Suppose that a firm's technology is given by the following production function:
f(k,L) = 6k^1/6*L^1/6
1. Prove that this production function exhibits diminishing marginal product in both and . This is not the same thing as decreasing returns to scale.
2. Prove that this production function exhibits decreasing returns to scale.
Suppose that the rental rate of capital is $10, the wage rate of labor is $10, and the price of output is $40.
3. What is the profit-maximizing quantity of capital and labor?
4. What is the profit-maximizing quantity of output?
5. What is the maximum profit for this firm?