• An engineer has a talent t in {1,2} with equal probability (prob=1/2), and the value of t is private information to the engineer. The engineer's pure strategies are applying for a job or being an entrepreneur and doing a startup. • The company's pure strategies are either hiring or not hiring the engineer. • If the engineer applies for the job and the company does not hire, then the engineer becomes an entrepreneur and does a startup. • The utility of the engineer is t (talent) from being an entrepreneur, and w (wage) from being hired. • The utility of the company is (t-w) from hiring the engineer and 0 otherwise. • These are pictured in the payoff matrices below, with the engineer being the row player and the company being the column player.

• An engineer has a talent t in {1,2} with equal probability (prob=1/2), and the value of t is private information to the engineer. The engineer's pure strategies are applying for a job or being an entrepreneur and doing a startup. • The company's pure strategies are either hiring or not hiring the engineer. • If the engineer applies for the job and the company does not hire, then the engineer becomes an entrepreneur and does a startup. • The utility of the engineer is t (talent) from being an entrepreneur, and w (wage) from being hired. • The utility of the company is (t-w) from hiring the engineer and 0 otherwise. • These are pictured in the payoff matrices below, with the engineer being the row player and the company being the column player.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 18.1IP

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1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…
2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?
7. Principal-Agent II A risk-neutral principal can hire a risk-averse agent to undertake a project. There are two possible outcomes for the gross profit of the principal, TL There are also two possible effort levels that the agent can exert, e = 0 or 1; if e = 0, the probability of TH is only 1/3, but if e = 1, the probability of TH increases to 2/3. 20 and TH = 50. The agent's utility from receiving a wage wand exerting effort e is Vw – e, and the agent has a reservation utility of ū = 2. (a) Assume that effort is observable. What wage will the principal offer if she wants to induce low effort? What wage will she offer if she wants to induce high effort? What contract is optimal for the principal?
1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this decision in the second. Question 6 options: 2. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the conservative approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to derive this solution in the second. Question 7 options: 8 3. Suppose a company must consider two…
4. You wish to hire Ricky to manage your Dallas operations. The profits from the operations depend partially on how hard Ricky works, as follows. Probabilities Profit $10,000 Profit= $50,000 Lazy worker 40% 60% 20% Hard worker 80% If Ricky is lazy, he will surf the Internet all day, and he views this as a zero cost opportunity. However, Ricky would view working hard as a "personal cost" valued at $1,000. What fixed percentage of the profits should you offer Ricky? Assume Ricky only cares about his expected payment less any "personal cost."
24. Consider adverse selection in the car insurance market. Drivers are either risky or safe. The insurance companies cannot distinguish between the two types of drivers, but they know that 50% of all drivers are risky. Insuring a risky driver costs $3,000, while insuring a safe driver costs $1,000. The benefits of insurance is $4,000 for a risky driver and $1,500 for a safe driver. If insurers cannot observe the type of buyer they are insuring, what is the minimum equilibrium price of insurance? a. $1,000 b. $1,500 c. $2,000 d. $3,000 e. $4,000
2. Alex plays football for a local club in Kumasi. If he does not suffer any injury b y the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coa ch worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = √X Assume he could buy insurance at price P that could pay $9,900 in case of inj ury. What is the highest value of P that makes it worthwhile for Alex to purcha se insurance? What is the certainty equivalence for this lottery?
3. The day prior to the release of yearly profits, a stock has price equal to 1. An investor is deciding whether to buy the stock or not. The investor has a wealth equal to 10. Yearly profits can be high with probability 0.4 or low with probability 0.6. If profits are high, the price will double on the following day; if profits are low, the price will halve on the following day. If the investor does not buy the stock, her wealth remains unchanged. If the inverstors buys the stock, she will sell the stock on the following day (regardless of whether the profits are high or low) and she will accrue the relative profit or loss. In other words, she cannot hold the stock for more than one day. The investor does not discount the future and she abides von-Neumann and Morgenstern axioms. Her vNM utility index over money is u (x) = r with 3 E (0,2). • Write down the two possible gambles faced by the investor. • Does the investor buy the stock or not? Explain. • Compute the Arrow-Pratt measure of…
The manager of XYZ Company is introducing a new product that will yield N$1000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for normal good will fall so sharply that the company will lose N$4000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?
You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
23. Captain Kidd has a map that has a 20% probability of leading him to a treasure worth 400,000 guineas. Independent of the fact of having a map, Capitan Kidd already has his own income equal to 90,000 guineas. Another pirate wants to buy the map from the Capitan Kidd (after selling the map Capitan Kidd has no chance to find a treasure). What is the minimum price for a map which the Captain Kidd will accept if Capitan Kidd has von Neuman- Morgenstern utility function is U(w) = w0.5, where w is his income level? a) 54,400 b) 32,500 c) 45,000 d) 90,000 e) There is no correct answer
5. Consider a weather forecaster who is paid based on her performance. Each day, she forecasts the probability q = [0, 1] that it will rain the following day. She is given a bonus that depends on her forecast and whether it rains. Assume that the forecaster knows the true probability, p, and when choosing her forecast, q, cares only about maximizing her bonus for that day (in particular, she may lie about the probability if doing so increases her pay). (a) Suppose the bonus is equal to the percentage the forecast assigns to what actually happens. For example, if the forecaster says there is a 72% chance of rain (i.e. q = 0.72), then she is paid $72 if it rains and $28 if it does not rain. If the forecaster is a risk neutral expected utility maximizer, what forecast will she make (as a function of p)? (b) Suppose instead that the bonus is equal to 100(1 − (1 − q)2) dollars if it rains and 100(1-q²) dollars if it does not rain. For example, if the forecaster says there is an 80% chance…