Question

(b) A representative consumer has a utility function U (x, y) = xy. A representative firm makes

good x and has a production function x = f(k, l) = (kl)^0.25and an unavoidable fixed cost

equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = P_y = 1 and P_x is determined in a competitive market. Representative consumer income is I = 2.

(b) Find the representative firm’s supply of good x?

Answer 1

production Here the fun of "good x" is given by - -3/4 114 MPL = 1/4L K x = K L - - 3/4 144 MPK = 1/4K L and - MRTS = MPL / MPK - 314 114 114 LK = k/L 14214 314 Now at the eam MRTS must be equal to V so, MRTS= W/v = 1 = x=L. the proden fin is – x = kell & KL = xe =)2=X" = = t - At the optimum Kal. Implied K=X². the Cost faz is - e=WL + vk =L+K - c = 2x² the profit fun of the firm is - = Bxx- C =Bex - 2x² . So, profit maximization require ale =0 - Px- 4X=0 = x= Pell , be the indrudual supply for firrm. The respective firum supply fun.is - x = Px/4.