(Answered) Suppose that a firms technology is given by the following

Economics

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?

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