Problem Set #4: Elasticity Key Concepts Elasticity of Demand ...
Problem Set #4: Elasticity Key Concepts Elasticity of Demand
= % change in Quantity Demanded % change in Price Income Elasticity of Demand = % change in Quantity Demanded % change in Income Cross Price Elasticity of Demand = % change in Quantity Demanded of X % change in Price of Y Price Elasticity of Supply = % change in Quantity Supplied % change in Price Formulas to calculate elasticity depending on information: Elasticity of Demand = % ∆ Qd % ∆P = (∆Q)/Q (∆P)/P = ∆Q * P ∆P Q = (1/slope)*P/Q Arc Elasticity: Define P and Q in the usual formula as the average of the range P = (P1 + P2)/2 and Q = (Q1 + Q2)/2 Symbols: η = elasticity ηd = elasticity of demand ηy elasticity of income ηxz = elasticity of X with respect to price of Z ηs = elasticity of supply Problems 1.a) What is the price elasticity of demand for peanuts if the quantity demanded of peanuts increases by 15% when the price of peanuts decreases by 10%? b) What percentage change in price would cause a 12% decrease in quantity demanded given a price elasticity of –0.75? c) What is the point price elasticity of demand for refrigerators if a fall in price from $640 to $560 causes an increase in quantity demanded from 12,000 to 15,600 refrigerators? 2.a) Suppose that when the price of gasoline increases from $0.48 to $0.52 per litre, gasoline consumption falls from 10.1 million litres per year to 9.9 million litres in a given town. Compute the arc elasticity of demand for gasoline. b) If the income elasticity of demand for a commodity is +0.5, is the commodity an inferior good? Exactly what does an income elasticity of 0.5 mean? 3.
The equations of the market demand and supply curves for potatoes are as follows: P = 50 - 4.0 Q
P = 25 + 1.0 Q (P is in cents/kilo and Q is in thousands of kilos)
(a) Graph the demand and supply curves and find the equilibrium price and quantity. Note: Do not plot the values but draw curves with appropriate intercepts and approximate slopes. (b) Calculate the point elasticity of demand at: P = 40 cents ; P = 25 cents, P = 15 cents. As one moves to lower prices, what happens to the "point elasticity of demand"? As one moves to lower prices, what happens to the slope of the demand curve? (c) Suppose that the government legislates a price floor of 32 cents per kilo as a farm support measure and agrees to buy any surplus resulting from this program. Calculate the cost of this policy to the government. (d) Suppose a fungus destroys much of the potato crop and, as a result, the equilibrium price rises to -1-
Problem Set #4: Elasticity 40 cents per kilo. Calculate the "arc price elasticity" of demand between the original and the new equilibrium prices. Will the farm revenue rise or fall as a result of the crop failure? 4.
You are an analyst employed by an automobile manufacturer that last year sold 50,000 compact cars at $6,000 each. Your market research indicates that:
(i) price elasticity of demand for your cars is -3.0 (ii) income elasticity of demand for your cars is +0.7 (iii) cross price elasticity for your cars with respect to the price of a comparable car made by a competitor is +1.2 a) Suppose that you expect a ceteris paribus decrease in average incomes of 5% this year compared to last year. How many cars will your company will sell this year? b) Assume now that you do not think incomes will change, but that you expect your competitor will decrease price by 5%. Assuming that your company does not change the price of its cars, how many cars would expect your company will sell this year? c) Now estimate sales this year if the only change you expect is an increase in the price of your car to $6,600. 5.
The short-run market demand and supply curves for good X are as follows: P = 100 - 2.0 Q
P = 40 + 3.0 Q
(P is in $ per unit)
(NB: Graphs are not necessary to answer the questions in this problem and are much less efficient than algebra. A graph, though, may clarify your understanding) a) Find the equilibrium price and quantity. b) What is the equilibrium price and quantity due to a tax of $5 per unit on producers? c) What is the arc elasticity of demand between the initial and after tax equilibria? Is total revenue at the after tax equilibrium higher or lower than at the before tax equilibrium? Try to answer the question before your calculate total revenue. d) How much of the tax do consumers pay? How much of the tax do producers pay? e) How would your answers to (c) change if the demand curve was vertical? horizontal? How would your answers to (c) change if the supply curve was vertical? horizontal? Given these results, what general conclusion can one make relating the relative elasticities of the demand and supply curves to the fraction of the tax paid by consumers in the short run? 6.
Suppose that the demand curve for carrots ( $/ton) is linear and has a slope of -0.2.
a) What is the elasticity of demand at equilibrium if supply intersects demand at P = $1,500 and Q = 5,000 tons? b) Suppose that a carrot disease causes a shift in supply that results in a new equilibrium at P = $2,000 and Q = 2,500 tons. What is the arc elasticity of demand between the pre-disease equilibrium (part a) and this new equilibrium? c) i) If commodity Z has an income elasticity of -2.5, what type of good is good Z? ii/ What is the percentage change in quantity demanded of good Z when income increases by 10%? iii)If commodity Z also has a price elasticity of Demand of +0.4, what type of good is Z? d) The cross price elasticity of demand for good A given a change in price of good B is +0.25. i/ What is A's relationship to B? ii/ What is the percentage change in the quantity demanded of good A if the price of good B falls $1 from $10 to $9? e) What is the price elasticity of demand at the point where marginal revenue is zero? What is the price elasticity of demand at the point where total revenue is at a maximum? 7. Look back at the milk diagram given in Question #1 of Problem Set #3. -2-
Problem Set #4: Elasticity Suppose that the government abandons the price floor in favour of a subsidy to each farmer of $0.40 per unit of milk produced. a) Draw the impact of this program in the Demand/Supply diagram. b) What is the new equilibrium Price and Quantity? Why is Price not $0.40 below the original equilibrium price? c) How much does this program cost the government? 8.
A student claims that a firm's total revenue always increases when there is an supply induced increase in the price of its product. Briefly explain the truth or falsity of this statement.
9.
A politician argues that the benefit of a per unit subsidy will accrue entirely to producers if the demand for a commodity is perfectly elastic and the supply curve is upward sloping. Prove the truth or falsity of this statement by drawing a diagram incorporating this information. Be sure to indicate the original equilibrium price (Po), the equilibrium price with the subsidy (Ps), and the net price for the producers after the subsidy (Ps+s). Explain your answer briefly. Multiple Choice
1.
If a 10% increase in price results in a a 5% reduction in quantity demanded, the price elasticity of demand (ignoring the minus sign) is a) 5 b) 2 c) 1 d) 0.5 e) 0.2
2.
The price elasticity of demand for Product W is calculated at 3 (technically, -3) for a small range on the downward sloping demand curve. Within this range, if the price were to increase by 10%, then the quantity demanded for Product W would: a) rise by 10% b) fall by 10% c) rise by 30% d) fall by 30% e) none of these
3.
If the price elasticity of demand for tape decks is -0.5, then a 20% increase in price will a/ reduce quantity demanded by 40% b/ reduce quantity demanded by 5% c/ increase total expenditure d/ reduce total expenditure e/ none of the above
4.
If the price for Good B were to decrease from $10 to $8 and as a result the quantity demanded were to increase from 10 million units to 12 million units, then the demand curve, in the range analyzed, using a formula for arc elasticity would be: a) elastic b) unitary elastic c) inelastic d) perfectly elastic
5.
Suppose that the quantity demanded of good X decreases by 2% when income increases by 5%. The income elasticity of good X is a/ +10% b/ -.1 c/ +.1 d/ -.4
6.
If two goods are complements in consumption, their cross price elasticity of demand is a/ zero b/ negative c/ positive d/ either positive or negative depending on whether the goods are normal or inferior e) inelastic
7.
If the demand for a good is elastic, then a/ as price rises, total revenue of producers falls b/ as price falls, total revenue of producers falls c/ as price rises, total revenue of producers rises d/ as price rises, total revenue of producers is constant e) as price rises, total expenditure of consumers rises
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Problem Set #4: Elasticity 8.
If the cross elasticity of demand for a good X relative to good Y is -0.5 and the price of good Y falls by 10%, the change in the quantity demanded of good X is: a/ +5% b/ -5%c/ -0.5% d/ +0.5 e/ none of the above
9.
If the price elasticity of demand for opera was inelastic, then total receipts from opera a/ increase with a rise in price of opera b/ decrease with a rise in price of opera c/ increase with a fall in price of opera d/ increase with a fall in price of ballet e/ increase with an increase in income
10. If Supply is infinitely inelastic and Demand is downward sloping, then at equilibrium a/ supply and demand both determine price and quantity b/ supply determines price and demand determines quantity c/ supply determines quantity and demand determines price d/ supply determines price and quantity e/ demand determines price and quantity 11. If the cross price elasticity of X in relation to Y is positive, then X in relation to Y is a) a substitute good in consumption b) a complement good in production c) a normal good d) an inferior good with a downward sloping Demand e) a Giffen good 12. If a 10% increase in price results in a 10% reduction in total revenue, the elasticity of demand with respect to price is: a) elastic b) inelastic c) unit elastic d) unknown without more information 13. With respect to price elasticity of demand, which one of the following statements is correct: a) if unitary price elasticity of demand were reported for an industry, then small changes in quantity demanded would not change the industry's total revenue b) if a blizzard devastated a Florida orange grove and as a result the Florida orange industry received more total revenue for its crop, then industry demand for oranges must be elastic c) if the price elasticity of demand for Industry Z were computed at 3.0 (more technically, -3.0), then a 12% increase in quantity demanded would lead to a 4% increase in price d) if the price elasticity of demand for Industry Y were computed at 0.3 (more technically, - 0.3), then the demand curve is judged to be elastic. 14. The demand curve for cod would shift outward (increase) if a) the price of salmon (a substitute good) were to decrease b) disposable incomes were to decrease and cod has a negative income elasticity c) the price of rice (a complementary good) were to increase d) cod workers received a pay reduction and cod is a normal good Solutions 1.a) Elasticity = +15%/-10% = -1.5 (but accept 1.5 as well) b) 0.75 = -12%/%changeP => % change P = 12/-0.75 = +16% (must be positive) c) Elasticity = (3600/12000)/(80/640) or 30%/12.5% (but must have some work) 1 mark: correct answer = -2.4 (accept 2.4)
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Problem Set #4: Elasticity 2.a) ηd =
%_∆_Qd % ∆P Arc ηD = ∆Q * P where P = (P1 + P2)/2 ∆P Q Q = (Q1 + Q2)/2 = 10,100,000-9,900,000 * (.48 + .52)/2 0.48-0.52 (10,100,000 + 9,900,000)/2 = -0.25 (or note that quantity falls by 2% [-200,000/10,000,000] when price increases by 8% [0.04/0.50] giving elasticity of -.25. b) Income Elasticity is negative in the case of an inferior good because demand and income change in opposite directions. A income elasticity of +0.5 means that demand changes by half the percentage that income changes in the same direction that income changes. X is therefore a normal good with inelastic income elasticity.
3.a) Demand Curve: Y-intercept = 50 Supply Curve: Y-intercept = 25 slope = -4 slope = +1 Equilibrium: Pd = Ps 50 - 4.0Q = 25 1.0Q => Q = 5 => P = 30 cents by substitution into demand or supply equation b) Point Elasticity: Use ηd = (1/slope)*(P/Q) P = 40 => Q = 2.5=> ηd = (-1/4)*(40/2.5) = -4 P = 25 => Q = 6.25 ηd = (-1/4)*(25/6.25) = -1 P = 15 => Q = 8.75 ηd = (-1/4)*(15/8.75) = -3/7 As P falls, Q increases so that P/Q declines. Since the slope of the linear relationship doesn't change, elasticity also declines. c/ Excess supply exists because the price floor of $0.32 is greater than equilibrium price. Excess supply is Qs-Qd at P = 32. Substituting P =32 into the supply and demand equations -> Qs-Qd = 7 - 4.5 = 2.5 (000) Cost to the government: $0.32 * 2,500 = $800 d/ Original Equilibrium (part a)): PO = 30, QO = 5 P2 = 40 => Q2 = 2.5 (from part b/) Arc ηd = (5-2.5) * (30+40)/2 = - 2.33 (-7/3) 30-40 (5+2.5)/2 When P rises over an elastic (ηd > 1) segment of the demand curve, total revenue falls. ηY = +0.7 (1% increase in income => 0.7% increase in Qd) ηPxz = +1.2 (1% increase in Pz (a substitute for X) => 1.2% increase in Qdx) ηd = -3.0 (1% increase in price => 3% fall in Qd a) 5% fall in income => 5 (0.7)% fall in Qd = -3.5% (50,000) = -1750 cars => 50,000 - 1,750 = 48,250 cars will sell this year. b) 5% fall in Psubstitute => -5 (1.2)% = -6% change in Qd => 50,000 - .06(50,000) = 47,000 cars sold this year c) If the car's price rises from $6,000 to $6,600 (+10%), then expect quantity to fall by +10 (-3.0)% = -30% => Estimated sales = 50,000 - .3(50,000) = 35,000. 4.
Given:
5.a) Equilibrium => Pd=Ps => 100 - 2.0Q = 40 + 3.0Q => Q = 12 and P = $76 b) Tax = $5/unit => Supply shifts to P = 45 + 3.0Q => Equilibrium at P = $78 and Q = 11 c) ηd = (12-11) * (76+78)/2= -3.35 76-78) (12+11)/2 Total Revenue falls because Price rises when Demand is elastic. [Revenue goes from 76*12 = 912 to 78*11 -5-
Problem Set #4: Elasticity = 858] d) Change in price from $76 to $78 effectively means that consumers pays $2 of tax. Producers now receive $78 but have to remit $5 to the government, leaving them with $73. They receive $76-$73 = $$3 less than before and thus 'pay' $3 of the tax e) Vertical Demand => ηd = 0, i.e., perfectly inelastic Demand => Consumer pays the entire tax Horizontal Demand => ηd = -infinity (perfectly elastic Demand) => Consumer pays no tax. Vertical Supply => ηs = 0, i.e., perfectly inelastic Supply => Producer pays the entire tax Horizontal Supply => ηs = infinity (perfectly elastic Supply) => Producer pays no tax. The more inelastic Demand is, therefore, the more consumers pay of the tax because Qd is little affected by an increase in Price. The more inelastic Supply is, the more producers pay of the tax because Qs is little affected by an increase in Price. The division of the tax between consumers and producers therefore depends on the relative elasticities of Demand and Supply. 6.a) ηd = (1/-0.2) * (1500/5000) = -1.5 b) ηd = (1/-0.2) * (1500+2000)/(5000+2500) = -7/3 c) i) Inferior ii) % ∆Qd = +10% * (-2.5) = -25% iii) A Giffen good Demand must be upward sloping d) i) A substitute ii) % ∆QdA = (100% *-1/10) * 0.25 = -2.5% [$10, not $9, is the original price] e) Marginal Revenue = 0 => no change in Total Revenue => unit elasticity. Maximum Total Revenue => no change in total revenue at that point => Marginal Revenue = 0 7.a) Supply shifts down by exactly $0.40 at each quantity. In particular, this means the Supply shifts down by $0.40 at the original equilibrium quantity of 60 so that Supply with the subsidy goes through $0.30 ($0.70 - $0.40) and 60. b) $0.40 and 70 million. Producers are charging $0.40 per unit less but quantity demanded increases as Price falls. c) $0.40 * 70 million = $28 million
1.4
Demand for and Supply of Milk
P
So
1.3 1.2 1.1 1
Ss
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Do
0.1 0 0
10
20
30
40
50
60
70
80
90
100
110
120
8.
The statement is false. An increase in supply lowers price and increases quantity at equilibrium. Total revenue increases for a decrease in price along the Demand function only if demand is price elastic. If demand is inelastic, an decrease in price will decrease total revenue. (Note that a decrease in price due to a decrease in Demand will always decrease the firm's revenue because the shift down in Demand causes movement down the Supply Curve which decreases both price and quantity)
9.
The politician (surprisingly) is correct. The subsidy reduces cost, shifting Supply down.
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Problem Set #4: Elasticity Equilibrium price does not change since Demand is perfectly elastic. Consumers pay the same price so they are unaffected by the tax except for increased consumption. Producers receive the original price plus the full amount of the subsidy. Multiple Choice 1. 2. 3. 4. 5.
d) d) c) c) d)
6. 7. 8. 9. 10.
b) a) a) a) c)
11. 12. 13. 14.
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a) a) a) b)
= % change in Quantity Demanded % change in Price Income Elasticity of Demand = % change in Quantity Demanded % change in Income Cross Price Elasticity of Demand = % change in Quantity Demanded of X % change in Price of Y Price Elasticity of Supply = % change in Quantity Supplied % change in Price Formulas to calculate elasticity depending on information: Elasticity of Demand = % ∆ Qd % ∆P = (∆Q)/Q (∆P)/P = ∆Q * P ∆P Q = (1/slope)*P/Q Arc Elasticity: Define P and Q in the usual formula as the average of the range P = (P1 + P2)/2 and Q = (Q1 + Q2)/2 Symbols: η = elasticity ηd = elasticity of demand ηy elasticity of income ηxz = elasticity of X with respect to price of Z ηs = elasticity of supply Problems 1.a) What is the price elasticity of demand for peanuts if the quantity demanded of peanuts increases by 15% when the price of peanuts decreases by 10%? b) What percentage change in price would cause a 12% decrease in quantity demanded given a price elasticity of –0.75? c) What is the point price elasticity of demand for refrigerators if a fall in price from $640 to $560 causes an increase in quantity demanded from 12,000 to 15,600 refrigerators? 2.a) Suppose that when the price of gasoline increases from $0.48 to $0.52 per litre, gasoline consumption falls from 10.1 million litres per year to 9.9 million litres in a given town. Compute the arc elasticity of demand for gasoline. b) If the income elasticity of demand for a commodity is +0.5, is the commodity an inferior good? Exactly what does an income elasticity of 0.5 mean? 3.
The equations of the market demand and supply curves for potatoes are as follows: P = 50 - 4.0 Q
P = 25 + 1.0 Q (P is in cents/kilo and Q is in thousands of kilos)
(a) Graph the demand and supply curves and find the equilibrium price and quantity. Note: Do not plot the values but draw curves with appropriate intercepts and approximate slopes. (b) Calculate the point elasticity of demand at: P = 40 cents ; P = 25 cents, P = 15 cents. As one moves to lower prices, what happens to the "point elasticity of demand"? As one moves to lower prices, what happens to the slope of the demand curve? (c) Suppose that the government legislates a price floor of 32 cents per kilo as a farm support measure and agrees to buy any surplus resulting from this program. Calculate the cost of this policy to the government. (d) Suppose a fungus destroys much of the potato crop and, as a result, the equilibrium price rises to -1-
Problem Set #4: Elasticity 40 cents per kilo. Calculate the "arc price elasticity" of demand between the original and the new equilibrium prices. Will the farm revenue rise or fall as a result of the crop failure? 4.
You are an analyst employed by an automobile manufacturer that last year sold 50,000 compact cars at $6,000 each. Your market research indicates that:
(i) price elasticity of demand for your cars is -3.0 (ii) income elasticity of demand for your cars is +0.7 (iii) cross price elasticity for your cars with respect to the price of a comparable car made by a competitor is +1.2 a) Suppose that you expect a ceteris paribus decrease in average incomes of 5% this year compared to last year. How many cars will your company will sell this year? b) Assume now that you do not think incomes will change, but that you expect your competitor will decrease price by 5%. Assuming that your company does not change the price of its cars, how many cars would expect your company will sell this year? c) Now estimate sales this year if the only change you expect is an increase in the price of your car to $6,600. 5.
The short-run market demand and supply curves for good X are as follows: P = 100 - 2.0 Q
P = 40 + 3.0 Q
(P is in $ per unit)
(NB: Graphs are not necessary to answer the questions in this problem and are much less efficient than algebra. A graph, though, may clarify your understanding) a) Find the equilibrium price and quantity. b) What is the equilibrium price and quantity due to a tax of $5 per unit on producers? c) What is the arc elasticity of demand between the initial and after tax equilibria? Is total revenue at the after tax equilibrium higher or lower than at the before tax equilibrium? Try to answer the question before your calculate total revenue. d) How much of the tax do consumers pay? How much of the tax do producers pay? e) How would your answers to (c) change if the demand curve was vertical? horizontal? How would your answers to (c) change if the supply curve was vertical? horizontal? Given these results, what general conclusion can one make relating the relative elasticities of the demand and supply curves to the fraction of the tax paid by consumers in the short run? 6.
Suppose that the demand curve for carrots ( $/ton) is linear and has a slope of -0.2.
a) What is the elasticity of demand at equilibrium if supply intersects demand at P = $1,500 and Q = 5,000 tons? b) Suppose that a carrot disease causes a shift in supply that results in a new equilibrium at P = $2,000 and Q = 2,500 tons. What is the arc elasticity of demand between the pre-disease equilibrium (part a) and this new equilibrium? c) i) If commodity Z has an income elasticity of -2.5, what type of good is good Z? ii/ What is the percentage change in quantity demanded of good Z when income increases by 10%? iii)If commodity Z also has a price elasticity of Demand of +0.4, what type of good is Z? d) The cross price elasticity of demand for good A given a change in price of good B is +0.25. i/ What is A's relationship to B? ii/ What is the percentage change in the quantity demanded of good A if the price of good B falls $1 from $10 to $9? e) What is the price elasticity of demand at the point where marginal revenue is zero? What is the price elasticity of demand at the point where total revenue is at a maximum? 7. Look back at the milk diagram given in Question #1 of Problem Set #3. -2-
Problem Set #4: Elasticity Suppose that the government abandons the price floor in favour of a subsidy to each farmer of $0.40 per unit of milk produced. a) Draw the impact of this program in the Demand/Supply diagram. b) What is the new equilibrium Price and Quantity? Why is Price not $0.40 below the original equilibrium price? c) How much does this program cost the government? 8.
A student claims that a firm's total revenue always increases when there is an supply induced increase in the price of its product. Briefly explain the truth or falsity of this statement.
9.
A politician argues that the benefit of a per unit subsidy will accrue entirely to producers if the demand for a commodity is perfectly elastic and the supply curve is upward sloping. Prove the truth or falsity of this statement by drawing a diagram incorporating this information. Be sure to indicate the original equilibrium price (Po), the equilibrium price with the subsidy (Ps), and the net price for the producers after the subsidy (Ps+s). Explain your answer briefly. Multiple Choice
1.
If a 10% increase in price results in a a 5% reduction in quantity demanded, the price elasticity of demand (ignoring the minus sign) is a) 5 b) 2 c) 1 d) 0.5 e) 0.2
2.
The price elasticity of demand for Product W is calculated at 3 (technically, -3) for a small range on the downward sloping demand curve. Within this range, if the price were to increase by 10%, then the quantity demanded for Product W would: a) rise by 10% b) fall by 10% c) rise by 30% d) fall by 30% e) none of these
3.
If the price elasticity of demand for tape decks is -0.5, then a 20% increase in price will a/ reduce quantity demanded by 40% b/ reduce quantity demanded by 5% c/ increase total expenditure d/ reduce total expenditure e/ none of the above
4.
If the price for Good B were to decrease from $10 to $8 and as a result the quantity demanded were to increase from 10 million units to 12 million units, then the demand curve, in the range analyzed, using a formula for arc elasticity would be: a) elastic b) unitary elastic c) inelastic d) perfectly elastic
5.
Suppose that the quantity demanded of good X decreases by 2% when income increases by 5%. The income elasticity of good X is a/ +10% b/ -.1 c/ +.1 d/ -.4
6.
If two goods are complements in consumption, their cross price elasticity of demand is a/ zero b/ negative c/ positive d/ either positive or negative depending on whether the goods are normal or inferior e) inelastic
7.
If the demand for a good is elastic, then a/ as price rises, total revenue of producers falls b/ as price falls, total revenue of producers falls c/ as price rises, total revenue of producers rises d/ as price rises, total revenue of producers is constant e) as price rises, total expenditure of consumers rises
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Problem Set #4: Elasticity 8.
If the cross elasticity of demand for a good X relative to good Y is -0.5 and the price of good Y falls by 10%, the change in the quantity demanded of good X is: a/ +5% b/ -5%c/ -0.5% d/ +0.5 e/ none of the above
9.
If the price elasticity of demand for opera was inelastic, then total receipts from opera a/ increase with a rise in price of opera b/ decrease with a rise in price of opera c/ increase with a fall in price of opera d/ increase with a fall in price of ballet e/ increase with an increase in income
10. If Supply is infinitely inelastic and Demand is downward sloping, then at equilibrium a/ supply and demand both determine price and quantity b/ supply determines price and demand determines quantity c/ supply determines quantity and demand determines price d/ supply determines price and quantity e/ demand determines price and quantity 11. If the cross price elasticity of X in relation to Y is positive, then X in relation to Y is a) a substitute good in consumption b) a complement good in production c) a normal good d) an inferior good with a downward sloping Demand e) a Giffen good 12. If a 10% increase in price results in a 10% reduction in total revenue, the elasticity of demand with respect to price is: a) elastic b) inelastic c) unit elastic d) unknown without more information 13. With respect to price elasticity of demand, which one of the following statements is correct: a) if unitary price elasticity of demand were reported for an industry, then small changes in quantity demanded would not change the industry's total revenue b) if a blizzard devastated a Florida orange grove and as a result the Florida orange industry received more total revenue for its crop, then industry demand for oranges must be elastic c) if the price elasticity of demand for Industry Z were computed at 3.0 (more technically, -3.0), then a 12% increase in quantity demanded would lead to a 4% increase in price d) if the price elasticity of demand for Industry Y were computed at 0.3 (more technically, - 0.3), then the demand curve is judged to be elastic. 14. The demand curve for cod would shift outward (increase) if a) the price of salmon (a substitute good) were to decrease b) disposable incomes were to decrease and cod has a negative income elasticity c) the price of rice (a complementary good) were to increase d) cod workers received a pay reduction and cod is a normal good Solutions 1.a) Elasticity = +15%/-10% = -1.5 (but accept 1.5 as well) b) 0.75 = -12%/%changeP => % change P = 12/-0.75 = +16% (must be positive) c) Elasticity = (3600/12000)/(80/640) or 30%/12.5% (but must have some work) 1 mark: correct answer = -2.4 (accept 2.4)
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Problem Set #4: Elasticity 2.a) ηd =
%_∆_Qd % ∆P Arc ηD = ∆Q * P where P = (P1 + P2)/2 ∆P Q Q = (Q1 + Q2)/2 = 10,100,000-9,900,000 * (.48 + .52)/2 0.48-0.52 (10,100,000 + 9,900,000)/2 = -0.25 (or note that quantity falls by 2% [-200,000/10,000,000] when price increases by 8% [0.04/0.50] giving elasticity of -.25. b) Income Elasticity is negative in the case of an inferior good because demand and income change in opposite directions. A income elasticity of +0.5 means that demand changes by half the percentage that income changes in the same direction that income changes. X is therefore a normal good with inelastic income elasticity.
3.a) Demand Curve: Y-intercept = 50 Supply Curve: Y-intercept = 25 slope = -4 slope = +1 Equilibrium: Pd = Ps 50 - 4.0Q = 25 1.0Q => Q = 5 => P = 30 cents by substitution into demand or supply equation b) Point Elasticity: Use ηd = (1/slope)*(P/Q) P = 40 => Q = 2.5=> ηd = (-1/4)*(40/2.5) = -4 P = 25 => Q = 6.25 ηd = (-1/4)*(25/6.25) = -1 P = 15 => Q = 8.75 ηd = (-1/4)*(15/8.75) = -3/7 As P falls, Q increases so that P/Q declines. Since the slope of the linear relationship doesn't change, elasticity also declines. c/ Excess supply exists because the price floor of $0.32 is greater than equilibrium price. Excess supply is Qs-Qd at P = 32. Substituting P =32 into the supply and demand equations -> Qs-Qd = 7 - 4.5 = 2.5 (000) Cost to the government: $0.32 * 2,500 = $800 d/ Original Equilibrium (part a)): PO = 30, QO = 5 P2 = 40 => Q2 = 2.5 (from part b/) Arc ηd = (5-2.5) * (30+40)/2 = - 2.33 (-7/3) 30-40 (5+2.5)/2 When P rises over an elastic (ηd > 1) segment of the demand curve, total revenue falls. ηY = +0.7 (1% increase in income => 0.7% increase in Qd) ηPxz = +1.2 (1% increase in Pz (a substitute for X) => 1.2% increase in Qdx) ηd = -3.0 (1% increase in price => 3% fall in Qd a) 5% fall in income => 5 (0.7)% fall in Qd = -3.5% (50,000) = -1750 cars => 50,000 - 1,750 = 48,250 cars will sell this year. b) 5% fall in Psubstitute => -5 (1.2)% = -6% change in Qd => 50,000 - .06(50,000) = 47,000 cars sold this year c) If the car's price rises from $6,000 to $6,600 (+10%), then expect quantity to fall by +10 (-3.0)% = -30% => Estimated sales = 50,000 - .3(50,000) = 35,000. 4.
Given:
5.a) Equilibrium => Pd=Ps => 100 - 2.0Q = 40 + 3.0Q => Q = 12 and P = $76 b) Tax = $5/unit => Supply shifts to P = 45 + 3.0Q => Equilibrium at P = $78 and Q = 11 c) ηd = (12-11) * (76+78)/2= -3.35 76-78) (12+11)/2 Total Revenue falls because Price rises when Demand is elastic. [Revenue goes from 76*12 = 912 to 78*11 -5-
Problem Set #4: Elasticity = 858] d) Change in price from $76 to $78 effectively means that consumers pays $2 of tax. Producers now receive $78 but have to remit $5 to the government, leaving them with $73. They receive $76-$73 = $$3 less than before and thus 'pay' $3 of the tax e) Vertical Demand => ηd = 0, i.e., perfectly inelastic Demand => Consumer pays the entire tax Horizontal Demand => ηd = -infinity (perfectly elastic Demand) => Consumer pays no tax. Vertical Supply => ηs = 0, i.e., perfectly inelastic Supply => Producer pays the entire tax Horizontal Supply => ηs = infinity (perfectly elastic Supply) => Producer pays no tax. The more inelastic Demand is, therefore, the more consumers pay of the tax because Qd is little affected by an increase in Price. The more inelastic Supply is, the more producers pay of the tax because Qs is little affected by an increase in Price. The division of the tax between consumers and producers therefore depends on the relative elasticities of Demand and Supply. 6.a) ηd = (1/-0.2) * (1500/5000) = -1.5 b) ηd = (1/-0.2) * (1500+2000)/(5000+2500) = -7/3 c) i) Inferior ii) % ∆Qd = +10% * (-2.5) = -25% iii) A Giffen good Demand must be upward sloping d) i) A substitute ii) % ∆QdA = (100% *-1/10) * 0.25 = -2.5% [$10, not $9, is the original price] e) Marginal Revenue = 0 => no change in Total Revenue => unit elasticity. Maximum Total Revenue => no change in total revenue at that point => Marginal Revenue = 0 7.a) Supply shifts down by exactly $0.40 at each quantity. In particular, this means the Supply shifts down by $0.40 at the original equilibrium quantity of 60 so that Supply with the subsidy goes through $0.30 ($0.70 - $0.40) and 60. b) $0.40 and 70 million. Producers are charging $0.40 per unit less but quantity demanded increases as Price falls. c) $0.40 * 70 million = $28 million
1.4
Demand for and Supply of Milk
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8.
The statement is false. An increase in supply lowers price and increases quantity at equilibrium. Total revenue increases for a decrease in price along the Demand function only if demand is price elastic. If demand is inelastic, an decrease in price will decrease total revenue. (Note that a decrease in price due to a decrease in Demand will always decrease the firm's revenue because the shift down in Demand causes movement down the Supply Curve which decreases both price and quantity)
9.
The politician (surprisingly) is correct. The subsidy reduces cost, shifting Supply down.
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Problem Set #4: Elasticity Equilibrium price does not change since Demand is perfectly elastic. Consumers pay the same price so they are unaffected by the tax except for increased consumption. Producers receive the original price plus the full amount of the subsidy. Multiple Choice 1. 2. 3. 4. 5.
d) d) c) c) d)
6. 7. 8. 9. 10.
b) a) a) a) c)
11. 12. 13. 14.
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a) a) a) b)
