TUTORIAL 16 - MONDAY â AUGUST 11, 2014 - 4PM ...
TUTORIAL 16 - MONDAY – AUGUST 11, 2014 - 4PM - 5PM QUESTION 15.2 – p. 563 Clare manages a piano store. Her utility function is given by Utility = w – 100 where w is the total of all monetary to her and 100 represents the cost to her of the effort of running the store. Clare's next best alternative to managing the store provides her with zero utility. The store's gross profit depends on random factors. There is a 50% chance it earns $1,000 (where by earnings we mean gross profits, not including payments to the manager) and a 50% chance it earns only $400. (a) If shareholders offered to share half of the store's gross profit, what would her expected utility be? Would she accept such a contract? What if she were only given a quarter share? What would be the lowest share she would accept to manage the firm? (b) What is the most Clare would pay to buy out the store if shareholders decided to sell it to her? (c) Suppose instead that shareholders decided to offer her a $100 bonus if the store earns $1,000. What fixed salary would Clare need to be paid in addition to get her to accept the contract? QUESTION 15.3 – p. 563 Return to QUESTION 15.2. Suppose that Clare can still choose to exert effort, as in QUESTION 15.2, but that she can also choose not to exert effort. If she does not exert effort, she has no effort cost, so her utility is just the wage, w, and the shop's return is $400 for certain. (a) If shareholders offered to share half of the store's gross profit, what effort would Clare choose? Would she accept such a contract? What if she were only given a quarter share? What would be the lowest share that would get her to exert effort? (b) Suppose instead that shareholders decided to offer her a $100 bonus if the store earns $1,000. Show that this would not get her to work hard. What is the minimum bonus that she would need to be paid? What fixed salary would she need to be paid in addition to get her to accept the contract?
QUESTION 15.6 – p. 564 L. L. Bean, among other stores, has a policy of replacing shoes that wear out with new ones. Suppose there are two types of shoe buyers. Half of them have desk jobs and only have a 20% chance of wearing out their shoes. The other half active jobs (construction, nursing) and have a 60% percent chance of wearing out their shoes. A pair of shoes costs $25 to produce. (a) If the store cannot distinguish between the two types, what is the lowest price it can charge for shoes and still break even on average? (This is the price that would prevail in a competitive market.) (b) What would happen to the equilibrium if the desk workers' valuation
for shoes was less than the market price in part (a)? What is a possible source of inefficiency in this new equilibrium? (c) Compute the competitive equilibrium if shoe manufacturers can
charge an extra price for shoes with a replacement guarantee, assuming that only the active workers purchase the guarantee. QUESTION 15.8 – p. 564 Suppose 100 cars will be offered on the used-car market, 50 of them good cars, each worth $10,000 to a buyer, and 50 of them lemons, each worth $2,000. (a) Compute a buyer's maximum willingness to pay for a car if he or she cannot observe the car's type. (b) Suppose that there are enough buyers that competition among them leads cars to be sold at their maximum willingness to pay. What would the market equilibrium be if sellers value good cars at $8,000? At $6,000? QUESTION 16.1 – p. 597 A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm's average costs, meaning this firm alone (although still a price taker) can earn real economic profits in the long run. (a) If the market price is $20 per widget and the firm's marginal cost curve is given by MC = 0.4q, where q is the daily widget production for the firm, how many widgets will the firm produce? (b) Suppose a government study has found that the firm's new process is polluting the air and the study estimates the social marginal cost of widget
production by this firm to be MCS = 0.5q. If the market price is still $20, what is the socially optimal level of production for the firm? What should the amount of a government-imposed excise tax be in order to bring about this optimal level of production? QUESTION 16.3 – p. 598 Suppose the oil industry in Utopia is perfectly competitive and that all firms draw oil from a single (and practically inexhaustible) pool. Each competitor believes that he or she can sell all the oil he or she can produce at a stable world price of $10 per barrel and that the cost of operating a well for one year is $1,000.00. Total output per year (Q) of the oil field is a function of the number of wells (N) operating in the field. In particular, Q = 500N – N2 and the amount of oil produced by each well (q) is given by q = Q/N = 500 – N The output from the Nth well is given by MPN = 500 - 2N (a) Describe the equilibrium output and the equilibrium number of wells in this perfectly competitive case. Is there a divergence between private marginal cost and social marginal cost in this industry? (b) Suppose that the government nationalizes the oil field. How many oil wells should it operate? What would total output be? What will the total output per well be? (c) As an alternative to nationalization, the Utopian government is considering an annual licence fee per well to discourage over-drilling. How large should this licence fee be to prompt the industry to drill the optimal number of wells?
QUESTION 15.6 – p. 564 L. L. Bean, among other stores, has a policy of replacing shoes that wear out with new ones. Suppose there are two types of shoe buyers. Half of them have desk jobs and only have a 20% chance of wearing out their shoes. The other half active jobs (construction, nursing) and have a 60% percent chance of wearing out their shoes. A pair of shoes costs $25 to produce. (a) If the store cannot distinguish between the two types, what is the lowest price it can charge for shoes and still break even on average? (This is the price that would prevail in a competitive market.) (b) What would happen to the equilibrium if the desk workers' valuation
for shoes was less than the market price in part (a)? What is a possible source of inefficiency in this new equilibrium? (c) Compute the competitive equilibrium if shoe manufacturers can
charge an extra price for shoes with a replacement guarantee, assuming that only the active workers purchase the guarantee. QUESTION 15.8 – p. 564 Suppose 100 cars will be offered on the used-car market, 50 of them good cars, each worth $10,000 to a buyer, and 50 of them lemons, each worth $2,000. (a) Compute a buyer's maximum willingness to pay for a car if he or she cannot observe the car's type. (b) Suppose that there are enough buyers that competition among them leads cars to be sold at their maximum willingness to pay. What would the market equilibrium be if sellers value good cars at $8,000? At $6,000? QUESTION 16.1 – p. 597 A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm's average costs, meaning this firm alone (although still a price taker) can earn real economic profits in the long run. (a) If the market price is $20 per widget and the firm's marginal cost curve is given by MC = 0.4q, where q is the daily widget production for the firm, how many widgets will the firm produce? (b) Suppose a government study has found that the firm's new process is polluting the air and the study estimates the social marginal cost of widget
production by this firm to be MCS = 0.5q. If the market price is still $20, what is the socially optimal level of production for the firm? What should the amount of a government-imposed excise tax be in order to bring about this optimal level of production? QUESTION 16.3 – p. 598 Suppose the oil industry in Utopia is perfectly competitive and that all firms draw oil from a single (and practically inexhaustible) pool. Each competitor believes that he or she can sell all the oil he or she can produce at a stable world price of $10 per barrel and that the cost of operating a well for one year is $1,000.00. Total output per year (Q) of the oil field is a function of the number of wells (N) operating in the field. In particular, Q = 500N – N2 and the amount of oil produced by each well (q) is given by q = Q/N = 500 – N The output from the Nth well is given by MPN = 500 - 2N (a) Describe the equilibrium output and the equilibrium number of wells in this perfectly competitive case. Is there a divergence between private marginal cost and social marginal cost in this industry? (b) Suppose that the government nationalizes the oil field. How many oil wells should it operate? What would total output be? What will the total output per well be? (c) As an alternative to nationalization, the Utopian government is considering an annual licence fee per well to discourage over-drilling. How large should this licence fee be to prompt the industry to drill the optimal number of wells?
