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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Question
Chapter 6, Problem 9E
(a)
To determine
The output produced.
(b)
To determine
The marginal product of labor.
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Miguel and Jake run a paper company. Each week they need to produce 1,000
reams of paper to ship to their customers. The paper plant's long-run
production function is: q= 4K¾L where q is the number of reams produced,
K is the quantity of capital rented, and L is the quantity of labor hired.
(K
For this production, MP,
L
and MP = 3
K
K
The weekly cost function for the paper plant is C= 10K +2L where C is the
total weekly cost
What ratio of capital to labor minimizes Miguel and Jake's total costs?
(Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital
and labor.)
Consider the following production function of DVDS: Q = K0.5L 0.5, where Q represents DVDS
(boxes per hour), K denotes capital input (units per hour), and L denotes labour input (units of
worker time per hour). The unit cost of capital and labour are $40 and $20, respectively.
a) What is the optimal input ratio of labour and capital for the production?
b) Determine the appropriate input mix to produce 800 boxes of DVDS. Compute the cost of
production.
c) Suppose the government decided to offer a subsidy that would make the cost of labour $15.
What is the optimal input mix to produce the same level of output, and the new cost of
production? Also, compute the substitution effect in the employment of labour.
1. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5,where q is the number of computers produced per day, K is hours of machine time, and L ishours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4.
a. If both companies use the same amounts of capital and labor, which will generatemore output?b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. Inwhich company is the marginal product of labor greater? Explain.
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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- Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q= 4K^L+ where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. K For this production, MP, =| L and MP, = 34 K K The weekly cost function for the paper plant is C=10K+2L where C is the total weekly cost How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week, and how much will hiring these inputs cost them?arrow_forward7. A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where L is the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6)arrow_forwardTrotter Inc is a polling company. Trotter uses both labor, L, (measured in hours worked) and capital, K, (measured in phone lines) to conduct surveys. The production function of Trotter’s is given by Q=10L^0.25 K^0.25 where Q is measured in surveys completed per hour. The price of a unit of L is $16 per hour and the price of a unit of K is $1 per hour. Trotter’s has additional fixed costs of $227 per hour. For parts (a) – (b) below assume that the number of phone lines is fixed in the short run. In particular, Trotter's has 16 phone lines (so K = 16). This results in additional fixed costs in the short run of $16 (ie in addition to the 227). a) In the short run what is Trotter’s (compensated) demand curve for labor? What is the variable cost curve? What is the total cost curve? b) In the short run, what is the marginal cost curve of Trotter’s? What is the average cost curve? What is the optimal size of the firm? Illustrate the short run marginal and average cost curves. For parts (c)-…arrow_forward
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