Suppose a firm is subject to the production function, q=f(K,L)=K^1/2 L^1/2
This is called a Cobb-Douglas production function. By inspection you can see that this production function implies that output increases in both K and L and that it is subject to diminishing marginal productivity in the inputs. To see the latter characteristic, try plugging alternate values of L into the Cobb-Douglas production function while holding K constant and observing the effect on output. a What is the profit-maximizing ratio of capital to labor? rice C. Produce an expression for the optimal capital-labor ratio in terms of W and C.)
b Using your expression from part (a), explain what happens to the profit maximizing ratio of K to L when the labor input price increases. What effect is being illustrated?