Question

Consider a firm whose production technology can be represented by a production function of the form q = f(x1, x2) = x α 1 x 1−α 2 . Suppose that this firm is a price taker in both input markets, with the price of input one being w1 per unit and the price of input two being w2 per unit. 1. Does this production technology display increasing returns to scale, constant returns to scale, decreasing returns to scale, or variable returns to scale? Justify your answer. 2 2. What is the firm’s long-run cost minimisation problem? 3. Derive the firm’s output-conditional input demand functions for each of the two inputs. 4. Verify that each of the output conditional input demand functions are homogeneous of degree zero in input prices. 5. Derive the firm’s (minimum total) cost function. 6. Verify Shephard’s lemma for each of the inputs. 7. Verify that the cross-price effects in the output-conditional input demand functions are symmetric.

Answer 1