Question 3 The 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 Ko through investment I. In particular, we have the firm can, however, choose future capital stock following capital accumulation equation: Kº= I. Note that this capital accumulation equation implies that capital is fully depreciated in each period (d=1). The firm's profit is = Y- WN - I in the current period, where Y = ZF (K,N) is output, w is wage, and N is employed labor. Similarly, the profit in the future period is given by π°= Y₁- w°N° where Yo= z°F (KN) is future output, wo is future wage, N° is future labor demand. Note that there is no value of capital left over after production in the future period due to full depreciation (d= 1). The firm maximizes the present value of profits given by Answer the following questions. 1. 2. 3. πο V = x+ 1+1 Write down the firm's profit maximization problem. Derive labor demands for both the current period and the future period as functions of K and K 2 Derive the optimal rule of investment.
Question 3 The 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 Ko through investment I. In particular, we have the firm can, however, choose future capital stock following capital accumulation equation: Kº= I. Note that this capital accumulation equation implies that capital is fully depreciated in each period (d=1). The firm's profit is = Y- WN - I in the current period, where Y = ZF (K,N) is output, w is wage, and N is employed labor. Similarly, the profit in the future period is given by π°= Y₁- w°N° where Yo= z°F (KN) is future output, wo is future wage, N° is future labor demand. Note that there is no value of capital left over after production in the future period due to full depreciation (d= 1). The firm maximizes the present value of profits given by Answer the following questions. 1. 2. 3. πο V = x+ 1+1 Write down the firm's profit maximization problem. Derive labor demands for both the current period and the future period as functions of K and K 2 Derive the optimal rule of investment.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question 3
The
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
Ko through investment I. In particular, we have the
firm can, however, choose future capital stock
following capital accumulation equation:
Kº= I.
Note that this capital accumulation equation implies that capital is fully depreciated in each period
(d=1).
The firm's profit is = Y- WN - I in the current period, where Y = ZF (K,N) is output, w is
wage, and N is employed labor. Similarly, the profit in the future period is given by π°= Y₁- w°N°
where Yo= z°F (KN) is future output, wo is future wage, N° is future labor demand. Note that
there is no value of capital left over after production in the future period due to full depreciation
(d= 1). The firm maximizes the present value of profits given by
Answer the following questions.
1.
2.
3.
πο
V = x+
1+1
Write down the firm's profit maximization problem.
Derive labor demands for both the current period and the future period as functions
of K and K
2
Derive the optimal rule of investment.
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