Answered: Consider the problem of a firm who…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the problem of a firm who produces output in the present and the future period. This firm is endowed with K units of capital in the current period which is exogenously given. The firm can, however, choose future capital stock K′ through investment I. In particular, we have the following capital accumulation equation:

K′ =(1−d)K+I.

The firm’s profit is π = Y − wN − I in the current period, where Y = zF(K,N) is output, w is wage, and N is employed labour. Similarly, the profit in the future period is given by π′ =Y′−w′N′+(1−d)K′,whereY′ =z′F(K′,N′)is future output,w′ is future wage, N′ is future labour demand, and (1 − d)K′ is the value of capital left over after production in the future period. The firm maximizes the present value of profits given by

V=π+(π'/1+r)

Answer the following questions.

Write down the firm’s profit maximization problem.
Derive labour demands for both the current period and the future period.
Suppose the production function is given by
Y =zF(K,N)=zKαN1−α and Y′ =z′F(K′,N′)=z′(K′)α(N′)1−α.
Write the labour demands as functions of K and K′.
Derive the optimal rule of investment.

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