2. Bearcat University hires Mr. LeBron to coach its basketball team. LeBron's utility function is=u = √w - 6e, where w denotes his wage and e his effort. He can choose either low efforte 1 or high effort e = 2. If Bearcat wins its division, the university's profit will be 600.Otherwise the university's profit will be 200. LeBron's reservation utility is 4. The universitycannot observe LeBron's effort. The probabilities of outcomes given LeBron's effort are:e = 1еH = 2(Bearcat does not winits division)π = 2000.80.2(Bearcat wins itsdivision)π₂ = 6000.20.8a. Let w₁ and w₂ be the wage paid to LeBron if profit is ₁ and ₂, respectively. What arethe individual rationality condition and the incentive compatibility condition needed toinduce еx?b. Assuming e, is the more desirable of the two effort levels, find the optimal wagecontract. What is the university's expected net profit?c. If the university wanted to induce LeBron to choose e, what wage contract should ituse? What would be the university's expected net profit?

A utility function is a mathematical representation of an individual's preferences over different…

Bearcat University hires Mr. LeBron to coach its basketball team. LeBron's utility function is u= √w-6e, where w denotes his wage and e his effort. He can choose either low effort e 1 or high effort eH=2. If Bearcat wins its division, the university's profit will be 600. Otherwise the university's profit will be 200. LeBron's reservation utility is 4. The university cannot observe LeBron's effort. The probabilities of outcomes given LeBron's effort are: e = 1 еH=2 (Bearcat does not win its division) TL1 200 0.8 0.2 (Bearcat wins its division) T₂=600 0.2 0.8 a. Let w, and we be the wage paid to LeBron if profit is ₁ and ₂, respectively. What are the individual rationality condition and the incentive compatibility condition needed to induce ex? b. Assuming e, is the more desirable of the two effort levels, find the optimal wage contract. What is the university's expected net profit? c. If the university wanted to induce LeBron to choose e, what wage contract should it use? What would be the university's expected net profit?

Bearcat University hires Mr. LeBron to coach its basketball team. LeBron's utility function is u= √w-6e, where w denotes his wage and e his effort. He can choose either low effort e 1 or high effort eH=2. If Bearcat wins its division, the university's profit will be 600. Otherwise the university's profit will be 200. LeBron's reservation utility is 4. The university cannot observe LeBron's effort. The probabilities of outcomes given LeBron's effort are: e = 1 еH=2 (Bearcat does not win its division) TL1 200 0.8 0.2 (Bearcat wins its division) T₂=600 0.2 0.8 a. Let w, and we be the wage paid to LeBron if profit is ₁ and ₂, respectively. What are the individual rationality condition and the incentive compatibility condition needed to induce ex? b. Assuming e, is the more desirable of the two effort levels, find the optimal wage contract. What is the university's expected net profit? c. If the university wanted to induce LeBron to choose e, what wage contract should it use? What would be the university's expected net profit?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.11P

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Consider the following graph: AR, MR, ATC, MC w* W* MC = ATC AR=D W A MR a. Indicate the price a profit maximizing firm faces for a win, PPR. Shade in the area that indicates the team's profit. b. Indicate the price a win maximizing firm faces for a win, Pw. Shade in the area that indicates the team's profit.
You are the manager of a monopolist that produces women shoes and faces a random marginal cost. The demand for women shoes is O = 1000 - 0.1P Marginal cost can be constant at either $60 with a probability of 50% or $40 with a probability of probability of 50%. Draw a graph and plot the demand for shoes. Derive the marginal revenue curve and plot it on the graph. Find the price and output that maximize profits. Find the firm's profits.
Exercise A.9 You are an executive of Super Computer, INC. (SC), which rents supercomputers. SC receives a fixed rent for a period of time in exchange for the right to use unlimited computers equal to P cents per second. SC has two types of potential clients of equal numbers: 10 companies and 10 academic institutions. Each company has the demand function Q = 10 – P, where Q is expressed in millions of seconds per month; each academic institution has the demand Q = 8 – P. The marginal cost to SC of additional computer utilization is 2 cents per second, regardless of volume. a) Suppose you can distinguish companies from academic clients. What rental and usage fee would you charge each group? Calculate the profits you would get? b) Suppose that you cannot separate the two types of customers and that you did not charge a rental fee. What usage quota would maximize your profits? How many benefits would you get?
Exercise A.9 You are an executive of Super Computer, INC. (SC), which rents supercomputers. SC receives a fixed rent for a period of time in exchange for the right use unlimited computers equal to P cents per second. SC has two types of potential clients of equal numbers: 10 companies and 10 academic institutions. Each company has the demand function Q = 10 - P, where Q is expressed in millions of seconds per month; each academic institution has the demand Q = 8 - P. The marginal cost to SC of additional computer utilization is 2 cents per second, regardless of volume. a) Suppose you can distinguish companies from academic clients. What rental and usage fee would you charge each group? Calculate the profits you would get? b) Suppose that you cannot separate the two types of customers and that you did not charge a rental fee. What usage quota would maximize your profits? How many benefits would you get?
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The Broadway show Hamilton is coming to perform for one night. There are two types of consumers interested in the show- current students and rich alumni. The demand curve for the student market is Q= 300-0.4P with marginal revenue MR= 750-5Q. The demand curve for the alumni market segment is Q=600-0.1P with marginal revenue MR=6000-20Q. If the two types of consumers are in the market, the MR=1800-4Q. The cost function is C(Q)=200Q and the marginal cost of serving either customer is MC=200. 1. Assume the show knows there are different types of consumers but can not tell the difference so they must sell tickets at a single price. At what price do all consumers enter the market? What profit-maximizing price and quantity are the tickets sold at?
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Verizon can be viewed as a first mover. Now suppose both ATT and Verizon are considering whether and how to enter a potential market. Market demand is given by the inverse demand function p= 900−q1−q2, where p is the market price margin, q1 is the quantity sold by Verizon and q2 is the quantity sold by ATT. To enter the market, a retailer must build a store. Two types of stores can be built: Small and Large. The Small store requires an investment of $50,000, and it allows the retailer to sell as many as 100 units of the goods at zero marginal cost. Alternatively, they can pay $175,000 to construct a Large store that will allow it to sell any number of units at zero marginal cost. Assume Verizon enters and builds a Large store (i.e. chooses to build a Large store L1 at the first stage.) Calculate Verizon's profit for the following cases: a.) ATT chooses not to enter N at the second stage after viewing Verizon's choice. b.) ATT chooses to build a Small store S at the second stage…
Verizon can be viewed as a first mover. Now suppose both ATT and Verizon are considering whether and how to enter a potential market. Market demand is given by the inverse demand function p= 900−q1−q2, where p is the market price margin, q1 is the quantity sold by Verizon and q2 is the quantity sold by ATT. To enter the market, a retailer must build a store. Two types of stores can be built: Small and Large. The Small store requires an investment of $50,000, and it allows the retailer to sell as many as 100 units of the goods at zero marginal cost. Alternatively, they can pay $175,000 to construct a Large store that will allow it to sell any number of units at zero marginal cost. Assume Verizon stays out of the potential market (i.e. chooses not to enter N1 at the first stage, q1= 0). Calculate Verizon's profit for the following cases: a.) ATT chooses not to enter N at the second stage after viewing Verizon's choice. b.) ATT chooses to build a Small store S at the second stage…