Microeconomics
11th Edition
ISBN: 9781260507140
Author: David C. Colander
Publisher: McGraw Hill Education
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Chapter 12.A, Problem 1QE
To determine
Determine the changes in the marginal rate of substitution, when a firm increases the use of one input, keeping the output constant.
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Consider a firm that produces output using industrial robots and skilled labor. Suppose it is the case
that a reduction in the price of industrial robots causes the firm's labor demand curve for skilled
workers to increase (i.e., to shift to the right). This implies that:
There is diminishing marginal product of robots.
O There is diminishing marginal product of skilled labor.
O Robots and skilled labor are complements.
O Robots and skilled labor are substitutes.
The unit cost of skilled labor is below the unit cost of robots.
IV.
Will can produce a higher grade, Gw, on an upcoming
economic exam by studying. His production function depends
on the number of hours he studies marginal analysis problems,
A, and the number of hours he studies supply and demand
problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate
David's grade production function is G) = 2.5A0.25R0.75
a. What is Will's marginal productivity from studying
supply and demand problems? What is David's?
b. What is Will's marginal rate of technical substitution
between studying the two types of problems? What is
David's?
Gopher Excavators produces shovels in a small factory and sells the shovels in a competitive
market. The following table shows the company's production function:
Output
(Number of workers) (Shovels)
Labor
1
100
195
275
4
340
380
Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the
following graph.
40
Producion Function
340
100
130
40
LABOR (Number of workana)
Calculate the marginal product of labor (MPL) of each worker, and then plot the MPL curve on the
following graph using the blue points (circle symbol).
Note: Remember to plot each point halfway between two integers. For example, when the number
of workers increases from 0 to 1, the MPL of the first worker should be plotted with a horizontal
coordinate of 0.5, the value halfway between 0 and 1. Line segments will automatically connect
the points.
(genoygl indino
Chapter 12 Solutions
Microeconomics
Ch. 12.1 - Prob. 1QCh. 12.1 - Prob. 2QCh. 12.1 - Prob. 3QCh. 12.1 - Prob. 4QCh. 12.1 - Prob. 5QCh. 12.1 - Prob. 6QCh. 12.1 - Prob. 7QCh. 12.1 - Prob. 8QCh. 12.1 - Prob. 9QCh. 12.1 - Prob. 10Q
Ch. 12.A - Prob. 1QECh. 12.A - Prob. 2QECh. 12.A - Prob. 3QECh. 12.A - Prob. 4QECh. 12.A - Prob. 5QECh. 12.A - Prob. 6QECh. 12.A - Prob. 7QECh. 12 - Prob. 1QECh. 12 - Prob. 2QECh. 12 - Prob. 3QECh. 12 - Prob. 4QECh. 12 - Prob. 5QECh. 12 - Prob. 6QECh. 12 - Prob. 7QECh. 12 - Prob. 8QECh. 12 - Prob. 9QECh. 12 - Prob. 10QECh. 12 - Prob. 11QECh. 12 - Prob. 12QECh. 12 - Prob. 13QECh. 12 - Prob. 14QECh. 12 - Prob. 15QECh. 12 - Prob. 16QECh. 12 - Prob. 17QECh. 12 - Prob. 1QAPCh. 12 - Prob. 2QAPCh. 12 - Prob. 3QAPCh. 12 - Prob. 4QAPCh. 12 - Prob. 5QAPCh. 12 - Prob. 1IPCh. 12 - Prob. 2IPCh. 12 - Prob. 3IPCh. 12 - Prob. 4IPCh. 12 - Prob. 5IPCh. 12 - Prob. 6IP
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Similar questions
- Bulldog, 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_forward1. Juan Valdez owns a coffee farm in Colombia. His production function is: f (x1, x2) = (x1 – 1)0.25 x9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x" with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.arrow_forwardWhat effect will a reduction in commodity price have on the input demand curve of the firmarrow_forward
- Now assume there is production in the economy. What is the relation between the marginal rate of substitution and the marginal rate of transformation in a general competitive equilibrium? Derive such relation and explain the intuition behind it.arrow_forwardJuan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?arrow_forwardBrian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the long run total cost function, C(q)? Sketch it on the diagram.arrow_forward
- Can 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_forwardSuppose that labor is the only input used by a perfectly competitive firm.The firm's production function is as follows:a.Calculate the marginal product for each additional worker.b.Each unit of output sells for $10.Calculate the marginal product for each additional worker.cCompute the demand for schedule showing the number of workers hired.arrow_forwardA firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?arrow_forward
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