Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (9th Edition) (Pearson Series in Economics)
9th Edition
ISBN: 9780134643175
Author: Robert Pindyck, Daniel Rubinfeld
Publisher: PEARSON
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Chapter 6, Problem 10RQ
To determine
The diminishing
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If the marginal product of labor is 25 and the marginal product of capital 10, what is the marginal rate of technical substitution of labor for capital?
For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?
a) A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant.
b) A firm requires exactly two full-time workers to operate each piece of machinery in the factory.
Prunella raises peaches. She uses L units of labor, and T units of land to produce peaches. Her production function is f(L, T)= L1/2T 1/2
A: Write the equation and plot the isoquant for the output quantity 4.
B: What is the returns to scale of this production function?
C: Find the marginal products of labor and land. What is the rate of technical substitution between land and labor?
D: In the short-run, Prunella cannot vary the amount of land she uses. Plot the output as a function of labor only for the fixed level of land of T=1.
E: Find the marginal product of labor from L=4 and show it on the graph. Is the marginal product of labor diminishing, constant or increasing in labor?
F: Suppose wages are constant and equal w, fixed costs are zero. Find the short-run profit maximizing level of labor for T=1.
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Chapter 6 Solutions
Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (9th Edition) (Pearson Series in Economics)
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- What is the difference between a fixed input and a variable input?arrow_forwardPlease answer accuratelyarrow_forwardAssume a technological change in production that makes both inputs, capital and labour more productive, but that increases more the productivity of capital than the productivity of labour. Explain how this change translates into the shape of the isoquant curves and in the marginal rate of technical substitution. Provide graphs to illustrate your arguments.arrow_forward
- For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution? A firm can hire only full-time employees to produce its output, or it can hire some combination of full-time and part-time employees. For each full-time worker let go, the firm must hire an increasing number of temporary employees to maintain the same level of output. Using the three-point curved line drawing tool, graph an isoquant curve for the firm in the top diagram. Label this curve 'Isoquant'. Carefully follow the instructions above, and only draw the required object. Part-time workers 20 19- 18- 17- 1654 13- 12- 11- 10- 8- 4- 3- O 6 8 10 12 14 16 Full-time workers 18 20arrow_forwardBulldog, Inc. measures the technical rate of substitution at ???/??? = 3. The prices of labor and capital faced by Bulldog are such that currently ??/?? = 4. Is Bulldog producing its current level of output at the minimum cost? If not, how could they do better? Very briefly explain your answer.arrow_forwardIn production theory, diminishing rate of technical substitution(RTS) shows how one input is substituted for the other. This also means that isoquants must be convex . True or false and explainarrow_forward
- Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- Barrow_forwardSuppose a production function is given by the equation Q = LVK. 1. Graph the isoquants corresponding to Q = 10, and Q = 20. 2. MP = √K and MP = 0.5(L/VK). Find the Marginal Rate of Technical Substitution LK (MRTSLK). Do these isoquants exhibit diminishing marginal rates of technical substitution? (Does the slope get flatter as L increases?) 3. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1500 iso-cost curve?arrow_forwardWhen analyzing isoquants, if the marginal product of all inputs double, how would that change the input mix you would use to produce a given level of output?arrow_forward
- Does additional input of labor entail a steady increase in the output of a firm? Why or Why not?arrow_forwardPlease answer this question in few hours please. Thanks.arrow_forwardCan you please check my answers for the following question? Mandy owns a small coffee shop. Her production function is q=2K0.5L where q is the number of cups of coffee produces, K is the number of coffee machines, and L is the number of employees. If K=10 and L=20, the marginal rate of technical substitution is: 1 MLP= 2K0.5 MLK = L/K0.5 MRTS= 2K/L = 2(10)/20 =1 MRTS = w/r Starting from 10 machines and 20 employees, if Joe hires one more employee, then he can use ______ fewer machine(s) and still produce the same quantity of coffee. 1 fewer machinearrow_forward
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