A firm has a production function Q =($=($KL)$)$

0.5$0\mathrm{.}5$ The cost of each unit of labor is 10$10$ TL,$,$ the cost of each

unit of capital used is 25$25$ TL and the firm can sell as much output as it wants at the price of 50$50$ 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$1600$ 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$1600$ 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$100$ TL per unit, instead

of 25$25$ 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.)$)$