Microeconomics: Principles and Applications

Robert E. Hall, Marc Liberman

Chapter 7

Production and Cost - all with Video Answers

Educators

Chapter Questions

Problem 1

The following table shows total output (in tax returns completed per day ) of the accounting firm of Hoodwink and Finagle:
$$\begin{array}{cc}\text { Number of } & \text { Number of Returns } \\\text { Accountants } &\text { per Day } \\\hline 0 & 0 \\1 & 5 \\2 & 12 \\3 & 17 \\4 & 20 \\5 & 22\end{array}$$
Assuming the quantity of capital (computers, adding machines, desks, etc. ) remains constant at all output levels:
a. Calculate the marginal product of each accountant.
b. Over what range of employment do you see increasing returns to labor? Diminishing returns?
c. Explain why $M P L$ might behave this way in the context of an accounting firm.

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Problem 2

In mid-2009, the Obama administration announced it would cancel orders for a new fleet of presidential helicopters. About 3 dollar billion had already been spent on developing the helicopters, which had special protective and telecommunications features. But another 8 dollar billion would have been needed to complete the project and deliver the fleet. The administration suggested it might look for a less expensive design and start from scratch. Some media commentators criticized the decision, arguing that cancelling the project would mean wasting the 3 billion dollar already spent.
a. Suppose that starting from scratch on a new proposal that would be just as good as the original would cost a total of $\$ 5$ billion from beginning to end. Which would be the wiser choice sticking with the original or starting from scratch? Why?
b. Would your answer change if the new proposal

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Problem 3

Down On Our Luck Studios has spent 100 million dollar n producing an awful film, $A$ Depressing Story About a Miserable Person. If the studio releases the film, the most cost-effective marketing plan would cost an additional 5 million dollar, bringing the total amount spent to 105 million dollar. Box office sales under this plan are predicted to be 12 million dollar, which would be split evenly between the theaters and the studio. Additional studio revenue from video and DVD sales would be about 2 million dollar. Should the studio release the film? If no, briefly explain why not. If yes, explain how it could make sense to release a film that cost $\$ 105$ million but earns only 12 million dollar

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Problem 4

The following table gives the short-run and long-run total costs for various levels of output of Consolidated National Acme, Inc.:
$$\begin{array}{ccc}Q & T C_{1} & T C_{2} \\\hline 0 & 0 & 350 \\1 & 300 & 400 \\2 & 400 &435 \\3 & 465 & 465 \\4 & 495 & 505 \\5 & 540 & 560 \\6 & 600 & 635 \\7 & 700 & 735\end{array}$$
a. Which column, $T C_{1}$ or $T C_{2},$ gives long-run total cost, and which gives short-run total cost? How do you know?
b. For each level of output, find short-run $T F C, T V C$ $A F C, A V C,$ and $M C$
c. At what output level would the firm's short-run and long-run input combinations be the same?
d. Starting from producing two units, Consolidated's managers decide to double their production to four units. So they simply double all of their inputs in the long run. Comment on their managerial skills.
e. Over what range of output do you see economies
of scale?

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Problem 5

In a recent year, a long, hard winter gave rise to stronger-than-normal demand for heating oil. The following summer was characterized by strong demand for gasoline by vacationers. Show what these two events might have done to the short-run $M C, A V C,$ and $A T C$ curves of American Airlines. (Hint: How would these events affect the price of oil and the price of jet fuel made from oil?)

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Problem 6

Draw the long-run total cost and long-run average cost curves for a firm that experiences:
a. Constant returns to scale over all output levels.
b. Diseconomies of scale over low levels of output, constant returns to scale over intermediate levels of output, and economies of scale over high output levels. Does this pattern of costs make sense? Why or why not?

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Problem 7

Ludmilla's House of Schnitzel is currently producing
10 schnitzels a day at point $A$ on the following diagram. Ludmilla's business partner, Hans (an impatient sort $,$ wants her to double production immediately.
a. What point will likely illustrate Ludmilla's cost situation for the near future? Why?
b. If Ludmilla wants to keep producing 20 schnitzels, at what point does she want to be eventually? How can she get there?
c. Eventually, Ludmilla and company do very well, expanding until they find themselves making 70 schnitzels a day. But after a few years, Ludmilla discovers that profit was greater when she produced 20 schnitzels per day. She wants to scale back production to 20 schnitzels per day, laying off workers, selling off equipment, renting less space, and producing fewer schnitzels. Hans wants to reduce output by just cutting back on flour and milk and laying off workers. Who's right? Discuss the situation with reference to the relevant points on the diagram.
d. Does the figure tell us what output Ludmilla should aim for? Why or why not?

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Problem 8

Clean "n' Shine is a competitor to Spotless Car Wash. Like Spotless, it must pay 150 dollar per day for each automated line it uses. But Clean "n' Shine has been able to tap into a lower-cost pool of labor, paying its workers only 100 dollar per day. Clean "n' Shine's production technology is given in the following table. To determine its short-run cost structure, fill in the blanks in the table.
a. Over what range of output does Clean "n' Shine experience increasing marginal returns to labor? Over what range does it experience diminishing marginal returns to labor?
b. As output increases, do average fixed costs behave as described in the text? Explain.
c. As output increases, do marginal cost, average variable cost, and average total cost behave as described in the text? Explain.
d. Looking at the numbers in the table, but without drawing any curves, is the relationship between $M C$ and $A V C$ as described in the text? What about the relationship between $M C$ and $A T C$ ?

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Problem 9

In Table $3,$ when output rises from 90 to 130 units, marginal cost is 3.00 . For this change in output, marginal cost is greater than the previous A V C 2.67 dollar but less than the previous A T C (4.22 dollar) . According to the relationship between marginals and averages you learned in this chapter:
a. What should happen to $A V C$ due to this change in output? Does it happen?
b. What should happen to $A T C$ due to this change in output? Does it happen?

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Problem 10

A soft drink manufacturer that uses just labor (variable) and capital (fixed) paid a consulting firm thousands of dollars to calculate short-run costs at various output levels. But after the cost table (see below) was handed over to the president of the soft drink company, he spilled Dr Pepper on it, making some of the entries illegible. The consulting firm, playing tough, is demanding another payment to provide a duplicate table.
a. Should the soft-drink president pay up? Or can he fill in the rest of the entries on his own? Fill in as many entries as you can to determine your answer. (Hint: First, determine the price of labor.)
b. Do $M C, A V C,$ and $A T C$ have the relationship to each other that you learned in this chapter? Explain.

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Problem 11

"If a firm has diminishing returns to labor over some range of output, it cannot have economies of scale over that range." True or false? Explain briefly.

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Problem 12

A study $^{3}$ of immunizing children in poor countries against diphtheria, pertussis, and tetanus estimated that, in the long run, a $10 \%$ increase in the number of children vaccinated increases the total cost of vaccinations by $8.4 \% .$ According to this study:
a. Is immunization over this range characterized by economies of scale, constant returns to scale, or diseconomies of scale?
b. $[\text { More difficult }]$ We can define long-run marginal $\operatorname{cost}(L R M C)$ as the cost of increasing output by one unit when all inputs can be varied (as they can be in the long run). Based on the study, at current vaccine levels, would $L R M C$ for vaccinations be greater than, less than, or equal to longrun average total cost $(L R A T C) ?$ Why?
c. If we want to know what it will cost to vaccinate additional children, and we use "cost per vaccine" as given by the current $L R A T C,$ do we overestimate, underestimate, or accurately estimate the cost per additional vaccine?

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Problem 13

A firm has the strange $A T C$ curve drawn in the following figure. Sketch in the marginal cost curve this firm must have.

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Problem 14

The following curve shows the marginal product of labor for a firm at different levels of employment.
a. Show what the corresponding total product curve would look like.
b. Do the total and marginal product curves for this firm ever exhibit diminishing marginal returns to labor? Increasing marginal returns to labor?

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Numerade Educator