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# ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 4: Social coordination of public outcomes

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Economics 601 -Microeconomics: Theory and Applications

Final Exam

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4.     Social coordination of public outcomes (30 points) Consider a classic tragedy of the fishers where two individuals’ actions have negative external effects on each other and also act as substitutes. Assume that individuals lower and Upper are maximizing utility functions:

u = α(1 – βE)e e2 and U = α(1 – βe)E E2

4.1.  Derive each individual’s best response function to the other as a function of effort, plot these best response functions in effort space (i.e., e-E axes), draw in corresponding indifference curves, and circle the Nash Equilibrium.

4.2.  On the same graphs draw in indifference curves and identify (a) the egalitarian social planner’s optimal choice (b) the outcome when lower has property rights and can make a take-it-or-leave-it offer to Upper to fish the lake for a permit and (c) the outcome when lower gets to choose their fishing effort first. Which of the three is pareto rankable compared to the Nash Equilibrium? Explain.

4.3.  Now consider a scenario where fishing has positive externalities and is a complement rather than a substitute. Graph linear best response functions in e-E space, show the Nash equilibrium, graph indifference curves for each of the three scenarios a,b,c in question 4.2 and comment on the welfare outcomes for first vs. second movers in part (c) relative to the Nash Equilibrium.

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