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

Engineering

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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