3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e₁,a = 0 of good a and e₁,b = 10 of good b, while €1,6 Consumer 2 is initially endowed with e2,a = 10 of good a and €2,6 = 0 of good b. The utility of Consumer 1 from consuming x1, a ER+ of good a and 1,6 ER is u1(x1,a,x1,b) = x1,a + x1,b, while the utility of Consumer 2 from consuming x2,a Є R+ of good a and x2,6 ЄR is U2(x2,a, X2,b) = √√x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. (b) Consider the game in which, simultaneously, Consumer 1 submits a “demand curve" and Consumer 2 submits a “supply curve” to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the demand curve D₁ in which D₁(Pa) = d Pa is the amount of good a being demanded at price pa of good a. Similarly, the strategy space of Consumer 2 is [0,10]], and the strategy s of Consumer 2 corresponds to the supply curve S2 in which S2 (Pa) = −s + Pa is the amount of good a being supplied at price pa of good a. If Consumer 1 chooses a strategy d and Consumer 2 chooses a strategy s such that d≤s, then no trade occurs and each consumer consumes their initial endowments. If Consumer 1 chooses strategy d and Consumer 2 chooses a strategy s such that d>s, then trade occurs, the market mediator chooses the price pt at which D₁ (pa) = d − pa = −s + P₁ = p* S2(p), Consumer 1 consumes D₁(p) of good a and 10 - p* D₁ (pa) of good b, and Consumer 2 consumes 10 - - S2 (pt) of good a and pS2 (pt) of good b. Find a pure-strategy Nash equilibrium of this game in which trade occurs, and give the resulting equilibrium price p* of good a as well as the corresponding quantities of the goods consumed by the consumers. * *

3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e₁,a = 0 of good a and e₁,b = 10 of good b, while €1,6 Consumer 2 is initially endowed with e2,a = 10 of good a and €2,6 = 0 of good b. The utility of Consumer 1 from consuming x1, a ER+ of good a and 1,6 ER is u1(x1,a,x1,b) = x1,a + x1,b, while the utility of Consumer 2 from consuming x2,a Є R+ of good a and x2,6 ЄR is U2(x2,a, X2,b) = √√x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. (b) Consider the game in which, simultaneously, Consumer 1 submits a “demand curve" and Consumer 2 submits a “supply curve” to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the demand curve D₁ in which D₁(Pa) = d Pa is the amount of good a being demanded at price pa of good a. Similarly, the strategy space of Consumer 2 is [0,10]], and the strategy s of Consumer 2 corresponds to the supply curve S2 in which S2 (Pa) = −s + Pa is the amount of good a being supplied at price pa of good a. If Consumer 1 chooses a strategy d and Consumer 2 chooses a strategy s such that d≤s, then no trade occurs and each consumer consumes their initial endowments. If Consumer 1 chooses strategy d and Consumer 2 chooses a strategy s such that d>s, then trade occurs, the market mediator chooses the price pt at which D₁ (pa) = d − pa = −s + P₁ = p* S2(p), Consumer 1 consumes D₁(p) of good a and 10 - p* D₁ (pa) of good b, and Consumer 2 consumes 10 - - S2 (pt) of good a and pS2 (pt) of good b. Find a pure-strategy Nash equilibrium of this game in which trade occurs, and give the resulting equilibrium price p* of good a as well as the corresponding quantities of the goods consumed by the consumers. * *

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.13P

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