Principles of Economics (12th Edition)
12th Edition
ISBN: 9780134078779
Author: Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher: PEARSON
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Chapter 7.A, Problem 1P
To determine
The decision on substituting the capital for labor.
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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.
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.
A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is;
X=-0.1L3 + 6L2 + 12L.
Where X is the output in tons, and L is the number of persons employed.
How many persons are employed if the average physical product of labor is maximized?
How many persons are employed if the marginal physical product of labor is maximized?
What is the quantity of X when the average variable cost is minimized?
Chapter 7 Solutions
Principles of Economics (12th Edition)
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Similar questions
- Suppose there are two primary factors of production, labour (L) and capital (K), and there are nosecondary factors of production. The production function for this economy is simply Y = cKL,where c is a constant and α= 0.5. Which of the following is true? 1.This economy exhibits constant marginal product of labour 2.This economy exhibits decreasing returns to scale 3.This economy exhibits constant marginal product of capital 4.This economy exhibits diminishing marginal product of labourarrow_forwardA cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?arrow_forwardA firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labour is maximized? How many persons are employed if the marginal physical product of labour is maximized? What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?arrow_forward
- Given the production function Q(K,L) = 96K^0.3L^0.7, find the MPK (i.e. Marginal Product of Capital) and MPL (i.e. Marginal Product of Labor) functions. Is the MPK a function of K, L, or both? What about MPL?arrow_forward3. A firm employs labor and capital by paying $40 per unit of labor (MCL) and $200 per hour to rent a unit of capital (MC). The production function is given by Q = 30L-2L2+ 120K-3K2, where Q is total output. a. Derive MPL and MPK b. Determine the firm's optimal combination of capital (K) and labor (L)? Hint state the combination in the format L = Using your answer in part b, if the firm is committed to spending $3,240 on capital and labor per hour, how many units of labor (L) and capital (K) should the firm employ. Recall that the firm is paying $40 per unit of labor and $200 per hour to rent a unit of capital. d. How much output (Q) is produced if the firm uses the input values found in the previous question?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
- A firm's production function is given by the 4L0.5K0.5. Which of the following equation Q = is false? %3D The marginal product of labor is the partial derivative ƏQ/ƏL. The marginal product of capital is the partial derivative aQ/aK. JQ/ƏL = 2L-0.5KO.5 = dQ/ƏK = 4L0.5K-0.5 –arrow_forwardThe production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $6 and the price of factor 2 is $12, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Question 21 Answer a. x1 = 12x2. b. x 1 = x2. c. x1 = 2x2. d. We can't tell without knowing the price of the output. e. x1 = 0.50x2.arrow_forwardA 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?arrow_forward
- A firm uses capital and labour to produce widgets . In the short run capital is fixed ,while labour is variable . The short-run production is X = -L^3 +24l^2 +240L where X is the number of widgets produced in per week,and L is the number of workers employed .Each worker works a 40-hourweek. The wage rate is $12 per hour. a. Calculate the ranges of variables for L over which the firm is in stage 1,2 and 3 b. What is the minimum product price at which the firm will operate in the short run? c. The product price, over which the firm has no control is such that the firm's maximum posible pure profit $ 1096 per week. In order to achieve that level of profit it must employ 16 workers .How much is the firm's total cost?.arrow_forwardGiven the production function for labor and capital: Q = L^½(K^½), and q = 100. If the firm wants to increase all inputs by a common factor t, where t > 0. What happens to the output that the firm produces?arrow_forwardA firm produces good Y with just 2 factors: Capital which is fixed in supply and labour which is variable. Identify the stages of production in the diagram and explain why the firm still hire labour even though it is in the range of diminishing returns. What is the number of workers after which diminishing marginal returns starts? Is this a short run or long run phenomenon? Labour (units) 1 2 3 4 5 6 7 8 9 Total Product (TP) in Units 8 15 24 30 35 37 38 38 36 Average Product (AP) in units 8 7.5 8 7.5 7 6.17 5.43 4.75 4 Marginal Product (MP) in units 8 7 9 6 5 2 1 0 -2arrow_forward
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