Microeconomics (9th Edition) (Pearson Series in Economics)
9th Edition
ISBN: 9780134184890
Author: PINDYCK
Publisher: PEARSON
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Question
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.
Chapter 6 Solutions
Microeconomics (9th Edition) (Pearson Series in Economics)
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- For its current level of production, a firm is attempting to minimize its costs. The firm has determined that the marginal product of labor is 10, the marginal product of capital is 20 and the cost per unit of labor is $5, whereas the cost per unit of capital is $10. To minimize cost for the given output the firm should Increase the amount of capital and decrease the amount of labor Leave the amount of capital and labor as they are Decrease the amount of capital and increase the amount of laborarrow_forwardA firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?arrow_forwardAssume that Donnell Corp. is currently producing 500 units of output per period, using 25 units of labor and 20 units of capital. Values for the marginal product of each input and the prices of the inputs are as follows: MPK = 100, MPL = 200, w = 2, and r = 3. Given the information above, which of the following is true? a. The firm is currently using the optimal levels of capital and labor. b. The firm should increase labor and reduce capital usage. c. The firm is not using the optimal levels of capital and labor, and it is impossible to determine the optimal levels from the given information.arrow_forward
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