Question

Two firms, A and B are producing shirts. They face the same wage and rent in the factor market (where labor and capital are traded)The production functions of the firms are given by

F^A = K^0.4 L^0.6 (1)

F^B = min(K/3, L/5) (2)

(a) Draw Firm A’s and Firm B’s isoquant. Label properly.

(b) Given that both firms face the same expansion path, find the (absolute)slope of isocost line.

Answer 1

(a) The isoquants are as below.

Note the difference in production output for the same scale of graph.

(b) The isoquant of firm B at a particular level, say FA=2, would have the the same number optimum input mix regardless of the slope of the isocost line, as the optimum input would be at the corner of the isoquant. The expansion path of this isoquant would be or , since it is the optimum combination of input for cost minimization or product maximization.

Given is that is also the expansion path of firm A. The firm A have the MRTS as or or or . The optimum input mix would be where the the MRTS is equal to the slope of the isocost line , which is for a constant C. Hence, the expansion path for firm A would be where or .

Now, since this expansion path is equal to or , we have , which is equal to , and hence, comparing both, we have , which is the absolute slope of the isocost line.

As can be seen in the above graph, the expansion path is same for both firm's isoquants, and the isocost lines have the same slope of 0.9 for different costs.