1.A firm uses labor (L) and capital (C) (including machines, trucks, etc. to produce output and has the following production function: f(L, K) = m*(L^(1/2))*K^(1/2). The wage for a worker is PLN 25 and the price of a unit of capital is PLN 100. In the short run, the firm's workers have unbreakable contracts so the firm cannot hire or fire workers, but it can change the amount of capital (e.g. number of machines) it uses. In the long run, both the number of workers and the amount of capital can be adjusted. Currently the firm is employing 100 workers. [8 points]

a.Suppose that the firm wants to produce q units of output in the short run. Derive an expression for the units of capital the firm will need to use as a function of the desired level of output.

b.Based on your answer to part (a), derive the costs for the firm as a function of output in the short run.

c.Derive expressions for the number of workers hired by the firm and the units of capital used by the firm in the long run if the firm wants to produce q units of output and minimize costs.

d.Based on your answer to part (c), derive the long run cost function for the firm. How many workers will the firm hire at this level of output?