Question

Suppose your production function for baseball bats is f(K, L) = L^1/5 K^1/5 and you are a profit maximizing price taker. Use minimizing costs to:

(a) Determine the conditional factor demands for labor and capital (L = g(w, r, y) =? and K = h(w, r, y) =?). Use these to derive the cost function.

(b) Derive the marginal and average cost functions.

(c) Derive the supply function for baseball bats.

(d) Given this supply function, use the conditional factor demands in part a) to determine the actual factor demands (L* = L*(w, r) =? and K = K*(w, r) =?)

Answer 1

The production function is given to be . The cost of production would be .

(a) The condition for cost minimization would be that or or or or . Now, putting it in the production function, we have or or or , and since , we have or . These are the required labor and capital that would minimize cost and maximize profit, for the given values.

The cost function would be or or or .

(b) The marginal cost would be or . The average cost would be or .

(c) The supply function would be where the price is equal to the marginal cost, ie or or .

(d) Putting in the factor demands, we have or or , and or or . For the given P and Y, these are the actual factor demands.