where i and Yi, " 14. a) Let there be two consumers 1 and 2, and two goods X and Y. The utility functions are U₁ = x0.5y₁0.5 and U₂ = x0.5y2 0.5 i = 1,2 are the amount of good bought by agent i, x = x₁ + x2. Here good x is a public good. The income of the two consumers is Rs. 2400 each. Assume that the prices of good X and Y is Rs. 1 each. i) If they decide to choose the amount of the goods to buy simultaneously and independently, what is the Nash equilibrium amount of goods that each will buy? ii) Is free rider problem possible in this context?

where i and Yi, " 14. a) Let there be two consumers 1 and 2, and two goods X and Y. The utility functions are U₁ = x0.5y₁0.5 and U₂ = x0.5y2 0.5 i = 1,2 are the amount of good bought by agent i, x = x₁ + x2. Here good x is a public good. The income of the two consumers is Rs. 2400 each. Assume that the prices of good X and Y is Rs. 1 each. i) If they decide to choose the amount of the goods to buy simultaneously and independently, what is the Nash equilibrium amount of goods that each will buy? ii) Is free rider problem possible in this context?

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 8PA

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Just north of the town of Muskrat, Ontario is the town of Brass Monkey, population 4,500. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single private good, Labatt Ale. Everyone's utility function is UXX₁, XY) = X; - 81/Y, where X; is the number of bottles of ale consumed by i and Yis the size of the skating rink in square meters. The price of ale is $1 per bottle. The cost of the skating rink to the city is $5 per square meter. Everyone has an income of at least $5,000. What is the Pareto efficient size for the town skating rink? 270 square meters. 140 square meters. 195 square meters. 390 square meters. 545 square meters.
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Consider an economy with n consumers, one private good and one public good. We think of the private good as "all other goods," and measure it in terms of money. There aren individuals in the economy with utility functions Ui(xi , y) = ai In y + xi , where y is the public good, xi is the private good consumed by individual i = 1, . .., n, and 0 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
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6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (b) Suppose MRSa = Ya/Xa, MRSb = Yb/Xb, Xa = 10, Ya, = 100, Xb= 50, Yb = 20, and let good Y be the numeraire (Py = 1). Verify that the competitive equilibrium price is Px = 2.
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