Download Econ 2230, Spring 2011 Lise Vesterlund Public Economics

Econ 2230, Spring 2011 Lise Vesterlund Public Economics Homework 1‐Due February 7 1.
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Suppose that there are two individuals, 1 and 2, who consume a private good xi and a public good G. Each individual has a utility function Ui = xi + αi ln G, i = 1,2, and each i is endowed with wealth wi > 0. Assume α1 > α2. Suppose this public good is supplied through voluntary contributions. Let gi be i’s contribution to the public good, and let the total provision be given by G = g1 + g2. Let px = pG =1 a. Find the Nash equilibrium of the simultaneous move game. How much does each individual contribute and what is the total provision of the public good? b. Show that the Nash equilibrium is inefficient. c. Suppose instead that the public good is supplied sequentially. In particular, assume that person 1 contributes first, and person 2 gets to see person 1’s contribution before deciding how much to contribute. d. Does sequential play enhance or diminish the free rider problem relative to Nash equilibrium? Give a brief intuitive explanation for why this is so. Suppose that there are two individuals, Al and Betty, who consume a private good xi and a public good G. Each individual has a utility function Ui = xi G, i=A, B. and an endowment w. Let px = pG = 1. a. Find the set of Pareto efficient allocations b. Suppose that the public good is supplied through voluntary contributions. Let gi denote i’s contribution. Determine the Nash Equilibrium for this economy (i.e., determine (xi , gi ,G)). c. Consider an income transfer of w/4 from Al to Betty. Show that this transfer will have no effect on the Nash equilibrium (i.e., the provision of the public good, nor on the individual’s consumption of the private good). d. Draw a graph to illustrate how the income transfer of w/4 affects the utility maximization problem for Al and Betty. e. Consider instead an income transfer of 3w/4 from Al to Betty. How does the transfer influence (xi, gi ,G)? Who benefits from the income transfer? f. Draw a graph to illustrate the effect the transfer of 3w/4 from Al to Betty has on the utility maximization problem for Al and Betty g. Suppose instead that the government imposes a tax of w/4 on each individual, and contributes the resulting tax to the public good. Show that this lump sum tax has no effect on the individuals’ consumption of the private and public good. Suppose we want to empirically determine the extent to which an increase in government funding influences private donations. Use concrete examples to explain why causal inference would require that we instrument for government funding.