Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Question
Chapter 7, Problem 7E
a)
To determine
To evaluate the percentage increase in output if labor input is increased by 10 percent; keeping the capital constant.
b)
To determine
To evaluate the percentage increase in output if capital input is increased by 25 percent; keeping the labor constant.
c)
To determine
To evaluate the percentage increase in output if capital if both labor and capital are increased by 20 percent.
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Students have asked these similar questions
Suppose that a firm's production function is given by the following relationship:
Q = 2.5√/LK
(i.e., Q = 2.5L0.5 K0.5)
where is output, L is labor input, and K is capital input.
What is the percentage increase in output if labor input is increased by 10%? (Assume that capital input is held constant.)
What is the percentage increase in output if capital input is increased by 25%? (Assume that labor input is held constant.)
What is the the percentage increase in output if both labor and capital are increased by 10%?
11
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.
Consider the following production function:
q = (KL)“, where a > 0.
Answer the following questions:
(a) Under what conditions (i.e. values of a) 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 production
function 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.
Chapter 7 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Similar questions
- A firm has a production function of ?(?,?) = ??.???.? a) Explain the concept of returns to scale. Does the function provide increasing, decreasing, or constant returns to scale? b) Provide an example of a typical sector with increasing returns to scale. c) Explain the concept of MRTS and argue whether the MRTS for this production function is diminishing. Please also provide a graphical illustration using numbers.arrow_forwardAssume labor (L) is the only variable input used in the production process, a firm’s production function is given by Q=7L+10L2-L3 where Q represents total product. Classify the production function in to the three stages of production.arrow_forwardSuppose the production function for widgets is given by q=KL+6L²-0.1L³ where q represents the annual quantity of widgets produced, K represents annual capital input and L represents annual labor input. A) Suppose K=10. At what level of labor input does average product of labor reach a maxiumum? How many widgets are produced at that point? B) Again assuming that K=10, at what level of labor input does MPL=0? C)Determine and show whether the production process exhibits law of diminishing returns.arrow_forward
- Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?arrow_forwardIn the short run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), where q is output, L is workers, and K is the fixed number of units of capital. A specific equation for the production function is given by: or, when K = 20, q 8KL+ 5L² = q = (8×20×L) + 5L² The level of output q for 10 units of labor input is (enter your response rounded up to two decimal places). The average productivity of these 6 units of labor is (enter your response rounded up to two decimal places). The marginal productivity of using one more unit of labor input is (enter your response rounded up to two decimal places). Given the relationship between the average productivity and the marginal productivity, the average productivity of labor is 3arrow_forwardA firm can manufacture a product according to the production function: Q = F(K, L) = K3/4L1/4.a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. (Enter your responses rounded to three decimal places)(Part of A): What is the average product of labor when the firm uses 256 units of labor?Answer:b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. (The second response is the exponent on L in the expression. Enter your responses rounded to two decimal places).MPL = × L ^ Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. (Enter your responses rounded to three decimal places).MPL when L = 16: MPL when L = 81: c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at…arrow_forward
- For the following production function: Y(K,L)= 25(KL)^(1/2) a) Compute the MRTS b) Define if it exhibits increasing, constant, or decreasing returns to scale c) Is the MRTS decreasing, increasing or constant as we increase the labor input? Provide numerical evidences and an economic interpretation of your answer d) Compute again the MRTS for this new production function: Y(K,L)= 2K+5L e) Compare now the MRTS of the two production functions and explain why the second case is a special case of the general result obtained at point a).arrow_forwardExercise 3 3.1 Consider the following production function: F(K,L) = K0.3L0.7 State if this function exhibits constant, increasing or decreasing returns to scale. 3.2 Consider the following production funetion: F(K,L) = K0.5L0.8 State if this function exhibits constant, increasing or decreasing returns to scale. 3.3 Consider the following production function: F(K, L) = K°L Find out what relation should exist between a and b in order for this function to exhibit constant returns to scale. 3.4 Constant returns to scale is an assumption that fits the reality most of the times. But it does not always hold. Make an example of a firm or a type of business in the real world that exhibits increasing or decreasing returns to scalearrow_forwarda) The production function q = 9K0.8LO.1 exhibits [ increasing returns to scale, constant return to scale,decreasing returns to scale, none of the above ] b) The production function q = K1.2 + 3L1.2 exhibits [ increasing returns to scale, constant return to scale,decreasing returns to scale, none of the above] a) The production function q = 9KO.8L0.1 exhibits [ Select ] %3D b) The production function q = K1.2 + 3L1.2 exhibits [Select] %3Darrow_forward
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