ECON30001 Advanced Microeconomics Final Assessment, Semester 1 2022/23
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ECON30001 Advanced Microeconomics
Final Assessment, Semester 1 2022/23
Question 1 (20 marks).
A risk neutral business owner is designing a wage contract for a risk averse manager. There are two states, B and G. In state B revenue is £1000, and in state G revenue is £2000.
The manager can choose to exert one of three effort levels: low effort, high effort, or very high effort. If the employee exerts a low level of effort, the probability of state B is 0.8. If the employee exerts a high level of effort, the probability of state B is 0.6. If the employee exerts a very high level of effort, the probability of state B is 0.4.
The manager maximises expected utility, with utility for wages u(w) = ^w. Low effort decreases the manager’s expected utility by eL = 4 units, high effort decreases expected
utility by eH = 6 units, and very high effort decreases expected utility by eV = 10 units. The manager has reservation utility equal to 25.
Explain and derive the optimal wage contract when effort is unobservable.
Question 2 (15 marks).
Consider a first-price sealed-bid auction with n > 1 bidders. Bidders have private values that are independent and uniformly distributed on the interval [0, 1]. Each bidder submits a non-negative bid bi . A bidder with private value U who submits a bid b gets expected payoff 几(b"U) = Pr(win)u(U −b). Bidders are risk averse and have common von Neumann- Morgenstern utility u(x) = x
, where 0 < a ⩽ 1.
Derive the Symmetric Nash Equilibrium bidding function of this auction, clarifying any assumptions you make, and discuss.
Question 3 (15 marks). Professor Bob is designing an experiment to test if the Nash bargaining solution accurately predicts the behaviour of real decision makers. He plans to present pairs of subjects with problems such as the following:
|
Each point in the diagram below corresponds to some money for each of you:
Money for Player 2. Each point in the shaded area, including the boundaries, is feasible. Please agree on which feasible point you would like. Failure to agree means £0 for both of you. |
The experiment will present a variety of different shapes of feasible payment pairs for consideration. Professor Bob claims, correctly, that these represent bargaining problems if the subjects are risk neutral. The editor of an economics journal, however, is very critical of the assumption of risk neutrality. Explain how Professor Bob could adapt the experiment to allow for risk aversion and discuss the relative costs and benefits of doing so.
2023-01-17