2.3 Exercises on the cost function for a firm with two variable inputs
- A firm uses two inputs to produce output; both inputs may be varied. Its production function is y = min{z1,z2/2}. (That is, there are fixed proportions; one unit of input 1 and two units of input 2 efficiently produce one unit of output.) The firm wishes to maximize its profit. Find the firm's cost function
TC(y,w1,w2) (where y is output and w1 and w2 are the input prices).
The isoquants of the production function are right-angled; the corner of the y-isoquant is at the point (y,2y). (If you have y units of input 1 and 2y units of input 2 then you can efficiently produce y units of output.) Thus to produce any output y the cost-minimizing input bundle is (y,2y). Thus the firm's cost function is TC(y,w1,w2) = w1y + 2w2y = (w1 + 2w2)y.