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APEC 343 / ECON 343 Makeup Quiz 1
发布时间:2022-05-27
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APEC 343 / ECON 343 Makeup Quiz 1 (20 Points)
For answers requiring mathematical computation, your answers must include the mathematical steps you took to derive it. Not showing these steps will result in zero points. Please write neatly - if I can’t read it I won’t give you points.
Problem 1 (7 Points)
Suppose there are two utility maximizing players, each facing the following utility function:
ui =
where ci is player i’s cost associated with making an investment into a public good.
(a) Suppose that each player has only two strategies, either ci = 10 or ci = 0. Summarize the
given information in a 2x2 table that includes players (there are two), strategies (there are two), and payoffs (measured in utility). Derive the Nash Equilibrium and comment on the equilibrium’s efficiency.
(b) Look at the payoffs you derived in part (a). Do you think this situation is a social dilemma?
Why or why not?
Problem 2 (6 Points)
Assume an isolated town in Alaska has large underground oil reserves. Suppose there are substantial fixed costs associated with the development of oil (for example infrastructure investments) that amout to $25, 000, 000. Total costs are: TC = 25, 000, 000 + 2q2 . The amount of total benefits (called revenue) depends on the number of pumps built. Suppose the following revenue function: R = 20, 000q − 2q2 . Obviously, the town is interested in maximizing net benefits (called profit or π), where π = R − TC .
(a) Assume property rights are well assigned and the town jointly decides to develop this resource
(i.e. no single person can drill on their own). Compute the profit maximizing number of pumps and the profit (net benefit) generated by the town. Purely based on your analysis, do you think the town should go ahead and develop the profit maximizing number of pumps?
(b) Now compute the quantity developed if access is free and unrestricted.
(c) Graph your results from part (a) and part (b), placing marginal revenue, average revenue and marginal cost on the vertical axis and quantity (number of pumps) on the horizontal axis.
(d) How might distributional issues affect how we think about the maximization problem?
Problem 3 (7 Points)
Consider the following threshold public goods game:
ui =
if ci + c −i < T
if ci + c −i ≥ T
where ci is the contribution of player i, T is a threshold such that T = 3, and cmax is the maximum contribution of each player such that cmax = 2 (neither player can reach the threshold on their own, i.e. cmax < T). Suppose that each player’s strategy set consists of discrete choices, such that ci = {0, 1, 2}.
(a) Summarize the given information in a strategic form (3x3) table including players, strategies
and payoffs.
(b) Derive the Nash Equilibrium/Equilibria.
(c) If you were a player in this game, what would you do? Why?