EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Question
Chapter 6.2, Problem 2MQ
To determine
To describe: The changes in values of marginal product and average product according to the given equation.
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Consider the following production function: Q = (6L + 3K)¹/2
1. What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital
(MPK)? Are they diminishing?
2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)?
3. What is the TRSL,K? Is the absolute value of TRSLK diminishing in L or K?
4. Are there constant, decreasing, or increasing returns to scale?
The production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital.
(a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor?
(b. Sketch several isoquants in the K-L space.
(c. Find the Technical Rate of Substitution between capital and labor.
(d. What are the returns to scale of this production function?
Please explain it with details
The production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital.
(a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor?
(b. Sketch several isoquants in the K-L space.
(c. Find the Technical Rate of Substitution between capital and labor.
(d. What are the returns to scale of this production function?
Chapter 6 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 6.2 - Prob. 1TTACh. 6.2 - Prob. 2TTACh. 6.2 - Prob. 1MQCh. 6.2 - Prob. 2MQCh. 6.3 - Prob. 1TTACh. 6.3 - Prob. 2TTACh. 6.3 - Prob. 1MQCh. 6.3 - Prob. 2MQCh. 6.4 - Prob. 1TTACh. 6.4 - Prob. 2TTA
Ch. 6.5 - Prob. 1MQCh. 6.5 - Prob. 2MQCh. 6.5 - Prob. 3MQCh. 6.6 - Prob. 1TTACh. 6.6 - Prob. 2TTACh. 6.7 - Prob. 1MQCh. 6.7 - Prob. 2MQCh. 6.7 - Prob. 3MQCh. 6.7 - Prob. 4MQCh. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - Prob. 3RQCh. 6 - Prob. 4RQCh. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Prob. 10RQCh. 6 - Prob. 6.1PCh. 6 - Prob. 6.2PCh. 6 - Prob. 6.3PCh. 6 - Prob. 6.4PCh. 6 - Prob. 6.5PCh. 6 - Prob. 6.6PCh. 6 - Prob. 6.7PCh. 6 - Prob. 6.8PCh. 6 - Prob. 6.9PCh. 6 - Prob. 6.10P
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- A farmer uses a certain technology that produces electricity. His production function is given as: q = f (k, l) = 1000k¹⁰/20 – 201³ Where q is the no. of megawatts of electricity his company is producing. Suppose that their electrical generators, k=20, calculate for the following: 1. Marginal product of labor 2. Average product of labor if k=20 3. If k decreases from 20 to 17, calculate the new MP of labor and the average product. Explain intuitively what happens to the MP and the average product.arrow_forwardThe amount of fish caught per week an a trawler is a function of the crew size assigned to operate the boat. Based on past data, consider the following production function identifying the relationship between output and labor input. You may assume that capital is fixed at 10 units.Labour Input (No of. Workers) (L) Total Product TPL (Q). From the table below :-(a) Calculate APL and MPL. (b) Graph APL and MPL. Do they have the expected shape? (c) On your graph, identify the three stages of production Labour input (No of Workers) (L) Total Product TP L (Q) 0 0 1 80 2 170 3 300 4 450 5 540 6 620 7 700 8 770 9 830 10 880 11 920 12 950 13 970 14 980 15 985 16 988 17 988arrow_forwardSuppose the production function is Cobb-Douglas and f(x1,x2)) = x11/2x3/221. Write an expression for the marginal product of x1.2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain3. Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain4. What is the the technical rate of substitution between x2 and x1?5. What is the type of returns to scale of this production function? (Increasing, decreasing,constant)arrow_forward
- Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q = 2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. = $5 per kg. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi?arrow_forward1. For each of the following production functions, (a) F(L, K) = LK³ (b) F(L, K) = L+3K (c) F(L, K) = (min{L, K})³ i. Sketch a representative isoquant. ii. Calculate the marginal product for each input, and indicate whether each marginal product is diminishing, constant, or increasing. iii. Calculate the marginal rate of technical substitution for each function. iv. Also indicate whether the function exhibits constant, increasing, or diminishing returns to scale.arrow_forwardEach extra worker produces an extra unit of output up to six workers. After six, no additional output is produced. Draw the total product, the average product of labor, and the marginal product of labor curves. (3)arrow_forward
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