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Consider a firm with a production function of the following form

Consider a firm with a production function of the following form:F (L, K) = L(1/4)K(1/2)

20

the corresponding marginal products are
MPL = 1 L(−3/4)K(1/2)

4 20MPK = 1 L(1/4)K(−1/2)

2 20
The cost of a unit of labour is the wage rate w and the cost of a unit of capital is the

rental rate r. The firm is free to adjust all factors of production. (19 points)
a. Does this production function exhibit decreasing returns, increasing returns, or

constant returns to scale?

b. Set up the cost minimization problem and derive the conditional input demand functions for the firm.

c. Provide an expression for the total cost curve for a given level of output q (the cost function should be a function of only the exogenous variables).

Feb 07 2020 View more View Less

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