Microeconomics (9th Edition) (Pearson Series in Economics)
Microeconomics (9th Edition) (Pearson Series in Economics)
9th Edition
ISBN: 9780134184890
Author: PINDYCK
Publisher: PEARSON
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Chapter 6, Problem 9E

(a)

To determine

The output produced.

(b)

To determine

The marginal product of labor.

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Consider the following production function:q = (KL)^α, where α > 0.Answer the following questions:(a) Under what conditions (i.e. values of α) will the production function exhibit decreasing returns to scale? Under what conditions will it exhibit constant returns to scale? Under what circumstances will it exhibit increasing returns to scale? (b) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale. (c) Derive an expression for the cost function of a firm using the productionfunction to produce output of a good. (d) Find the first and second partial derivatives of the cost function with respect to q. Interpret the second partial derivative and relate the sign of the derivative to the returns to scale.
If the production function of a firm is given by Q= K2L3  and the input prices are  r= birr 8 per unit and w= birr 2 per unit, find the levels of labor and capital that maximize the level of output for a total  of birr 240.
Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3)                  The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.
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