Question

Dina owns a firm in a compeitive industry that consists of a large number of firms, each of which has the same cost function of the form:
c(w1, w2, y) = (y2+1)w1 + (y2+2)w2. Given these information, answer the following questions:
a) Find the average cost curve of Dina’s firm and describe how it shifts as the factor price w1/w2 changes.
b) Find the short-run supply curve of Dina’s firm.
c) Find the long-run industry supply curve.

Answer 1

a) find the average cost curve of the firm and describe how it shifts as the factor price w1 /w2

changes.

$AC = c/y = y(w1 + w2) + (w1 + 2 w2)/y = y(w1/w2 + 1) + (w1/w2 + 2 )/y = (w1/w2)((y2 + 1)/y) + ((y2 + 2)/y)dAC/d(w1/w2) = ((y2 + 1)/y).$

b) The supply curve = the marginal cost curve:

$Supply = P = MC = dc/dy = 2yw1 + 2yw2 = 2(w1 + w2) y.$

c) In the long run, we will run along the minimum AC(y) = MC(y) line. So set MC = AC and solve for y*.