1. Consider a static economy. There are neither government spending nor taxes. The total amount of time available to consumers h for simplicity is set equal to 1. Suppose the utility function of the representative consumer is given by U(C,1)= y log C+ (1 - y) logl where 0 << 1 and C is a bundle of consumption goods and I is leisure. The technology available for production can be represented as: Y = 2KaN¹-a where 0 ≤ a ≤ 1, z > 0 is total factor productivity, K is the exogenously given capital stock and N is labour. (a) Write down the social planner's problem. State the variables with respect to which the social planner maximises. (b) Find the conditions characterising the Pareto efficient allocation. Interpret them. (c) Find the real wage w and the firm profits that decentralise the Pareto efficient allocation as a competitive equilibrium.

1. Consider a static economy. There are neither government spending nor taxes. The total amount of time available to consumers h for simplicity is set equal to 1. Suppose the utility function of the representative consumer is given by U(C,1)= y log C+ (1 - y) logl where 0 << 1 and C is a bundle of consumption goods and I is leisure. The technology available for production can be represented as: Y = 2KaN¹-a where 0 ≤ a ≤ 1, z > 0 is total factor productivity, K is the exogenously given capital stock and N is labour. (a) Write down the social planner's problem. State the variables with respect to which the social planner maximises. (b) Find the conditions characterising the Pareto efficient allocation. Interpret them. (c) Find the real wage w and the firm profits that decentralise the Pareto efficient allocation as a competitive equilibrium.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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