7. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is U(w,e₁)-√w-g(e.) where g(e) is the disutility associated with the effort level e, exerted on the project. The agent can choose one of two possible effort levels, es or ez, with associated disutility levels g(e) 4, and g(e₂) 2.5. If the agent chooses effort level e₁, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort?

7. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is U(w,e₁)-√w-g(e.) where g(e) is the disutility associated with the effort level e, exerted on the project. The agent can choose one of two possible effort levels, es or ez, with associated disutility levels g(e) 4, and g(e₂) 2.5. If the agent chooses effort level e₁, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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7. A risk-neutral principal hires an agent to work on a project at wage to. The agent's utility function is U(w,e₁)=√w-g(₁) where g(e) is the disutility associated with the effort level e, exerted on the project. The agent can choose one of two possible effort levels, ej or ez, with associated disutility levels g(e) = 4, and g(₂) 2.5. If the agent chooses effort level e, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort? (c) Suppose an insurance company observes the wage contract offered…
7. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is U(w,e₁)-√√w-g(e) where g(e) is the disutility associated with the effort level e, exerted on the project. The agent can choose one of two possible effort levels, e₁ or e2, with associated disutility levels g(e) = 4, and g(e₂) 2.5. If the agent chooses effort level ei, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level shoul the principal imple- ment? What is the best wage contract that implements this effort?
12) Melquiades is worried about his grades from the microeconomics course, according to the rules for grading, the final grade is obtained as the minimum between the grade for the midterm test (x) and the final test (y). The utility function of Melquiades will depend on the grades obtained from those two tests Now, Melquiades has researched that the average student needs to study 24 minutes an additional point in each test (tests are graded from 0 to 100) obtain a) If Melquiades has 20 hours to study for both tests (x and y), how much time would he employ for each test? Figure out the grade that Melquiades will obtain in each test and his final grade in microeconomics. Elaborate a graph. b) How much additional study time would Melquiades require to increase his final grade by 10 points. Elaborate a graph. c) Suppose the difficulty of the final test increases in such a way that now each additional point would require 26 minutes of study. What would be the total cost (in minutes)…
3. Consider an agent who evaluates utility delayed by k periods with a discount factor of B8k. Time is discrete and indexed by t E {0,1,2, ...}. This individual has to complete a project (which only takes one period to complete) before or during period T, where the (undiscounted) utility cost of completing the t project in period t is a) Explain the difference between an exponential discounter, a naïve hyperbolic discounter and a sophisticated hyperbolic discounter. b) Suppose the individual is an exponential discounter with B completed? = 1 and 8 = 1. When will the project be c) Now suppose the individual is a naïve hyperbolic discounter with B = and 8 = 1. Calculate when this individual will plan on completing the project, and when it will actually be completed. d) Now consider the behaviour of a sophisticated hyperbolic discounter with B = and & = 1. Prove that if T is even, then the individual will finish the project in period 0, whereas if T is odd the project will be completed in…
Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "10o0", not "$1000"
If agent is preferences under uncertainty can be represented by the utility function u = 10x, then they can also be represented by the utility function u = 20x - 10. O True False
Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSE
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3. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is: v(w)-g(e), where v(w)= Jw and g(e)=e/2 The agent can choose one of two possible effort levels, e¡ = 4 or e, = 6 . If the agent chooses effort level e, = 4 the project yields 100 with probability 1/4 and 0 with probability 3/4. If he chooses e, = 6 the project yields 100 with probability ½ and 0 with probability ½. The reservation utility of the agent is 0. (a) Suppose the effort level chosen by the agent is observable by the principal. Find the contract chosen by the principal. Show graphically in terms of contingent utilities v(w,00) and v(w.)
Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows: Kate's net worth is $4.5 million (decreased from $5.5 to $4.5 million) Mary's net worth $3.2 million (increased from $3 to $3.2 million) (First determine the reference point (use a parameter) and then derive reference utility function for each).
3. Consider a trader i has following utility function: 1-a U;(X1, x2) = xf x,-ª, where x; refers to the quantity of asset with price pi, and i the total money of this trader to be completely used for trading is M, and during the whole trading process the price of asset remains constant. 1,2 in this case. Suppose (a) buy when she wants to maximize her utility function. Determine the optimal quantity x; for each asset that this trader can (Ъ) and a = Describe in words about her preferences correponding to a = 0, a = 1, = 0.5.
ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically