3 In(e)Suppose that the representative household's utility function is given by U(c, l) = In(c) + n,Where c is consumption, l is leisure, and 1/8 e R+ is a parameter that determines how much therepresentative household values consumption versus leisure. Let h be the total time endowmentand normalize it to 1, w the wage, a the dividend payments, and T is the lump-sum tax.A representative firm has the following technology: Y = zF(K,N) = KªN!-a, where K is thegiven capital stock (the representative firm owns K but no market value if the firm sells it), N islabor demand by paying competitive market wage rate w, z is total factor productivity (TFP) andis normalized to z = 1, and a E (0, 1) Let's further assume the production function be a continuousconcave function. Without loss of generality, let's assume the output good price equals to 1.Let assume T = 0 and answer the following questions(a) Solve the Pareto optimal for this economy. (v .(b) Solve the competitive equilibrium for this economy.

(a) Pareto OptimalWhen no individual can be better off without making someone else worse off, the…

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(a) Solve the Pareto optimal for this economy. (.. (b) Solve the competitive equilibrium for this economy. (

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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Question

In(e)
Suppose that the representative household's utility function is given by U(c, l) = In(c) + n,
Where c is consumption, l is leisure, and 1/8 e R+ is a parameter that determines how much the
representative household values consumption versus leisure. Let h be the total time endowment
and normalize it to 1, w the wage, a the dividend payments, and T is the lump-sum tax.
A representative firm has the following technology: Y = zF(K,N) = KªN!-a, where K is the
given capital stock (the representative firm owns K but no market value if the firm sells it), N is
labor demand by paying competitive market wage rate w, z is total factor productivity (TFP) and
is normalized to z = 1, and a E (0, 1) Let's further assume the production function be a continuous
concave function. Without loss of generality, let's assume the output good price equals to 1.
Let assume T = 0 and answer the following questions
(a) Solve the Pareto optimal for this economy. (v .
(b) Solve the competitive equilibrium for this economy.

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