A firm has a production function Q = ( = ( KL ) ) 0 . 5
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Question:
A firm has a production function Q =(KL)
0.5 The cost of each unit of labor is 10 TL, the cost of each
unit of capital used is 25 TL and the firm can sell as much output as it wants at the price of 50 TL per
unit output.
(a) Write down the function for the marginal product of labor.
(b) How much labor does it hire in the short−run, when its capital stock is fixed at 1600 units ?
(c) Calculate the profits in the short−run. Confirm that the firm keeps producing and does not choose
to shut down.
(d) Assuming that firm still uses 1600 units of capital, calculate how much profit it makes when it hires
the amount of labor you found in part (a) in the long−run. (Long−run profit is revenue minus labor
and capital costs).
(e) What would your answers be to parts (b) and (d) if the cost of capital were 100 TL per unit, instead
of 25 TL ?
(f) Consider the short−run and long−run profits for the case described in part (e), and comment on
whether the firm can maintain production in the long−run without changing its capital demand.
(Hint: You should also consider the cost of the alternative, which is shutting down.)
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