A firm produces output that can be sold at a price of $100. The production function is given by Q = F (K,L) = .

a. If capital is fixed at 25 units in the short run, what is the short-run production function?

b. A profit maximizing competitive firm produces the amount of output, q, at which the market price, p, equals its marginal cost, MC: P= MC (q) [please note that this relation will be discussed more after midterm.]

In the class, we have discussed the firm's marginal cost is MC=w/MP_L . Then, we can derive value of marginal product of labour (VMP_L) equals wage, which is w = MC* MP_L =P * MP_L = VMP_L.

Question: How much labour should the firm employ in order to maximize profits if the wage rate is $250?

c. If capital costs $3 per unit, what are the firm's total costs?