to capture a larger market share?
38
Solutions
39
Supply and Demand Problem 1: (a) 20 (b) 100 (c) Shortage equal to 30 (d) Excess supply equal to 30 Problem 2: Q = 2, 388.9 units per week; P = $14.56 per unit. Problem 3: Q = 100, 000; P = $400 Problem 4: −2.75% Problem 5: 4.5% Problem 6: (a) The price elasticity of demand equals zero (is completely inelastic) at a price of zero. (b) Demand is infinitely elastic at a price of $60. (c) At a price of $30. (d) The price elasticity of demand equals Problem 7: (a)
P ∆Q Q ∆P
= −0.35
(b) The revenue drops by $334.36.
40
P ∆Q Q ∆P
= −2.
Consumer Behavior Problem 8: (a) Y = 5 (b) The first combination would be preferred as it leads to higher units of utility. Problem 9: −7/15 Problem 10: − PPBA Problem 11: B = PIB − PPBA A Problem 12: (a) 500 = 10X + 5Y (b) X = 16.67 and Y = 66.67 (c) X = 11.11 and Y = 66.67. Utility declines by roughly 74,141 units. Problem 13: (a) M RS =
M US M UC
(b) M RS = drinks
PS PC
=
⇒
3C 3S
C S
=
=
C S
0.5 0.25
=
1 2
Jane should by twice as many chips as soft
(c) Jane should spend her $5.00 to buy 5 soft drinks and 10 bags of chips. Problem 14: (a) I = PX X + PY Y ⇒ 25 = 3X + 2Y (b) X = 4.17 and Y = 6.25 41
(c) 13.03 units of utility per time period. Problem 15: (a) M UX =
2Y 0.5 X 0.5
and M UY =
2X 0.5 Y 0.5
(b) 750 = 25X + 50Y (c) X = 15 and Y = 7.5 (d) X = 10 and Y = 10 (e) U(X=15,Y =7.5) = 42.43 and U(X=10,Y =10) = 40. Utility declines. Problem 16: (a) M RS =
M UX M UY
(b) M RS =
PX PY
=
⇒
Y X
Y X
=
9 12
= 0.75
(c) No, the mix is not optimal. He should consume 0.75 times as much Y as X, rather than his current 0.67 Y for each X Problem 17: (a) M Uc = 0.9c−0.1 r0.1 and M Ur = 0.1c0.9 r−0.9 (b) c = 270 and r = 1 (c) U(c=300,r=0) = 0 and U(c=180,r=4) = 123.01. Natasha is better off with buying the four tickets. (d) U(c=270,r=1) = 154.25 > 123.01 = U(c=180,r=4) . Natasha would have a higher utility without the constrain. Constraining choices of fully rational actors always leads to lower utilities.
42
Individual and Market Demand Problem 18: (a) Budget line: 120 = Qc + Qd (b)
Qc Qd
= 1 or Qc = Qd
(c) Qc = 60 and Qd = 60 (d) Qc =
120 Pc +1
(e) Qd = 30 and Qc = 60 Problem 19: (a) The total effect of the price change is the difference in quantities before and after the price change. This change includes income and substitution effects. The reduction in consumption that resulted from the reduction in income to put Madame X back on the original indifference curve represents the income effect. The difference between the total effect and the income effect is the substitution effect. Total effect: 15 − 7 = 8 Income effect: 15 − 9 = 6 Substitution effect: (15 − 7) − (15 − 9) = 2 (b) Substitution and income effect are additive and both positive (6+2 = 8). Thus, we have a normal good. Problem 20: 25,000 bottles Problem 21: P = $96 Problem 22: (a) E =
40 (−4) 80
= −2 and demand is elastic.
43
(b) If the price of a good with elastic demand is increased, the total expenditures on the good will decrease (the percentage decrease of demand is bigger than the percentage increase of the price). Problem 23: (a) E = −1, unitary elasticity at this price. Problem 24: 0 (a) Q = 1000 − 200P 5000 − 1533.33P
,if P ≥ 5 ,if 5 ≥ P ≥ 3 ,if 3 ≥ P
(b) Domestic buyers at P ≤ 5 Foreign buyers at P ≤ 3. (c) Qd (P = 2.5) = 500.00 Qf (P = 2.5) = 666.68 Q(P = 2.5) = 1, 166.68 Check Q = Qd + Qf = 500.00 + 666.68 = 1, 166.68 (d) Only domestic demand for this price: Q = 200 Problem 25: (a) E = −0.5 (b) T E = P ∗Q. Total expenditures increase from $800 to $864, even though the total number of artichokes sold has fallen from 80 to 72. (c) Demand is infinitely elastic at the price where the demand curve intersects the vertical y-axis. Here, this occurs at P = $30 Problem 26: (a) Consumption falls from Q(T =5,000)=7 to Q(T =6,000)=6.8 by 0.2
44
(b) The choke price with the old tax is P = $80. His consumer surplus is 0.5($80 − $10)7 = $245. The choke price after the tax increase is P = $78. His consumer surplus decreases to 0.5($78 − $10)6.8 = $231.2. Problem 27: (a) CS = 0.5(5 − 2)12, 000, 000 = 18, 000, 000 (b) Government would have to by the whole excess supply: QS − QD = 1, 625, 000 CS = 0.5(5 − 2.25)11, 000, 000 = 15, 125, 000 Problem 28: 0 (a) Q = 17, 000 − 250P 42, 000 − 2, 250P
,if P ≥ 68 ,if 68 > P ≥ 12.5 ,if 12.5 > P
(b) Check if an equilibrium exists at a price at which art students and others buy rubbers: 42, 000 − 2, 250P = 35, 000 + 2, 000P It does exists; P ∗ = 1.65 and Q∗ = 38, 287.5 (c) CSA = 0.5(68 − 1.65)16, 587.5 = $550, 290.31 CSO = 0.5(12.5 − 1.65)21, 700 = $117, 722.5
45
Production and the Cost of Production Problem 29: APLabor = Lq =
5KL L
= 5K
Problem 30: ∆T C =5 ∆Q Problem 31: (a)
(i) T F C = 4000 (ii) AF C =
4000 Q
(iii) T V C = T C − T F C = 5Q + 10Q2 (iv) AV C = (v) AT C = (vi) M C =
TV C Q TC Q
∆T C ∆Q
= 5 + 10Q
=
4000+5Q+10Q2 Q
= 5 + 20Q
(b) M C = AT C ⇒ Q = 20 Problem 32: M PL and M RT S = wr M RT S = M PK 10 1.5 K = 25 ⇒ 1.5K = 0.4L ⇒ K = 0.266L L Problem 33: (a) 0.75 K = L
15 50
⇒
K L
= 0.4 ⇒ K = 0.4L
(b) Hint:C = wL + rK; insert wage, rent charge, and the ratio from (a) L ≈ 14, 286 hours; K ≈ 5, 714 and Q ≈ 157, 568, 202. (c) Hint: M RT S = 0.75 K ; new input price ratio: 22.5 L 50 New optimal capital-labor ratio: K = 0.6L Amount of labor is reduced (L ≈ 9, 524), amount of capital remains constant (K ≈ 5, 714) and output is reduced (Q ≈ 123, 541, 772) 46
Problem 34: (a) I = wL + rK ⇒ 150, 000 = 12L + 52K (b) L = 9, 375, K = 721.15, Q = 1, 234.29 Problem 35: (a)
K W
= 0.25 or K = 0.25W
(b) W = 20, 000, K = 5, 000 and Q = 600, 000, 000 (c) W ≈ 14, 142, K ≈ 7, 071 Cost for effluent fees F = 106, 065. The costs rises from $300,000 to $424,260 (C = PW W + PK K with PW including the the fee)
Profit Maximization and Competitive Supply Problem 36: (a) M C = 0.002Q (b) Q = 50, 000 and π = −$500, 000 (c) Firm should operate since P > AV C Problem 37: q = 50 and π = 6, 100 Problem 38: (a) q = 40 and π = 9, 880 (b) Short-run output is unaffected q = 40 and profit is reduced to π = 9, 840
47
Problem 39: 75 3 q (a) M C = 32 √ (b) q = 3 512 = 8 and π = −$3, 040 Homer will produce and make a loss, because P > AV C(8). Producing and loosing $3,040 is better than not producing and losing $10,240.
Problem 40: (a) Q = 75 (b) Q = 50 Problem 41: (a) Q = 232.07 and π = 4, 915.08 (b) Optimal output and profit falls: Q = 221.79 and π = 4, 675.11 Problem 42: (a) Q = 116.7 and P = 10.825 (b) q = 7.71 (c) π = 18.77 Problem 43: (a) P = 2 and Q = 50, 000, 000 (b) Q = 100, 000 and π = 10, 000 48
(c) Firms are earning an economic profit so we would expect other firms to join this market (supply curve shifts rightwards). The price would fall causing the firms to reduce their outputs. This will continue until we reach the long-term equilibrium with zero profits. Problem 44: (a) Q = 500, 000 and P = 1 (b) q = 1, 000 (c) Since Q = 500, 000 and q = 1, 000 there must be 500 firms.
49
The Analysis of Competitive Markets Problem 45: (a) P = 0.25 and Q = 1, 000 (b) QS = 520 and QD = 1360. We observe a shortage of 840 calls. Problem 46: (a) Q = 1, 250 and P = $50 (b) Deadweight loss 0.5(61.11 − 40)(1250 − 972.22) = 2, 931.97 Problem 47: (a) P ∗ = $30, Q∗ = 80, 000, PC = $50, QS(P =0) = 20, 000 CS = 0.5(50 − 30)80, 000 = $800, 000 P S = 30 · 20, 000 + 0.5(80, 000 − 20, 000)30 = $1, 500, 000 (b) QS(P =15) = 50, 000 CS = 0.5(50 − 37.5)50, 000 + 50, 000(37.5 − 15) = $1, 437, 500 P S = 15 · 20, 000 + 0.5(50, 000 − 20, 000)15 = $525, 000 Consumer surplus increases, but producers surplus decreases. Not all consumers are better off: some would be willing to pay $15, but because of the shortage they are unable to get cable TV. Problem 48: (a) Government will be forced to buy 150 units of pork (b) Government spending: 150 ∗ 2.25 = 337.5
50
(c) QS(P =0) = 800 P S ∗ = 800 · 2 + 0.5(1, 000 − 800)2 = $1, 800 P S 0 = 800 · 2.25 + 0.5(1, 025 − 800)2.25 = $2, 053.125 ∆P S = P S 0 − P S ∗ = $253.125 Problem 49: (a) P S ∗ = $22.5, P S 0 = $32.9, ∆P S = P S 0 − P S ∗ = $10.4 (b) Q0S = 21.6, Q0D = 4.8, Excess supply of 16.8 (c) Government spending 16.8 ∗ 1.75 = $29.4 The increase in producer surplus does not exceed the government spendings Problem 50: (a) W ∗ = $4, Q∗ = $16, 000 (b) A minimum wage of 3.35 would be below the equilibrium wage and would not be binding. Thus, the market would attain its free market equilibrium. (c) LD = 12, 000, and LS = 22, 000. The new minimum wage would create unemployment 0f 10,000 person hours per year. (d) Hint: For W = 0 we would have a negative supply of labor (LS ). Thus, instead of searching for LS(W =0) we search for a wage where LS = 0 (reservation price). Try to graph LS if you have problems understanding this point P S ∗ = 0.5(4 − 1.33)16, 000 = $21, 360 For which wage would workers supply the demanded quantity of work: W = 1.33 + 0.000167LS = 3.33 P S 0 = 0.5(3.33 − 1.33)12, 000 + (5 − 3.33)12, 000 = $32, 040 Overall producer surplus has increased, but single workers might be worse of because of the increased unemployment rate.
51
Problem 51: (a) P ∗ = 2 and Q∗ = 2, 300 (b) QS = 2, 645 and QD = 1937.5 Government would have to buy the difference of 707.5 millions bushels. (c) ∆CS ≈ −1, 059 Problem 52: (a) P ∗ = 60 and Q∗ = 20, 000 (b) P 0 = 67.69 and Q0 = 16, 155 Problem 53: (a) P S ∗ = P S 0 = 225, 000(31, 478.26−2, 000)+0.5(642, 608.7−225, 000)(31, 478.26− 2, 000) = $12, 787, 797, 732 (b) Q = 42, 608.7 (c) P S 00 = 225, 000(31, 478.26) + 0.5(642, 608.7 − 225, 000)(31, 478.26) = $13, 655, 406, 427 (d) They will favor the voluntary quota. They can sell the same amount of cars but receive the full price instead the price minus the tariff. Problem 54: (a) P = 1.2 and Q = 110, 000 (b) Four conditions must hold: QD = 140, 000 − 25, 000PB QS = 20, 000 + 75, 000PS QD = QS 52
PB = PS + 0.4 In equilibrium: 140, 000 − 25, 000PB = 20, 000 + 75, 000PS Hint: Substituting for PB PS = 1.10, PB = 1.50, Q = 102, 500 The tax is paid $0.3 by buyers (P = 1.2 ⇒ PB = 1.5) and $0.1 by sellers (P = 1.2 ⇒ PS = 1.1) (c) Area A: (110, 000 − 102, 500)(1.5 − 1.2)0.5 = 1, 125 Area B: (110, 000 − 102, 500)(1.2 − 1.1)0.5 = 375 Deadweight Loss: $1500 Revenue from tax: 0.4 ∗ 102, 500 = $41, 000 per day Problem 55: (a) P = 0.79, Q = 9.97, choke price PC = 250, reservation price PR = 0.53 CS = 0.5(250 − 0.79)9.97 = $1, 242.31 P S = 0.5(0.79 − 0.53)9.97 = $1.30 (b) New equilibrium if: 10 − 0.04P = 38(P + 0.1) − 20 P = 0.69, QS = 9.97 CS = 0.5(250 − 0.69)9.97 = $1, 242.81 P S = 0.5(0.79 − 0.53)9.97 = $1.30 (c) Government spending is $0.997. The increase in consumer surplus is $.50, the producer surplus did not change. The increase in consumer and producer surplus is less than government spending.
53
Market Power: Monopoly Problem 56: (a) Q = 72 (b) P = 22 (c) π = 1, 296 Problem 57: (a) Q = 100 (b) Q = 95 (c) P = $52.5 (d) π = $4, 512.5 Problem 58: (a) Q = 500 (b) Q = 250 Problem 59: p = $55 Problem 60: (a) ED = −1.5 M R = P + P E1D = 100 (b) M R = M C thus the quantity should be Q = 125. Firm sells less than 125 and is not maximizing the profit. 54
Problem 61: Deadweight loss from monopoly power is $1,012.5 Problem 62: P =
MC 1+ E1
= $37.5
D
Problem 63: (a) Q = 45 (b) Q = 30 (c) CS = $1, 800 (d) P S = $5, 400 (e) $900 Problem 64: (a) Q = 10, 000 and P = $20 (b) Q = 14, 000 and P = $16.8 (c) If the profit maximizing quantity is produced the deadweight loss from monopoly power is $16,000
55
Pricing with Market Power Problem 65: M RA = M RB = M C Problem 66: 1+(1/EA ) 1+(1/EC )
(a)
PC PA
= 1.68, but
(b)
PC PA
should be 1.5. Given PA = $25, PC should be $37.5
= 1.5. Thus current prices are not optimal.
Problem 67: Prices should be PB = $40 and PP = $15. Thus, prices are not optimal. Problem 68: EChild = −2.25 Problem 69: QA = 60, PA = $4.8 QCS = 40, PCS = $2 T RA = $288, T RCS = $368 Problem 70: (a) Q∗ = 400 and P ∗ = $6, 000 CS = 0.5(10, 000 − 6000)400 = $800, 000 (b) Lowest price would occur if MC=AR Q = 666.67 and P$ 3, 333.33 (c) π = $3, 333, 353.33 Loss in consumer surplus due to first-degree price discrimination is $800,000. Everything from answer (a). 56
Problem 71: Hint: Since LAC is constant, LMC is also constant and equal to LAC. LMC = $1.5 (a)
(i) Q = 1, 500, P = LAC, P S = $0, CS = 0.5(9 − 1.5)1500 = $5, 625 (ii) Q = 750, P = $5.25, P S = $2812.5, CS = 0.5(9 − 5.25)750 = $4, 218.75 (iii) Q = 1, 500, P S = $5, 625, CS = $0
(b) Comparison of Efficiency: (i) Competition: CS+PS = $5,625 (ii) Monopoly: CS+PS = $4,218.75 (iii) First Degree: CS+PS = $5,625 Monopoly results in a deadweight loss. First-degree price discrimination results in a redistribution of income, but does not change the overall welfare. Problem 72: (a) M R = 10 − 0.2Q (b) Q∗ = 40 and P ∗ = 6 (c) L =
2 3
Problem 73: (a) M R = 22.5 − 0.2Qd (b) M C = 0.3Q (c) Q∗ = 45 and P ∗ = 18 (d) No. The profit for One Guy’s Pizza is π = 506.25, which suggests that other firms will want to enter the market and in the long-run, other firms will enter, demand will shift away from One Guy’s Pizza, and their profits will fall to zero. 57
Problem 74: (a) Q = 600 and P = 600 (b) Q1 = Q2 = 400. Thus the total output is 800 and the price will be P = $400. (c) Q = 1, 200 and P = 0 Problem 75: (a) QA = 900 − 0.5QB (b) QB = 900 − 0.5QA (c) QA = 600 and QB = 600, while P = $3.50 Problem 76: (a) Q1 = Q2 = 33.33 and P = 16.66. (b) Q = 50 and if profits are shared equally, Q1 = Q2 = 25. Then P = 25. (c) Both cases result in inefficiency. However, the inefficiency (deadweight loss) is smaller when the firms compete with each other. When they collude, output is restricted even further and price is significantly higher than marginal cost (which is zero in this case). Problem 77: (a) QB = 400 − 0.5QG (b) QG = 400. Therefore, QB = 200. (c) If Grand River Brick Corporation did not have first-mover ability, the outcome would be the Cournot equilibrium, which is QG = QB = 266.66. Thus, first-mover ability has given Grand River a greater market share.
58
1
Supply and Demand Problem 1: The demand for books is: QD = 120 − P The supply of books is: QS = 5P
(a) What is the equilibrium price of books? (b) What is the equilibrium quantity of books sold? (c) If P = $15, do we observe a shortage or excess supply? How big is it? (d) If P = $25, do we observe a shortage or excess supply? How big is it? Problem 2: The inverse demand curve for product X is given by: PX = 25 − 0.005Q + 0.15PY , where PX represents price in dollars per unit, Q represents rate of sales in pounds per week, and PY represents selling price of another product Y in dollars per unit. The inverse supply curve of product X is given by: PX = 5 + 0.004Q. Determine the equilibrium price and sales of X when the price of product Y is PY = $10. Problem 3: The daily demand for hotel rooms on Manhattan Island in New York is given by the equation QD = 250, 000 − 375P. The daily supply of hotel rooms on Manhattan Island is given by the equation QS = 15, 000 + 212.5P. 2
What is the equilibrium price and quantity of hotel rooms on Manhattan Island? Problem 4: For U.S. consumers, the income elasticity of demand for fruit juice is 1.1. The economy enters a recession and consumer income declines by 2.5%. What is the expected percentage change in the quantity of fruit juice demanded? Problem 5: The cross-price elasticity of demand for peanut butter with respect to the price of jelly is -0.3. The price of jelly declines by 15%.What is the expected percentage change in the quantity demanded for peanut butter? Problem 6: Harding Enterprises has developed a new product called the Gillooly Shillelagh. The market demand for this product is given as follows: Q = 240 − 4P (a) At what price is the price elasticity of demand equal to zero? (b) At what price is demand infinitely elastic? (c) At what price is the price elasticity of demand equal to minus one? (d) If the shillelagh is priced at $40, what is the point price elasticity of demand? Problem 7: The demand for a bushel of wheat in 1981 was given by the equation QD = 3550 − 266P. (a) What is the price elasticity of demand at a price of $3.46? (b) If the price of wheat falls to $3.27 per bushel, what happens to the revenue generated from the sale of wheat? 3
Consumer Behavior Problem 8: Consider Gary’s utility function: U (X, Y ) = 5XY , where X and Y are two goods. (a) If Gary consumed 10 units of X and received 250 units of utility, how many units of Y must he have consumed? (b) Would a market basket of X = 15 and Y = 3 be preferred to the above combination? Problem 9: A consumer has $100 per day to spend on product A, which has a unit price of $7, and product B, which has a unit price of $15. What is the slope of the budget line if good A is on the horizontal axis and good B is on the vertical axis? Problem 10: If the quantity of good A (QA ) is plotted along the horizontal axis, the quantity of good B (QB ) is plotted along the vertical axis, the price of good A is PA , the price of good B is PB and the consumer’s income is I, then the . slope of the consumer’s budget constraint is Problem 11: The budget constraint for a consumer who only buys apples (A) and bananas (B) is PA A + PB B = I where consumer income is I, the price of apples is PA , and the price of bananas is PB . To plot this budget constraint in a figure with apples on the horizontal axis, we should use a budget line represented by which equation?
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Problem 12: Sally consumes two goods, X and Y . Her utility function is given by the expression U = 3XY 2 . The current market price for X is $10, while the market price for Y is $5. Sally’s current income is $500. (a) Write the expression for Sally’s budget constraint. (b) Determine the X, Y combination which maximizes Sally’s utility, given her budget constraint. (c) Calculate the impact on Sally’s optimum market basket of an increase in the price of X to $15. What would happen to her utility as a result of the price increase? Problem 13: Jane lives in a dormitory that offers soft drinks and chips for sale in vending machines. Her utility function is U = 3SC (where S is the number of soft drinks per week and C the number of bags of chips per week), so her marginal utility of S is 3C and her marginal utility of C is 3S. Soft drinks are priced at $0.50 each, chips $0.25 per bag. (a) Write an expression for Jane’s marginal rate of substitution between soft drinks and chips. (b) Use the expression generated in part (a) to determine Jane’s optimal mix of soft drinks and chips. (c) If Jane has $5.00 per week to spend on chips and soft drinks, how many of each should she purchase per week? Problem 14: An individual consumes products X and Y and spends $25 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y . The consumer in this case has a utility function expressed as: U (X, Y ) = 0.5XY 5
(a) Express the budget equation mathematically. (b) Determine the amount of consumption of X and Y that will maximize utility. (c) Determine the total utility that will be generated from the consumption bundle you calculated in part (b). Problem 15: Janice Doe consumes two goods, X and Y . Janice has a utility function given by the expression: U = 4X 0.5 Y 0.5 . The current prices of X and Y are 25 and 50, respectively. Janice currently has an income of 750 per time period. (a) Calculate the Marginal Utility of X and Y (b) Write an expression for Janice’s budget constraint. (c) Calculate the optimal quantities of X and Y that Janice should choose, given her budget constraint. (d) Suppose that the government rations purchases of good X such that Janice is limited to 10 units of X per time period. Assuming that Janice chooses to spend her entire income, how much Y will Janice consume? (e) Calculate the impact of the ration restriction on Janice’s utility. Problem 16: John consumes two goods, X and Y . The marginal utility of X and the marginal utility of Y satisfy the following equations: M UX = Y and M UY = X. The price of X is $9, and the price of Y is $12. (a) Write an expression for John’s MRS. (b) What is the optimal mix between X and Y in John’s market basket? 6
(c) John is currently consuming 15 X and 10 Y per time period. Is he consuming an optimal mix of X and Y ? Problem 17: Natasha derives utility from attending rock concerts (r) and from drinking colas (c) as follows: U (c, r) = c0.9 r0.1 (a) Calculate the marginal utility of cola (M Uc ) and the marginal utility of rock concerts (M Ur ) (b) If the price of cola (Pc ) is $1 and the price of concert tickets (Pr ) is $30 and Natasha’s income is $300, how many colas and tickets should Natasha buy to maximize utility? (c) Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the above prices and income, how many colas and tickets should Natasha buy to maximize utility? (d) Is Natasha better off with or without the constraint?
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Individual and Market Demand Problem 18: Donald derives utility from only two goods, carrots (Qc ) and donuts (Qd ). His utility function is as follows: U (Qc , Qd ) = Qc Qd The marginal utility that Donald receives from carrots (M Uc ) and donuts (M Ud ) are given as follows: M Uc = Qd and M Ud = Qc Donald has an income (I) of $120 and the price of carrots (Pc ) and donuts (Pd ) are both $1. (a) What is Donald’s budget line? (b) What is the optimal ratio of Qc and Qd ? (c) What quantities of Qc and Qd will maximize Donald’s utility? (d) Holding Donald’s income and Pd constant at $120 and $1 respectively, what is Donald’s demand curve for carrots? (e) Suppose that a tax of $1 per unit is levied on donuts. How will this alter Donald’s utility maximizing market basket of goods? Problem 19: The following data pertain to products A and B, both of which are purchased by Madame X. Initially, the prices of the products and quantities consumed are: PA = $10, QA = 3, PB = $10, QB = 7. Madame X has $100 to spend per time period. After a reduction in price of B, the prices and quantities consumed are: PA = $10, QA = 2.5, PB = $5, QB = 15. 8
Assume that Madame X maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Madame X to put her back on the original indifference curve, she would consume this combination of A and B: QA = 1.5, QB = 9 (a) Determine the change in consumption rate of good B due to (1) the substitution effect and (2) the income effect. (b) Determine if product B is a normal, inferior, or Giffen good. Explain. Problem 20: A local retailer has decided to carry a well-known brand of shampoo. The marketing department tells them that the quarterly demand by an average man is: QM d = 3 − 0.25P and the quarterly demand by an average woman is: QW d = 4 − 0.5P The market consists of 10,000 men and 10,000 women. How may bottles of shampoo can they expect to sell if they charge $6 per bottle? Problem 21: The price elasticity of demand for red herring is -4. The demand curve for red herring is: Q = 120 − P . What is the price of red herring? Problem 22: Harding Enterprises has developed a new product called the Gillooly shillelagh. The market demand for this product is given as follows: Q = 240 − 4P (a) If the shillelagh is priced at $40, what is the price elasticity of demand? Is demand elastic or inelastic? 9
(b) If the shillelagh price is increased slightly from $40, what will happen to the total expenditure on the Gillooly shillelagh? Problem 23: The demand for telephone wire can be expressed as: Q = 6000 − 1, 500P, where Q represents units, in pounds per day, and P represents price, in dollars per pound. Determine the price elasticity of demand at P = $2.00 per pound. Problem 24: The total world demand for power transmission wire is made up of both domestic and foreign demands. Thus, the total demand is the sum of the two sub-demands, which are given as: Domestic demand:Pd = 5 − 0.005Qd Foreign demand:Pf = 3 − 0.00075Qf , where Pd and Pf are in dollars per pound, and Qd and Qf are in pounds per day. (a) Determine the total world demand for power transmission wire. (b) Determine the prices at which domestic and foreign buyers would enter the market. (c) Determine the domestic and foreign quantities at P = $2.50 per pound. Check to see if the sum of Qd and Qf equals Q. (d) Determine total quantity sold at P = $4.00 per pound. Problem 25: Suppose that the demand for artichokes (Qa ) is given as: Qa = 120 − 4P 10
(a) What is the price elasticity of demand if the price of artichokes is $10? (b) Suppose that the price of artichokes increases to $12. What will happen to the number of artichokes sold and the total expenditure by consumers on artichokes? (c) At what price if any is the demand for artichokes infinitely elastic? Problem 26: Ronald’s monthly demand for Cap Rock Chardonnay is given by Q=6+
1 1 (I − T ) − P, 5, 000 10
where I is Ronald’s monthly income, T is his tax expense and P is the price of Cap Rock Chardonnay. Suppose the price of Cap Rock Chardonnay is $10, Ronald’s monthly income is $15,000, and his tax expense is $5,000. (a) How much does Ronald change his Chardonnay consumption if his taxes are increased by 20%. (b) Calculate Ronald’s Consumer Surplus from consuming Cap Rock Chardonnay before and after the increase in taxes. Problem 27: The wheat market is perfectly competitive, and the market supply and demand curves are given by the following equations: QD = 20, 000, 000 − 4, 000, 000P , and QS = 7, 000, 000 + 2, 500, 000P, where QD and QS are quantity demanded and quantity supplied measured in bushels, and P = price per bushel. (a) Determine consumer surplus at the equilibrium price and quantity. (b) Assume that the government has imposed a price floor at $2.25 per bushel and agrees to buy any resulting excess supply. How many bushels of wheat will the government be forced to buy? Determine consumer surplus with the price floor. 11
Problem 28: The market supply curve of rubber erasers is given by QS = 35, 000+2, 000P . The demand for rubber erasers can be segmented into two components. The first component is the demand for rubber erasers by art students. This demand is given by qA = 17, 000 − 250P . The second component is the demand for rubber erasers by all others. This demand is given by qO = 25, 000 − 2000P . (a) Derive the total market demand curve for rubber erasers. (b) Find the equilibrium market price and quantity. (c) Determine the consumer surplus for each component of demand.
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Production and the Cost of Production Problem 29: Joe owns a coffee house and produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). What is the average product of labor? Problem 30: The total cost (TC) of producing computer software dvds (Q) is given as: T C = 200 + 5Q. What is the marginal cost? Problem 31: A firm’s total cost function is given by the equation: T C = 4000 + 5Q + 10Q2 . (a) Write an expression for each of the following cost concepts: (i) Total Fixed Cost (ii) Average Fixed Cost (iii) Total Variable Cost (iv) Average Variable Cost (v) Marginal Cost (b) Determine the quantity that minimizes average total cost. Problem 32: Acme Container Corporation produces egg cartons that are sold to egg distributors. Acme has estimated this production function for its egg carton division: Q = 25L0.6 K 0.4 , 13
where Q = output measured in one thousand carton lots, L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $10 per hour and considers the relevant rental price for capital to be $25 per hour. Determine the optimal capital-labor ratio that Acme should use in the egg carton division. Problem 33: Davy Metal Company produces brass fittings. Davy’s engineers estimate the production function represented below as relevant for their long-run capitallabor decisions. Q = 500L0.6 K 0.8 , where Q = annual output measured in pounds, L =labor measured in person hours, K = capital measured in machine hours. The marginal products of labor and capital are: M PL = 300L−0.4 K 0.8 , and M PK = 400L0.6 K −0.2 Davy’s employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars. (a) Determine the firm’s optimal capital-labor ratio, given the information above. (b) How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm’s output. (c) Davy is currently negotiating with a newly organized union. The firm’s personnel manager indicates that the wage may rise to $22.50 under the proposed union contract. Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm’s employment of capital and labor. What will happen to the firm’s output?
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Problem 34: The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q = 0.25K 0.25 L0.75 , where Q represents memo pads (boxes per hour), K denotes capital input (units per hour), and L denotes labor input (units of worker time per hour). The marginal products of labor and capital are as follows: M PL = (0.75)(0.25)K 0.25 L−0.25 , and M PK = (0.25)(0.25)K −0.75 L0.75 (a) Construct the isocost equation. (b) Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute the level of output. Problem 35: A paper company dumps nondegradable waste into a river that flows by the firm’s plant. The firm estimates its production function to be: Q = 6KW, where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year. The marginal products of capital and waste generation are given as follows: M PK = 6W , and M PW = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. 15
(a) Determine the firm’s optimal ratio of waste water to capital. (b) Given the firm’s $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? (c) The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm’s cost as a result of the effluent fee?
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Profit Maximization and Competitive Supply Problem 36: Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for $100 per thousand. Conigan’s total cost curve is: T C = 3, 000, 000 + 0.001Q2 where Q is measured in thousand box bundles per year. (a) Calculate the marginal costs (b) Calculate Conigan’s profit maximizing quantity. Is the firm earning a profit? (c) Analyze Conigan’s position in terms of the shutdown condition. Should Conigan operate or shut down in the shortrun? Problem 37: Spacely Sprockets’ short-run cost curve is: C(q, K) =
25q 2 + 15K, K
where q is the number of Sprockets produced and K is the number of robot hours Spacely hires. Currently, Spacely hires 10 robot hours per period. The short-run marginal cost curve is: M C(q, K) = 50
q . K
Suppose the market is perfectly competitive. If Spacely receives $250 for every sprocket he produces, what is his profit maximizing output level? Calculate Spacely’s profits.
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Problem 38: Laura’s internet services has the following short-run cost curve: C(q, K) =
25q 2 + rK K 2/3
where q is Laura’s output level, K is the number of servers she leases and r is the lease rate of servers. Laura’s short-run marginal cost function is: M C(q, K) =
50q . K 2/3
Currently, Laura leases 8 servers, the lease rate of servers is $15, and since the market is perfectly competitive, Laura can sell all the output she produces for $500 per unit. (a) Find Laura’s short-run profit maximizing level of output. Calculate Laura’s profits. (b) If the lease rate of internet servers rise to $20, how does Laura’s optimal output and profits change? Problem 39: Homer’s Boat Manufacturing cost function is: C(q) = can sell all the boats he produces for $1,200.
75 4 q +10, 240. 128
Homer
(a) What is the marginal cost function? (b) What is his optimal output? Calculate Homer’s profit or loss. Problem 40: A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are: T C = 5 − 0.05Q + 0.001Q2 M C = −0.05 + 0.002Q, where T C is total cost and Q is output rate (units per time period). 18
(a) Determine the output rate that maximizes profit or minimizes losses in the shortterm. (b) If input prices increase and cause the cost functions to become T C = 5 − 0.10Q + 0.002Q2 M C = −0.10 + 0.004Q, what will the new equilibrium output rate be? Problem 41: Sarah’s Pretzel plant has the following short-run cost function: C(q, K) =
wq 3 + 50K 1000K 3/2
where q is Sarah’s output level, w is the cost of a labor hour, and K is the number of pretzel machines Sarah leases. Sarah’s short-run marginal cost curve is 3wq 2 M C(q, K) = . 1000K 3/2 At the moment, Sarah leases 10 pretzel machines, the cost of a labor hour is $6.85, and she can sell all the output she produces at $35 per unit. (a) Determine Sarah’s optimal output and profits. (b) The cost per labor hour rises to $7.50, what happens to Sarah’s optimal level of output and profits?
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Problem 42: The market demand for a type of carpet known as KP-7 has been estimated as: P = 40 − 0.25Q, where P is price ($/yard) and Q is rate of sales (hundreds of yards per month). The market supply is expressed as: P = 5.0 + 0.05Q. A typical firm in this market has a total cost function given as: C = 100 − 20.0q + 2.0q 2 . where q is the output produced by the typical firm. (a) Determine the equilibrium market output rate and price. (b) Determine the output rate for a typical firm. (c) Determine the rate of profit (or loss) earned by the typical firm. Problem 43: The market for wheat consists of 500 identical firms, each with the total and marginal cost functions shown: T C = 90, 000 + 0.00001q 2 M C = 0.00002q, where q is measured in bushels per year. The market demand curve for wheat is Q = 90, 000, 000 − 20, 000, 000P , where Q is the market quantity demanded, again measured in bushels, and P is the price per bushel. (a) Determine the short-run equilibrium price and quantity that would exist in the market. (b) Calculate the profit maximizing quantity for the individual firm. Calculate the firm’s short-run profit (loss) at that quantity. 20
(c) Assume that the short-run profit or loss is representative of the current long-run prospects in this market. You may further assume that there are no barriers to entry or exit in the market. Describe the expected long-run response to the conditions described in part b. Problem 44: Assume the market for tortillas is perfectly competitive. The market supply and demand curves for tortillas are given as follows: supply curve: P = .000002Q, demand curve: P = 11 − .00002Q The short run marginal cost curve for a typical tortilla factory is: M C = .1 + .0009q where q is the output for an individual firm, and Q is the market output. (a) Determine the equilibrium price for tortillas. (b) Determine the profit maximizing short run equilibrium level of output for a tortilla factory. (c) Assuming that all of the tortilla factories are identical, how many tortilla factories are producing tortillas?
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The Analysis of Competitive Markets Problem 45: The utilities commission in a city is currently examining pay telephone service in the city. The commission has been asked to evaluate a proposal by a city council member to place a $0.10 price ceiling on local pay phone service. The staff economist at the utilities commission estimates the demand and supply curves for pay telephone service as follows: QD = 1600 − 2400P , and QS = 200 + 3200P, where P = price of a pay telephone call, and Q = number of pay telephone calls per month. (a) Determine the equilibrium price and quantity that will prevail without the price ceiling. (b) Analyze the quantity that will be available with the price ceiling. Problem 46: In a competitive market, the following supply and demand equations are given: Supply P = 5 + 0.036Q, and Demand P = 100 − 0.04Q, where P represents price per unit in dollars, and Q represents rate of sales in units per year. (a) Determine the equilibrium price and sales rate. (b) Determine the deadweight loss that would result if the government were to impose a price ceiling of 40 dollars per unit.
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Problem 47: The demand and supply functions for basic cable TV in the local market are given as: QD = 200, 000 − 4, 000P and QS = 20, 000 + 2, 000P. (a) Calculate the consumer and producer surplus in this market. (b) If the government implements a price ceiling of $15 on the price of basic cable service, calculate the new levels of consumer and producer surplus. Are all consumers better off? Are producers better off? Problem 48: The market demand and supply functions for pork are: QD = 2, 000 − 500P and QS = 800 + 100P. To help pork producers, the U.S. Congress is considering legislation that would put a price floor at $2.25 per unit. To achieve this price floor the government wants to buy enough units of pork to keep the price at $2.25 per unit. (a) How many units of pork will the government be forced to buy to keep the price at $2.25? (b) How much will the government spend in total? (c) How much does producer surplus increase? Problem 49: The market demand and supply functions for milk are: QD = 58 − 30.4P and QS = 16 + 3.2P. To help milk producers the government considers implementing a price floor of $1.75 and the government will purchase all the excess units at $1.75. 23
(a) How does the price floor affect the producer surplus? Calculate the change in producer surplus. (b) How many surplus units of milk are being produced? (c) What are the milk expenditures of the government? (d) Does the increase in producer surplus due to the price floor exceed government spending on excess milk? Problem 50: The market for semiskilled labor can be represented by the following supply and demand curves: LD = 32000 − 4000W and LS = −8000 + 6000W, where L = millions of person hours per year, and W = the wage in dollars per hour. (a) Calculate the equilibrium price and quantity that would exist under a free market. (b) What impact does a minimum wage of $3.35 per hour have on the market? (c) The government is contemplating an increase in the minimum wage to $5.00 per hour. Calculate the impact of the new minimum wage on the quantity of labor supplied and demanded. (d) Calculate producer surplus (laborers’ surplus) before and after the proposed change. Problem 51: The supply and demand curves for corn are as follows: QD = 3, 750 − 725P and QS = 920 + 690P, where Q = millions of bushels and P = price per bushel. 24
(a) Calculate the equilibrium price and quantity that would prevail in the free market. (b) The government has imposed a $2.50 per bushel support price. How much corn will the government be forced to purchase? (c) Calculate the loss in consumer surplus that would occur under the support program. Problem 52: The market for all-leather men’s shoes is served by both domestic (U.S.) and foreign (F) producers. The domestic producers have been complaining that foreign producers are dumping shoes onto the U.S. market. As a result, Congress is very close to enacting a policy that would completely prohibit sales by foreign manufacturers of leather shoes in the U.S. market. The demand curve and relevant supply curves for the leather shoe market are as follows: QD = 50, 000 − 500P QSU S = 6000 + 150P QSF = 2000 + 50P, where Q = thousands of pairs of shoes per year, and P = price per pair. (a) Currently there are no restrictions covering all-leather men’s shoes. What are the current equilibrium values? (b) Calculate the price and quantity that would prevail if the proposed policy is enacted. Problem 53: The market demand and supply functions for imported cars are: 1 QD = 800, 000 − 5P and QS = (14 + )P + 225, 000. 6 The legislature is considering a tariff (a tax on imported goods) equal to $2,000 per unit to aid domestic car manufacturers. 25
(a) What is the producer surplus if the tariff is implemented? (b) How many cars are imported? (c) Suppose that instead of a tariff, importers agree to voluntarily restrict their imports to this level. If they do and no tariff is implemented, calculate producer surplus in this scenario. (d) Do you expect importers will be more in favor of a tariff or a voluntary quota? Problem 54: A country which does not tax cigarettes is considering the introduction of a $0.40 per pack tax. The economic advisors to the country estimate the supply and demand curves for cigarettes as: QD = 140, 000 − 25, 000P and QS = 20, 000 + 75, 000P, where Q = daily sales in packs of cigarettes, and P = price per pack. The country has hired you to provide the following information regarding the cigarette market and the proposed tax. (a) What are the equilibrium values in the current environment with no tax? (b) What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively? (c) Calculate the deadweight loss from the tax. What is the revenue from the tax? Problem 55: The market demand and supply functions for cotton are: QD = 10 − 0.04P and QS = 38P − 20. (a) Calculate the consumer and producer surplus. 26
(b) To assist cotton farmers, suppose a subsidy of $0.10 a unit is implemented. Calculate the new level of consumer and producer surplus. (c) Did the increase in consumer and producer surplus exceed the increased government spending necessary to finance the subsidy?
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Market Power: Monopoly Problem 56: Barbara is a producer in a monopoly industry. Her demand curve, total revenue curve, marginal revenue curve and total cost curve are given as follows: Q = 160 − 4P ; T R = 40Q − 0.25Q2 M R = 40 − 0.5Q; T C = 4Q; M C = 4 (a) How much output will Barbara produce? (b) What is the price of her product? (c) How much profit will she make? Problem 57: A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q = 200 − 2P ; M R = 100 − Q T C = 5Q; M C = 5 (a) What level of output maximizes total revenue? (b) What is the profit maximizing level of output? (c) What is the profit maximizing price? (d) How much profit does the monopolist earn? Problem 58: The marginal revenue of green ink pads is given as follows: M R = 2500 − 5Q The marginal cost of green ink pads is 5Q. 28
(a) How many ink pads will be produced to maximize revenue? (b) How many ink pads will be produced to maximize profit? Problem 59: The marginal cost of a monopolist is constant and is $10. The marginal revenue curve is given as follows: M R = 100 − 2Q What is the profit maximizing price? Problem 60: A firm’s demand curve is given by P = 500 − 2Q. The firm’s current price is $300 and the firm sells 100 units of output per week. (a) Calculate the firm’s marginal revenue at the current price and quantity using the expression for marginal revenue that utilizes the price elasticity of demand. (b) Assuming that the firm’s marginal cost is zero, is the firm maximizing profit? Problem 61: The marginal cost of a monopolist is constant and is $10. The demand curve and marginal revenue curves are given as follows: Q = 100 − P ; M R = 100 − 2Q What is the deadweight loss from monopoly power?
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Problem 62: Determine the rule-of-thumb price, when the monopolist has a marginal cost of $25 and the price elasticity of demand is -3.0 Problem 63: Maui Macadamia Inc. has a monopoly in the macadamia nut industry. The demand curve, marginal revenue and marginal cost curve for macadamia nuts are given as follows: P = 360 − 4Q; M R = 360 − 8Q; M C = 4Q (a) What level of output maximizes the sum of consumer surplus and producer surplus? (b) What is the profit maximizing level of output? (c) At the profit maximizing level of output, what is the level of consumer surplus? (d) At the profit maximizing level of output, what is the level of producer surplus? (e) At the profit maximizing level of output, what is the deadweight loss?
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Problem 64: John Gardner is the city planner in a medium-sized southeastern city. The city is considering a proposal to award an exclusive contract to Clear Vision, Inc., a cable television carrier. Mr. Gardner has discovered that an economic planner hired a year before has generated the demand, marginal revenue, and marginal cost functions given below: P = 28 − 0.0008Q; M R = 28 − 0.0016Q M C = 0.0012Q, where Q = the number of cable subscribers and P = the price of basic monthly cable service. Conditions change very slowly in the community so that Mr. Gardner considers the cost and demand functions to be reasonably valid for present conditions. Mr. Gardner knows relatively little economics and has hired you to answer the questions listed below. (a) What price and quantity would be expected if the firm is allowed to operate completely unregulated? (b) Mr. Gardner has asked you to recommend a price and quantity that would be socially efficient. Recommend a price and quantity to Mr. Gardner using economic theory to justify your answer. (c) Compare the economic efficiency implications of (a) and (b) above.
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Pricing with Market Power Problem 65: A firm sells an identical product to two groups of consumers, A and B. The firm has decided that third-degree price discrimination is feasible and wishes to set prices that maximize profits. Which price and output strategy will maximize profits? Problem 66: Calloway Shirt Manufacturers sells knit shirts in two sub-markets. In one sub-market, the shirts carry Calloway’s popular label and breast logo and receive a substantial price premium. The other sub-market is targeted toward more price conscious consumers who buy the shirts without a breast logo, and the shirts are labeled with the name Archwood. The retail price of the shirts carrying the Calloway label is $42.00 while the Archwood shirts sell for $25. Calloway’s market research indicates a price elasticity of demand for the higher priced shirt of -2.0, and the elasticity of demand for the Archwood shirts is -4.0. Moreover, the research suggests that both elasticities are constant over broad ranges of output. (a) Are Calloway’s current prices optimal? (b) Management considers the $25 price to be optimal and necessary to meet the competition. What price should the firm set for the Calloway label to achieve an optimal price ratio? Problem 67: American Tire and Rubber Company sells identical radial tires under the firm’s own brand name and private label tires to discount stores. The radial tires sold in both sub-markets are identical, and the marginal cost is constant at $10 per tire for both types. The firm has estimated the following demand curves for each of the markets. P B = 70 − 0.0005QB (brand name) 32
P P = 20 − 0.0002QP (private label). Quantities are measured in thousands per month and price refers to the wholesale price. American currently sells brand name tires at a wholesale price of $28.50 and private label tires for a price of $17. Are these prices optimal for the firm? Problem 68: A lower east-side cinema charges $3.00 per ticket for children under 12 years of age and $5.00 per ticket for anyone 12 years of age or older. The firm has estimated that the price elasticity of demand for tickets purchased by those 12 years of age or older is -1.5. Calculate the elasticity of demand for tickets purchased for children under 12 years of age if prices are optimal. Problem 69: The local zoo has hired you to assist them in setting admission prices. The zoo’s managers recognize that there are two distinct demand curves for zoo admission. One demand curve applies to those ages 12 to 64, while the other is for children and senior citizens. The two demand and marginal revenue curves are: PA = 9.6 − 0.08QA ; M RA = 9.6 − 0.16QA PC/S = 4 − 0.05QCS ; M RC/S = 4 − 0.10QCS where PA = adult price, PC/S = children’s/senior citizen’s price, QA = daily quantity of adults, and QC/S = daily quantity of children and senior citizens. Crowding is not a problem at the zoo, so that the managers consider marginal cost to be zero. If the zoo decides to price discriminate, what are the profit maximizing price and quantity in each market? Calculate total revenue in each sub-market.
33
Problem 70: The BCY Corporation provides accounting services to a wide variety of customers, most of whom have had a business association with BCY for more than five years. BCY’s demand and marginal revenue curves are: P = 10, 000 − 10Q; M R = 10, 000 − 20Q. BCY’s marginal cost of service is: M C = 5Q. (a) If BCY charges a uniform price for a unit of accounting service, Q, what price must it charge per unit, and how many units must it produce per time period in order to maximize profit? Calculate the consumer surplus. (b) If BCY could enforce first-degree price discrimination, what would be the lowest price that it would charge and how many units would it produce per time period? (c) With perfect price discrimination and ignoring any fixed cost, what is total profit? How much additional consumer surplus is captured by switching from a uniform price to first-degree price discrimination? Problem 71: The industry demand curve for a particular market is: Q = 1800 − 200P. The industry exhibits constant long-run average cost at all levels of output, regardless of the market structure. Long-run average cost is a constant $1.50 per unit of output. Compare the economic efficiency of each possibility. (a) Calculate market output, price (if applicable), consumer surplus, and producer surplus (profit) for each of the scenarios below. (i) Perfect Competition (ii) Pure Monopoly (Hint: M R = 9 − 0.01Q) (iii) First Degree Price Discrimination (b) Compare the economic efficiency of each scenario. 34
Monopolistic Competition & Oligopoly Problem 72: A firm operating in a monopolistically competitive market faces the following demand curve: P = 10 − 0.1Q The firm’s total and marginal cost curves are: C = −10Q + 0.15Q2 + 130
and
M C = −10 + 0.3Q,
where P is in dollars per unit, output rate Q is in units per time period, and total cost C is in dollars. (a) From the demand curve facing the firm, determine the firm’s Marginal Revenue equation. (b) Determine the price and output rate that will allow the firm to maximize profit or minimize losses. (c) Compute a Lerner index for the firm. Problem 73: The local pizza market is monopolistically competitive. One of the local producers in the market is a pizza place called One Guy’s Pizza. The demand equation facing One Guy’s Pizza is given by Qd = 225 − 10P or equivalently, P = 22.5 − 0.1Qd . One Guy’s Pizza has a cost function equal to: C(Q) = 0.15Q2 (a) What is the marginal revenue curve for One Guy’s Pizza? 35
(b) What is the marginal cost for One Guy’s Pizza? (c) Determine the profit maximizing level of output and the price charged to customers by One Guy’s Pizza. (d) Would you expect the price and output to be the same in a long-run equilibrium? Problem 74: Suppose that the market demand for mountain spring water is given as follows: P = 1200 − Q Mountain spring water can be produced at no cost (i.e. T C = M C = 0). (a) What is the profit maximizing level of output and price of a monopolist? (b) What level of output would be produced by each firm in a Cournot duopoly equilibrium? What will be the equilibrium price? (c) What would be the equilibrium level of output and price in the long run if the industry was perfectly competitive? Problem 75: Two large diversified consumer products firms are about to enter the market for a new pain reliever. The two firms (Firm A and Firm B) are very similar in terms of their costs, strategic approach, and market outlook. Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price. The market demand curve for the pain reliever is given as: Q = 2600 − 400P. Both firms have constant long-run average costs of $2.00 per bottle. Patent protection insures that the two firms will operate as a duopoly for the foreseeable future. Price and quantity values are stated in per-bottle terms. If the firms act as Cournot duopolists, solve for 36
(a) Firm A’s reaction curve; (b) Firm B’s reaction curve; (c) The Cournot equilibrium quantities and price. Problem 76: Consider two identical firms (Firm 1 and Firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 50 − 0.5Q, where Q = Q1 + Q2 . (a) Find the Cournot equilibrium Q1 , Q2 and P . (b) Find the equilibrium Q and P for each firm assuming that the firms collude and share the profit equally. (c) Compare the efficiency of the equilibrium outcomes derived in (a) and (b) above. Problem 77: The Grand River Brick Corporation (Firm G) uses Business-to-Business internet technology to set output before Bernard’s Bricks (Firm B). This gives the Grand River Brick Corporation ”first-move” ability. The market demand for bricks is Q = 1, 000 − 100P or P = 10 − 0.01Q. Total output is Q = (qB + qG ), where qB is the output produced by Bernard’s Bricks and qG is the output produced by Grand River Brick Corporation. The marginal cost of producing an additional unit of bricks is constant at $2.00 for each firm. (a) Determine the reaction curve for Bernard’s Bricks. (b) Given that the Grand River Brick Corporation has this information and moves first, determine the optimal output decision for Grand River Brick Corporation. 37
(c) Does the ”first-move” ability of the Grand River Brick Corporation allow them to capture a larger market share?
38
Solutions
39
Supply and Demand Problem 1: (a) 20 (b) 100 (c) Shortage equal to 30 (d) Excess supply equal to 30 Problem 2: Q = 2, 388.9 units per week; P = $14.56 per unit. Problem 3: Q = 100, 000; P = $400 Problem 4: −2.75% Problem 5: 4.5% Problem 6: (a) The price elasticity of demand equals zero (is completely inelastic) at a price of zero. (b) Demand is infinitely elastic at a price of $60. (c) At a price of $30. (d) The price elasticity of demand equals Problem 7: (a)
P ∆Q Q ∆P
= −0.35
(b) The revenue drops by $334.36.
40
P ∆Q Q ∆P
= −2.
Consumer Behavior Problem 8: (a) Y = 5 (b) The first combination would be preferred as it leads to higher units of utility. Problem 9: −7/15 Problem 10: − PPBA Problem 11: B = PIB − PPBA A Problem 12: (a) 500 = 10X + 5Y (b) X = 16.67 and Y = 66.67 (c) X = 11.11 and Y = 66.67. Utility declines by roughly 74,141 units. Problem 13: (a) M RS =
M US M UC
(b) M RS = drinks
PS PC
=
⇒
3C 3S
C S
=
=
C S
0.5 0.25
=
1 2
Jane should by twice as many chips as soft
(c) Jane should spend her $5.00 to buy 5 soft drinks and 10 bags of chips. Problem 14: (a) I = PX X + PY Y ⇒ 25 = 3X + 2Y (b) X = 4.17 and Y = 6.25 41
(c) 13.03 units of utility per time period. Problem 15: (a) M UX =
2Y 0.5 X 0.5
and M UY =
2X 0.5 Y 0.5
(b) 750 = 25X + 50Y (c) X = 15 and Y = 7.5 (d) X = 10 and Y = 10 (e) U(X=15,Y =7.5) = 42.43 and U(X=10,Y =10) = 40. Utility declines. Problem 16: (a) M RS =
M UX M UY
(b) M RS =
PX PY
=
⇒
Y X
Y X
=
9 12
= 0.75
(c) No, the mix is not optimal. He should consume 0.75 times as much Y as X, rather than his current 0.67 Y for each X Problem 17: (a) M Uc = 0.9c−0.1 r0.1 and M Ur = 0.1c0.9 r−0.9 (b) c = 270 and r = 1 (c) U(c=300,r=0) = 0 and U(c=180,r=4) = 123.01. Natasha is better off with buying the four tickets. (d) U(c=270,r=1) = 154.25 > 123.01 = U(c=180,r=4) . Natasha would have a higher utility without the constrain. Constraining choices of fully rational actors always leads to lower utilities.
42
Individual and Market Demand Problem 18: (a) Budget line: 120 = Qc + Qd (b)
Qc Qd
= 1 or Qc = Qd
(c) Qc = 60 and Qd = 60 (d) Qc =
120 Pc +1
(e) Qd = 30 and Qc = 60 Problem 19: (a) The total effect of the price change is the difference in quantities before and after the price change. This change includes income and substitution effects. The reduction in consumption that resulted from the reduction in income to put Madame X back on the original indifference curve represents the income effect. The difference between the total effect and the income effect is the substitution effect. Total effect: 15 − 7 = 8 Income effect: 15 − 9 = 6 Substitution effect: (15 − 7) − (15 − 9) = 2 (b) Substitution and income effect are additive and both positive (6+2 = 8). Thus, we have a normal good. Problem 20: 25,000 bottles Problem 21: P = $96 Problem 22: (a) E =
40 (−4) 80
= −2 and demand is elastic.
43
(b) If the price of a good with elastic demand is increased, the total expenditures on the good will decrease (the percentage decrease of demand is bigger than the percentage increase of the price). Problem 23: (a) E = −1, unitary elasticity at this price. Problem 24: 0 (a) Q = 1000 − 200P 5000 − 1533.33P
,if P ≥ 5 ,if 5 ≥ P ≥ 3 ,if 3 ≥ P
(b) Domestic buyers at P ≤ 5 Foreign buyers at P ≤ 3. (c) Qd (P = 2.5) = 500.00 Qf (P = 2.5) = 666.68 Q(P = 2.5) = 1, 166.68 Check Q = Qd + Qf = 500.00 + 666.68 = 1, 166.68 (d) Only domestic demand for this price: Q = 200 Problem 25: (a) E = −0.5 (b) T E = P ∗Q. Total expenditures increase from $800 to $864, even though the total number of artichokes sold has fallen from 80 to 72. (c) Demand is infinitely elastic at the price where the demand curve intersects the vertical y-axis. Here, this occurs at P = $30 Problem 26: (a) Consumption falls from Q(T =5,000)=7 to Q(T =6,000)=6.8 by 0.2
44
(b) The choke price with the old tax is P = $80. His consumer surplus is 0.5($80 − $10)7 = $245. The choke price after the tax increase is P = $78. His consumer surplus decreases to 0.5($78 − $10)6.8 = $231.2. Problem 27: (a) CS = 0.5(5 − 2)12, 000, 000 = 18, 000, 000 (b) Government would have to by the whole excess supply: QS − QD = 1, 625, 000 CS = 0.5(5 − 2.25)11, 000, 000 = 15, 125, 000 Problem 28: 0 (a) Q = 17, 000 − 250P 42, 000 − 2, 250P
,if P ≥ 68 ,if 68 > P ≥ 12.5 ,if 12.5 > P
(b) Check if an equilibrium exists at a price at which art students and others buy rubbers: 42, 000 − 2, 250P = 35, 000 + 2, 000P It does exists; P ∗ = 1.65 and Q∗ = 38, 287.5 (c) CSA = 0.5(68 − 1.65)16, 587.5 = $550, 290.31 CSO = 0.5(12.5 − 1.65)21, 700 = $117, 722.5
45
Production and the Cost of Production Problem 29: APLabor = Lq =
5KL L
= 5K
Problem 30: ∆T C =5 ∆Q Problem 31: (a)
(i) T F C = 4000 (ii) AF C =
4000 Q
(iii) T V C = T C − T F C = 5Q + 10Q2 (iv) AV C = (v) AT C = (vi) M C =
TV C Q TC Q
∆T C ∆Q
= 5 + 10Q
=
4000+5Q+10Q2 Q
= 5 + 20Q
(b) M C = AT C ⇒ Q = 20 Problem 32: M PL and M RT S = wr M RT S = M PK 10 1.5 K = 25 ⇒ 1.5K = 0.4L ⇒ K = 0.266L L Problem 33: (a) 0.75 K = L
15 50
⇒
K L
= 0.4 ⇒ K = 0.4L
(b) Hint:C = wL + rK; insert wage, rent charge, and the ratio from (a) L ≈ 14, 286 hours; K ≈ 5, 714 and Q ≈ 157, 568, 202. (c) Hint: M RT S = 0.75 K ; new input price ratio: 22.5 L 50 New optimal capital-labor ratio: K = 0.6L Amount of labor is reduced (L ≈ 9, 524), amount of capital remains constant (K ≈ 5, 714) and output is reduced (Q ≈ 123, 541, 772) 46
Problem 34: (a) I = wL + rK ⇒ 150, 000 = 12L + 52K (b) L = 9, 375, K = 721.15, Q = 1, 234.29 Problem 35: (a)
K W
= 0.25 or K = 0.25W
(b) W = 20, 000, K = 5, 000 and Q = 600, 000, 000 (c) W ≈ 14, 142, K ≈ 7, 071 Cost for effluent fees F = 106, 065. The costs rises from $300,000 to $424,260 (C = PW W + PK K with PW including the the fee)
Profit Maximization and Competitive Supply Problem 36: (a) M C = 0.002Q (b) Q = 50, 000 and π = −$500, 000 (c) Firm should operate since P > AV C Problem 37: q = 50 and π = 6, 100 Problem 38: (a) q = 40 and π = 9, 880 (b) Short-run output is unaffected q = 40 and profit is reduced to π = 9, 840
47
Problem 39: 75 3 q (a) M C = 32 √ (b) q = 3 512 = 8 and π = −$3, 040 Homer will produce and make a loss, because P > AV C(8). Producing and loosing $3,040 is better than not producing and losing $10,240.
Problem 40: (a) Q = 75 (b) Q = 50 Problem 41: (a) Q = 232.07 and π = 4, 915.08 (b) Optimal output and profit falls: Q = 221.79 and π = 4, 675.11 Problem 42: (a) Q = 116.7 and P = 10.825 (b) q = 7.71 (c) π = 18.77 Problem 43: (a) P = 2 and Q = 50, 000, 000 (b) Q = 100, 000 and π = 10, 000 48
(c) Firms are earning an economic profit so we would expect other firms to join this market (supply curve shifts rightwards). The price would fall causing the firms to reduce their outputs. This will continue until we reach the long-term equilibrium with zero profits. Problem 44: (a) Q = 500, 000 and P = 1 (b) q = 1, 000 (c) Since Q = 500, 000 and q = 1, 000 there must be 500 firms.
49
The Analysis of Competitive Markets Problem 45: (a) P = 0.25 and Q = 1, 000 (b) QS = 520 and QD = 1360. We observe a shortage of 840 calls. Problem 46: (a) Q = 1, 250 and P = $50 (b) Deadweight loss 0.5(61.11 − 40)(1250 − 972.22) = 2, 931.97 Problem 47: (a) P ∗ = $30, Q∗ = 80, 000, PC = $50, QS(P =0) = 20, 000 CS = 0.5(50 − 30)80, 000 = $800, 000 P S = 30 · 20, 000 + 0.5(80, 000 − 20, 000)30 = $1, 500, 000 (b) QS(P =15) = 50, 000 CS = 0.5(50 − 37.5)50, 000 + 50, 000(37.5 − 15) = $1, 437, 500 P S = 15 · 20, 000 + 0.5(50, 000 − 20, 000)15 = $525, 000 Consumer surplus increases, but producers surplus decreases. Not all consumers are better off: some would be willing to pay $15, but because of the shortage they are unable to get cable TV. Problem 48: (a) Government will be forced to buy 150 units of pork (b) Government spending: 150 ∗ 2.25 = 337.5
50
(c) QS(P =0) = 800 P S ∗ = 800 · 2 + 0.5(1, 000 − 800)2 = $1, 800 P S 0 = 800 · 2.25 + 0.5(1, 025 − 800)2.25 = $2, 053.125 ∆P S = P S 0 − P S ∗ = $253.125 Problem 49: (a) P S ∗ = $22.5, P S 0 = $32.9, ∆P S = P S 0 − P S ∗ = $10.4 (b) Q0S = 21.6, Q0D = 4.8, Excess supply of 16.8 (c) Government spending 16.8 ∗ 1.75 = $29.4 The increase in producer surplus does not exceed the government spendings Problem 50: (a) W ∗ = $4, Q∗ = $16, 000 (b) A minimum wage of 3.35 would be below the equilibrium wage and would not be binding. Thus, the market would attain its free market equilibrium. (c) LD = 12, 000, and LS = 22, 000. The new minimum wage would create unemployment 0f 10,000 person hours per year. (d) Hint: For W = 0 we would have a negative supply of labor (LS ). Thus, instead of searching for LS(W =0) we search for a wage where LS = 0 (reservation price). Try to graph LS if you have problems understanding this point P S ∗ = 0.5(4 − 1.33)16, 000 = $21, 360 For which wage would workers supply the demanded quantity of work: W = 1.33 + 0.000167LS = 3.33 P S 0 = 0.5(3.33 − 1.33)12, 000 + (5 − 3.33)12, 000 = $32, 040 Overall producer surplus has increased, but single workers might be worse of because of the increased unemployment rate.
51
Problem 51: (a) P ∗ = 2 and Q∗ = 2, 300 (b) QS = 2, 645 and QD = 1937.5 Government would have to buy the difference of 707.5 millions bushels. (c) ∆CS ≈ −1, 059 Problem 52: (a) P ∗ = 60 and Q∗ = 20, 000 (b) P 0 = 67.69 and Q0 = 16, 155 Problem 53: (a) P S ∗ = P S 0 = 225, 000(31, 478.26−2, 000)+0.5(642, 608.7−225, 000)(31, 478.26− 2, 000) = $12, 787, 797, 732 (b) Q = 42, 608.7 (c) P S 00 = 225, 000(31, 478.26) + 0.5(642, 608.7 − 225, 000)(31, 478.26) = $13, 655, 406, 427 (d) They will favor the voluntary quota. They can sell the same amount of cars but receive the full price instead the price minus the tariff. Problem 54: (a) P = 1.2 and Q = 110, 000 (b) Four conditions must hold: QD = 140, 000 − 25, 000PB QS = 20, 000 + 75, 000PS QD = QS 52
PB = PS + 0.4 In equilibrium: 140, 000 − 25, 000PB = 20, 000 + 75, 000PS Hint: Substituting for PB PS = 1.10, PB = 1.50, Q = 102, 500 The tax is paid $0.3 by buyers (P = 1.2 ⇒ PB = 1.5) and $0.1 by sellers (P = 1.2 ⇒ PS = 1.1) (c) Area A: (110, 000 − 102, 500)(1.5 − 1.2)0.5 = 1, 125 Area B: (110, 000 − 102, 500)(1.2 − 1.1)0.5 = 375 Deadweight Loss: $1500 Revenue from tax: 0.4 ∗ 102, 500 = $41, 000 per day Problem 55: (a) P = 0.79, Q = 9.97, choke price PC = 250, reservation price PR = 0.53 CS = 0.5(250 − 0.79)9.97 = $1, 242.31 P S = 0.5(0.79 − 0.53)9.97 = $1.30 (b) New equilibrium if: 10 − 0.04P = 38(P + 0.1) − 20 P = 0.69, QS = 9.97 CS = 0.5(250 − 0.69)9.97 = $1, 242.81 P S = 0.5(0.79 − 0.53)9.97 = $1.30 (c) Government spending is $0.997. The increase in consumer surplus is $.50, the producer surplus did not change. The increase in consumer and producer surplus is less than government spending.
53
Market Power: Monopoly Problem 56: (a) Q = 72 (b) P = 22 (c) π = 1, 296 Problem 57: (a) Q = 100 (b) Q = 95 (c) P = $52.5 (d) π = $4, 512.5 Problem 58: (a) Q = 500 (b) Q = 250 Problem 59: p = $55 Problem 60: (a) ED = −1.5 M R = P + P E1D = 100 (b) M R = M C thus the quantity should be Q = 125. Firm sells less than 125 and is not maximizing the profit. 54
Problem 61: Deadweight loss from monopoly power is $1,012.5 Problem 62: P =
MC 1+ E1
= $37.5
D
Problem 63: (a) Q = 45 (b) Q = 30 (c) CS = $1, 800 (d) P S = $5, 400 (e) $900 Problem 64: (a) Q = 10, 000 and P = $20 (b) Q = 14, 000 and P = $16.8 (c) If the profit maximizing quantity is produced the deadweight loss from monopoly power is $16,000
55
Pricing with Market Power Problem 65: M RA = M RB = M C Problem 66: 1+(1/EA ) 1+(1/EC )
(a)
PC PA
= 1.68, but
(b)
PC PA
should be 1.5. Given PA = $25, PC should be $37.5
= 1.5. Thus current prices are not optimal.
Problem 67: Prices should be PB = $40 and PP = $15. Thus, prices are not optimal. Problem 68: EChild = −2.25 Problem 69: QA = 60, PA = $4.8 QCS = 40, PCS = $2 T RA = $288, T RCS = $368 Problem 70: (a) Q∗ = 400 and P ∗ = $6, 000 CS = 0.5(10, 000 − 6000)400 = $800, 000 (b) Lowest price would occur if MC=AR Q = 666.67 and P$ 3, 333.33 (c) π = $3, 333, 353.33 Loss in consumer surplus due to first-degree price discrimination is $800,000. Everything from answer (a). 56
Problem 71: Hint: Since LAC is constant, LMC is also constant and equal to LAC. LMC = $1.5 (a)
(i) Q = 1, 500, P = LAC, P S = $0, CS = 0.5(9 − 1.5)1500 = $5, 625 (ii) Q = 750, P = $5.25, P S = $2812.5, CS = 0.5(9 − 5.25)750 = $4, 218.75 (iii) Q = 1, 500, P S = $5, 625, CS = $0
(b) Comparison of Efficiency: (i) Competition: CS+PS = $5,625 (ii) Monopoly: CS+PS = $4,218.75 (iii) First Degree: CS+PS = $5,625 Monopoly results in a deadweight loss. First-degree price discrimination results in a redistribution of income, but does not change the overall welfare. Problem 72: (a) M R = 10 − 0.2Q (b) Q∗ = 40 and P ∗ = 6 (c) L =
2 3
Problem 73: (a) M R = 22.5 − 0.2Qd (b) M C = 0.3Q (c) Q∗ = 45 and P ∗ = 18 (d) No. The profit for One Guy’s Pizza is π = 506.25, which suggests that other firms will want to enter the market and in the long-run, other firms will enter, demand will shift away from One Guy’s Pizza, and their profits will fall to zero. 57
Problem 74: (a) Q = 600 and P = 600 (b) Q1 = Q2 = 400. Thus the total output is 800 and the price will be P = $400. (c) Q = 1, 200 and P = 0 Problem 75: (a) QA = 900 − 0.5QB (b) QB = 900 − 0.5QA (c) QA = 600 and QB = 600, while P = $3.50 Problem 76: (a) Q1 = Q2 = 33.33 and P = 16.66. (b) Q = 50 and if profits are shared equally, Q1 = Q2 = 25. Then P = 25. (c) Both cases result in inefficiency. However, the inefficiency (deadweight loss) is smaller when the firms compete with each other. When they collude, output is restricted even further and price is significantly higher than marginal cost (which is zero in this case). Problem 77: (a) QB = 400 − 0.5QG (b) QG = 400. Therefore, QB = 200. (c) If Grand River Brick Corporation did not have first-mover ability, the outcome would be the Cournot equilibrium, which is QG = QB = 266.66. Thus, first-mover ability has given Grand River a greater market share.
58
