3. Amherst, MA, has 1,000 people. Citizens of Amherst consume one private good and one public good, the town skating rink. Although they may differ in other respects, citizens have the same utility function, which is given by u(x,G) = -100/G, where x; is the amount of the private good consumed by citizen i and G is the size of the town skating rink, measured in square meters. The price of the private good is normalized at 1 1 and the production function of the public good is given by G =z, where 10 1000 1000 z=w, is the amount of the private good used in producing the public good. (1) Write out the equation implied by the Samuelson condition, i.e.,the efficiency condition when there is a public good. (2) Show that this equation uniquely determines the efficient rink size for Muskrat. What is that size?
3. Amherst, MA, has 1,000 people. Citizens of Amherst consume one private good and one public good, the town skating rink. Although they may differ in other respects, citizens have the same utility function, which is given by u(x,G) = -100/G, where x; is the amount of the private good consumed by citizen i and G is the size of the town skating rink, measured in square meters. The price of the private good is normalized at 1 1 and the production function of the public good is given by G =z, where 10 1000 1000 z=w, is the amount of the private good used in producing the public good. (1) Write out the equation implied by the Samuelson condition, i.e.,the efficiency condition when there is a public good. (2) Show that this equation uniquely determines the efficient rink size for Muskrat. What is that size?
Essentials of Economics (MindTap Course List)
8th Edition
ISBN:9781337091992
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter11: Public Goods And Common Resources
Section: Chapter Questions
Problem 2PA
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