A firm’s production function is given by: F(L,K) = L^1/4K^3/4. You also know that the wage...

A firm’s production function is given by: F(L,K) = L^1/4K^3/4. You also know that the wage rate is $2, the price of capital is $6, and the price of the product is $216

a) In the short-run, capital is fixed at 1 unit. How many units of Labor (L) should this firm hire?

b) How much profit is the firm making in the short-run?

c) Assuming that in the long-run both capital (K) and labor (L) are variable inputs, what is the optimal combination (profit-maximizing/cost-minimizing L* and K* ) to produce the same amount of output as in the short-run?

d) What are the profits in the long-run?

e) Assume that the firm has a fixed cost of $200. Find the variable cost function, the total cost function, the marginal cost function, the average total cost function, the average fixed cost function, and the average variable cost function (hint: to answer this question, first, redo all calculations in part (c) in terms of a general level of output Q. In other words, first find L* and K* as a function of Q using the tangency condition, then find cost functions).

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Expert Solution

Rahul Sunny answered 8 months ago

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