Connect Online Access for Essentials of Economics
11th Edition
ISBN: 9781260521269
Author: Bradley Schiller, Karen Gebhardt
Publisher: Mcgraw-hill Higher Education (us)
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Question
Chapter 5, Problem 4P
To determine
(a)
The graph of the production function for the figures mentioned in the question.
To determine
(b)
The Marginal Physical Product of the figures given in the question.
To determine
(c)
The levels in which the law of diminishing returns becomes apparent.
To determine
(d)
The level at which the MPP hits zero.
To determine
(e)
The level at which the MPP starts becoming negative.
Expert Solution & Answer
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Question 2:
Consider the following production function that
depends only on labor:Q = 2L+6L² - 3L³
1. Compute the APL (average product of labor).
2. Compute the MPL (marginal product of labor).
3. What is the value of L* at which APL is the
highest?
4. For L > L*, which one is bigger, APL or
MPL? How about when I < L* and L = L* ?
5. Draw APL and MPL on the y-axis as a function
of L on the x-axis. Label the point of the
intersection of APL and MPL.
Consider the following production function:
q = 32LK + 10L2 -
Assume capital is fixed at K= 25.
At what level of employment does the marginal product of labor equal zero?
The marginal product of labor equals zero when
(Enter a numeric response using an integer.)
Beyond a labor input of 40, the marginal product of labor is
20
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A firm's production function is:
q = 20L1/2K1/2
where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit.
a. What is the equation for the marginal product of labor?
b. What is the equation for the marginal product of capital?
c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?
Chapter 5 Solutions
Connect Online Access for Essentials of Economics
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Similar questions
- What is a production function?arrow_forwardQuestion 7 The production function is f(x1, x2) = x¹/²₁x¹/22. 1X a. In the short run the amount of factor 2 (x2) is 100 units. Write down the short run production function and draw a graph of it with output on the vertical axis and the amount of factor 1 on the horizontal axis. b. How does the marginal product of x1 in the graph you drew in a) change with the amount of x₁? Discuss what you observed in the graph that helped you to determine your answer. Write out the equation for an iso-profit line and add it to the graph you drew in part (a). Show how you derive the iso-profit line from a profit function that depends on output (y) and the amount of the inputs (x1 and x2). d. If the price of factor 1 is $10, the price of factor 2 is $15, and the price of output is $20, what is the short run profit maximizing choice of x₁? (The marginal product of factor 1 is 5 1/2 You will need to use this information to solve for the answer to c.) How did you know that this was the answer? Use the…arrow_forwardQ8) Marginal Physical Product Given the productivity information in the table, Instructions: In parts a and b, enter your responses as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. a. Calculate marginal physical product (MPP). Labor Output (Q) 0 1 2 3 4 5 6 0 300 660 1,100 1,400 1,650 1,800 b. When does marginal productivity first diminish? When worker ......... is hired.arrow_forward
- MCQ 45 Suppose the production function exhibits constant returns to scale, with diminishing marginal productivities for both capital and labour. For this function, we would expect a fall in employment and an increase in the capital stock to generate: A a fall in the marginal product of labour and a fall in the marginal product of capital I do not want to answer this question. a fall in the marginal product of labour, but the change in the marginal product of capital can't be determined from the information provided D a rise in the marginal product of labour and a fall in the marginal product of capital E a rise in the marginal product of labour and a rise in the marginal product of capital F a fall in the marginal product of labour and a rise in the marginal product of capitalarrow_forward1) a. What is a production function? How does a long-run production function differ from a short-run production function?b. Explain the term “marginal rate of technical substitution.” What does a MRTS = 4 mean?arrow_forwardQuestion: Suppose the firm's only variable input is labor. Using the table, what level of output corresponds to where the firm's production fuction begins to rise at a diminishing rate? Also, at what level of output would the firm's average product of labor (APL) be maximized? Explain.arrow_forward
- Why does the marginal product of labor start to decrease after a certain number of workers are hired? What makes the difference? a) The variable input continues to increase while the fixed input is fixed. b) Both the variable and the fixed inputs are increasing at the same rate. is it a or b?arrow_forwardDefine marginal physical product of labor (MPP) and marginal cost of product (MC). How are these two related? Why is MC called the mirror image of MPP? Explain.give graph if neededarrow_forward2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).arrow_forward
- Consider the following production function that depends only on labor:Q = 4L + 12L² - 6L³ 1. Compute the APL (average product of labor). 2. Compute the MPL (marginal product of labor). 3. What is the value of L* at which APL is the highest? 4. For L > L*, which one is bigger, APL or MPL? How about when L < L* and L = L*? 5. Draw APL and MPL on the y-axis as a function of L on the x-axis. Label the point of the intersection of APL and MPL.arrow_forwardQuestion 3: Consider the following production function: Q = ALa K¹. Assume A > 0. Further assume 0 < a < 1, and 0 < b < 1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (APK)? 3. What is the TRSL,K? Is the absolute value of TRSL,K diminishing in K? Is it diminishing in L? 4. Are there constant, decreasing, or increasing returns to scale? How does this depend on the parameters?arrow_forward7 why is optimal employment important in the production function.arrow_forward
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