Economics 601 -Microeconomics: Theory and Applications
Please answer all questions below. Answers are due as a single document (pdf preferred) on Canvas. Feel free to scan / take photos of hand-drawn answers for math, figures, or diagrams, just make sure to embed them in your answers. Email me if you have any clarifying or similar questions, and good luck!
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.