3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K3 L3, with marginal products given by MPL = Ka and MPK = Define the unit prices of L and K as w and r, respectively. Kś Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? (b) (c) (d) Now suppose that set-up costs are £1. What is the shut down rule of the firm (e) when r = w = 1?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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3. Answer all parts (a)-(e) of this question.
Consider the following production function: Q = 3K&L, with marginal products given by
L3
MPL = K
and MPK
Define the unit prices of L and K as w and r, respectively.
Finally, assume that the firm takes the price of its product, p, as given and maximizes profits.
L3
K3
(a)
Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost
function of the firm? Explain briefly.
(b)
(c)
(d)
(e)
when rw = 1?
What is the long-run cost function of the firm?
What is the long-run supply function of the firm?
What is the profit function of the firm?
Now suppose that set-up costs are £1. What is the shut down rule of the firm
Transcribed Image Text:3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K&L, with marginal products given by L3 MPL = K and MPK Define the unit prices of L and K as w and r, respectively. Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 K3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. (b) (c) (d) (e) when rw = 1? What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? Now suppose that set-up costs are £1. What is the shut down rule of the firm
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