3. Consider a dynamic (two-period) representative firm's problem. This representative firm is given K unit of capital to produce in the current period. Firm can choose (current-period and future-period) labor demands and investment (to adjust future- period's capital stock) to maximize its present-value lifetime profit. Given that the market interest rate is r and the capital depreciation rate is & after production in each period. Let's further assume that this firm sells all the capital after future-period production. (a) Clearly definite the profit functions for both periods and write down this repre- sentative firm's problem. (b) Write down the optimal condition on investment. Intuitively explain the optimal condition. (c) Suppose K increases, graph the change of investment curve. Intuitively explain the changes on the graph you just drew.
3. Consider a dynamic (two-period) representative firm's problem. This representative firm is given K unit of capital to produce in the current period. Firm can choose (current-period and future-period) labor demands and investment (to adjust future- period's capital stock) to maximize its present-value lifetime profit. Given that the market interest rate is r and the capital depreciation rate is & after production in each period. Let's further assume that this firm sells all the capital after future-period production. (a) Clearly definite the profit functions for both periods and write down this repre- sentative firm's problem. (b) Write down the optimal condition on investment. Intuitively explain the optimal condition. (c) Suppose K increases, graph the change of investment curve. Intuitively explain the changes on the graph you just drew.
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.5P
Related questions
Question
![3. Consider a dynamic (two-period) representative firm's problem. This representative
firm is given K unit of capital to produce in the current period. Firm can choose
(current-period and future-period) labor demands and investment (to adjust future-
period's capital stock) to maximize its present-value lifetime profit. Given that the
market interest rate is r and the capital depreciation rate is & after production in each
period. Let's further assume that this firm sells all the capital after future-period
production.
(a) Clearly definite the profit functions for both periods and write down this repre-
sentative firm's problem.
(b) Write down the optimal condition on investment. Intuitively explain the optimal
condition.
(c) Suppose K increases, graph the change of investment curve. Intuitively explain
the changes on the graph you just drew.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80b75b69-7703-465c-aea5-f52a789399fb%2Ff37cd331-f0a8-4783-9fe5-ad4918eeeed9%2F15jcafd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider a dynamic (two-period) representative firm's problem. This representative
firm is given K unit of capital to produce in the current period. Firm can choose
(current-period and future-period) labor demands and investment (to adjust future-
period's capital stock) to maximize its present-value lifetime profit. Given that the
market interest rate is r and the capital depreciation rate is & after production in each
period. Let's further assume that this firm sells all the capital after future-period
production.
(a) Clearly definite the profit functions for both periods and write down this repre-
sentative firm's problem.
(b) Write down the optimal condition on investment. Intuitively explain the optimal
condition.
(c) Suppose K increases, graph the change of investment curve. Intuitively explain
the changes on the graph you just drew.
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