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Microeconomics : theory and applications with calculus

Jeffrey M. Perloff

Chapter 14

Oligopoly and Monopolistic Competition - all with Video Answers

Educators

Chapter Questions

03:07

Problem 1

Many retail stores offer to match or beat the price offered by a rival store. Explain why firms that belong to a cartel might make this offer.

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
05:13

Problem 1

Which market structure best describes (a) airplane manufacturing, (b) electricians in a small town, (c) farms that grow tomatoes, and (d) cable television in a city? Why?

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator

Problem 1

In the Challenge Solution's mathematical model, how much does Firm 1's best-response curve shift as the subsidy, $s$, increases?

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Problem 1

What is the effect of a government subsidy that reduces the fixed cost of each firm in an industry in a Cournot monopolistic competition equilibrium?

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Problem 1

What happens to the homogeneous-good NashBertrand equilibrium price if the number of firms increases? Why?

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10:49

Problem 1

What is the duopoly Nash-Cournot equilibrium if the market demand function is $Q=1000-1000 p$ and each firm's marginal cost is $28 \notin$ per unit? $\mathbf{M}$

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
10:49

Problem 1

Duopoly quantity-setting firms face the market demand
$$
p=150-q_1-q_2 .
$$
Each firm has a marginal cost of $$\$ 60$$ per unit.
a. What is the Nash-Cournot equilibrium?
b. What is the Stackelberg equilibrium when Firm 1 moves first? $\mathbf{M}$

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
03:53

Problem 2

Using the Challenge Solution's mathematical model, how much does Firm 1's profit (ignoring the subsidy) change as the subsidy, $s$, increases?

Narayan Hari
Narayan Hari
Numerade Educator

Problem 2

In the monopolistically competitive airlines model, what is the equilibrium if firms face no fixed costs?

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01:09

Problem 2

Will price be lower if duopoly firms set price or if they set quantity? Under what conditions can you give a definitive answer to this question?

Daniel Cisneros
Daniel Cisneros
Numerade Educator

Problem 2

Determine the Stackelberg equilibrium with one leader firm and two follower firms if the market demand curve is linear and each firm faces a constant marginal cost, $m$, and no fixed cost. $\mathbf{M}$

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Problem 2

A market has an inverse demand curve $p=100-2 Q$ and four firms, each of which has a constant marginal cost of $M C=20$. If the firms form a profit maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does each firm produce?

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Problem 2

In the initial Cournot oligopoly equilibrium, both firms have constant marginal costs, $m$, and no fixed costs, and the market has a barrier to entry. Use calculus to show what happens to the best-response function of firms if both firms now face a fixed cost of F. M

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Problem 3

The European Union fined Sotheby's auction house more than $€ 20$ million for operating a price-fixing cartel with Christie's auction house (see "The Art of Price Fixing" in MyLab Economics, Chapter Resources, Chapter 14). The two auction houses were jointly setting the commission rates sellers must pay. Let $r$ denote the jointly set auction commission rate, $D_i(r)$ represent the demand for auction house i's services by sellers of auctioned items, $p$ denote the average price of auctioned items, $F$ represent an auction house's fixed cost, and $v$ denote its average variable cost of auctioning an object. At the agreed-upon commission rate $r$, the profit of an auction house $i$ is $\pi_i=r p D_i(r)-\left[F+v D_i(r)\right]$.
a. What is the sum of the profits of auction houses $i$ and $j$ ?
b. Characterize the commission rate that maximizes the sum of profits. That is, show that the commission rate that maximizes the sum of profits satisfies an equation that looks something like the monopoly's Lerner Index profit-maximizing condition $(p-M C) / p=-1 / \varepsilon$ (Equation 11.11).
c. Do the auction houses have an incentive to cheat on their agreement? If Christie's changes its rate while Sotheby's continues to charge $r$, what will happen to their individual and collective profits? $\mathbf{M}$

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03:08

Problem 3

In a monopolistically competitive market, the government applies a specific tax of $$\$ 1$ $per unit of output. What happens to the profit of a typical firm in this market? Does the number of firms in the market change? Why?

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator

Problem 3

Suppose that identical duopoly firms have constant marginal costs of $$\$ 10$$ per unit. Firm 1 faces a demand function of $q_1=100-2 p_1+p_2$, where $q_1$ is Firm 1's output, $p_1$ is Firm 1's price, and $p_2$ is Firm 2's price. Similarly, the demand Firm 2 faces is $q_2=100-2 p_2+p_1$. Solve for the Nash-Bertrand equilibrium. M

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02:15

Problem 3

Show the effect of a subsidy on Firm 1's best response function in Solved Problem 14.3 if the firm faces a general demand function $p(Q)$. M

Niamat Khuda
Niamat Khuda
Numerade Educator
04:43

Problem 3

According to Robert Guy Matthews, "Fixed Costs Chafe at Steel Mills," Wall Street Journal, June 10, 2009 , stainless steel manufacturers were increasing prices even though the market demand curve had shifted to the left. In a letter to its customers, one of these companies announced that "Unlike mill increases announced in recent years, this is obviously not driven by increasing global demand, but rather by fixed costs being proportioned across significantly lower demand." If the firms are oligopolistic, produce a homogeneous good, face a linear market demand curve and have linear costs, and the market outcome is a Nash-Cournot equilibrium, does the firm's explanation as to why the market equilibrium price is rising make sense? (Hint: See Exercise 3.2.) What is a better explanation? $\mathbf{M}$

EA
Erwin Antoni
Numerade Educator

Problem 4

Two firms, each in a different country, sell homogeneous output in a third country. Government 1 subsidizes its domestic firm by $s$ per unit. The other government does not react. In the absence of government intervention, the market has a Nash Cournot equilibrium. Suppose demand is linear, $p=1-q_1-q_2$, and each firm's marginal and average costs of production are constant at $m$. Government 1 maximizes net national income (it does not care about transfers between the government and the firm, so it maximizes the firm's profit net of the transfers). Show that Government 1's optimal s results in its firm producing the Stackelberg leader quantity and the other firm producing the Stackelberg follower quantity in equilibrium.

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01:29

Problem 4

Does an oligopoly or a monopolistically competitive firm have a supply curve? Why or why not?

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator

Problem 4

The Federation of Quebec Maple Syrup Producers supplies over three-quarters of the world's maple syrup (see the Application "Cheating on the Maple Syrup Cartel"). Under government rules, the member firms jointly market their syrup through the federation, which sets quotas on how much each firm can produce. Show this cartel's price determination process using a graph similar to Figure 14.1. Show how much profit a firm would gain by cheating: by producing more than the cartel's quota.

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05:28

Problem 4

Solve for the Nash-Bertrand equilibrium for the firms described in Exercise 5.3 if both firms have a marginal cost of $$\$ 0$$ per unit. $\mathbf{M}$

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
09:48

Problem 4

From June 2017 to June 2018, the price of jet fuel jumped $33 \%$.
a. Based on a general Cournot model, use calculus to show how much a marginal change in the marginal cost, $m$, affects the equilibrium price.
b. In 2018 , fuel cost was about $23 \%$ of airlines' costs. Calculate how much a one-third increase in fuel costs would have affected the equilibrium price in the airline model in this chapter. Why did prices rise less than in proportion to per-passenger per-day cost? $M$

Paul A.
Paul A.
California State Polytechnic University, Pomona
10:19

Problem 5

Solve for the Nash-Bertrand equilibrium for the firms described in Exercise 5.3 if Firm 1's marginal cost is $$\$ 30$$ per unit and Firm 2's marginal cost is $$\$ 10$$ per unit. M

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
07:14

Problem 5

In a Nash-Cournot equilibrium, each of the $n$ firms faces a constant marginal $\operatorname{cost} m$, the inverse market demand function is $p=a-b Q$, and the government assesses a specific tax of $\tau$ per unit. What is the incidence of this tax on consumers? $\mathbf{M}$

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
04:31

Problem 5

Show that a monopolistically competitive firm maximizes its profit where it is operating at less than full capacity or minimum efficient scale, which is the smallest quantity at which the average cost curve reaches its minimum (the bottom of a $\mathrm{U}$-shaped average cost curve). The firm's minimum efficient scale is the quantity at which the firm no longer benefits from economies of scale.

Manasvee Singh
Manasvee Singh
Numerade Educator
03:30

Problem 5

In 2013, a federal judge ruled that Apple colluded with five major U.S. publishers to artificially drive up the prices of e-books (which could be read on Apple's iPad). Apple collects a $30 \%$ commission on the price of a book from the publisher. Why would Apple want to help publishers raise their price? Given Apple's commission, what price would a book cartel want to set? (Hint: The marginal cost of an e-book is virtually zero.)

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
11:40

Problem 5

Zipcar (now owned by Avis) initiated the business of renting cars by the hour and is still the industry leader. However, car2go (owned by Daimler), Enterprise CarShare, and Hertz 24/7 have more recently entered the market. As of 2015, the four companies control about $95 \%$ of the U.S. car sharing market. Zipcar's large network of members and cars may allow it to be a Stackelberg leader. Use graphs to show how the entry of rivals affects Zipcar. Discuss the difference between a market with a Stackelberg leader and one follower versus a market with three followers.

Mihir Nayar
Mihir Nayar
Numerade Educator
04:18

Problem 6

Your college is considering renting space in the student union to one or two commercial textbook stores. The rent the college can charge per square foot of space depends on the profit (before rent) of the firms and hence on the number of firms. Which number of stores is better for the college in terms of rent? Which is better for students? Why?

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator

Problem 6

In 2012, the U.S. government sued to block the world's biggest beer maker, Anheuser-Busch InBev, from buying Mexico's Grupo Modelo (which manufactures Corona and other beers) for $$\$ 20$$ billion (Brent Kendall and Valerie Bauerlein, "U.S. Sues to Block Big Beer Merger," Wall Street Journal, January 31, 2013). Currently, Anheuser-Busch InBev has $39 \%$ of the U.S. beer market, MillerCoors has $26 \%$, and Grupo Modelo has 7\%. When the suit was announced, both firms' stock prices dropped sharply. Why?

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01:18

Problem 6

In the Coke and Pepsi example, what is the effect of a specific tax, $\tau$, on the equilibrium prices?

Crystal Wang
Crystal Wang
Numerade Educator
01:17

Problem 7

Connecticut sets a maximum fee that bail-bond businesses can charge for posting a given-size bond (Ayres and Waldfogel, 1994). The bail-bond fee is set at virtually the maximum amount allowed by law in cities with only one active firm (Plainville, $99 \%$; Stamford, $99 \%$; and Wallingford, $99 \%$ ). The price is as high in cities with a duopoly (Ansonia, $99.6 \%$; Meriden, $98 \%$; and New London, $98 \%$ ). In cities with three or more firms, however, the price falls well below the maximum permitted price. The fees are only $54 \%$ of the maximum in Norwalk ( 3 firms), $64 \%$ in New Haven ( 8 firms), and $78 \%$ in Bridgeport (10 firms). Give possible explanations for this pattern.

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
01:54

Problem 7

In 2013, the U.S. Federal Trade Commission allowed the number two and number three office supply companies, OfficeMax Inc. and Office Depot, Inc., to merge. Office Depot's market value was $$\$ 1.3$$ billion and OfficeMax's was $$\$ 933$$ million. Reportedly, the efficiency gains from merging would save the new company between $$\$ 400$$ and $$\$ 500$$ million. However, in 2015, a federal judge agreed with the U.S. Federal Trade Commission (FTC) and blocked a merger valued at $$\$ 6.3$$ billion between Office Depot and Staples, the largest office supply company. Why might the FTC permit the earlier merger attempt but not the Staples-Office Depot merger?

Doris Bennett
Doris Bennett
Numerade Educator
03:07

Problem 7

At a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred's Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for Wawa's gas is $q_W=680-500 p_W+400 p_S$, and the demand for Fred's gas is $q_W=680-500 p_S+400 p_W$. Assume that the marginal cost of each gallon of gasoline is $$m=\$ 2$$. The gasoline retailers simultaneously set their prices.
a. What is the Bertrand-Nash equilibrium?
b. Suppose that for each gallon of gasoline sold, Wawa earns a profit of 25 c from its sale of salty snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium?

AG
Ankit Gupta
Numerade Educator
02:15

Problem 8

In 2005 , the prices for 36 prescription painkillers shot up as much as $15 \%$ after Merck yanked its once-popular arthritis drug Vioxx from the market due to fears that it caused heart problems. Can this product's exit be the cause of the price increases if the prices reflect a Nash-Cournot equilibrium? Explain.

Kaylee Mcclellan
Kaylee Mcclellan
Numerade Educator
01:54

Problem 8

In February 2005, the U.S. Federal Trade Commission (FTC) went to court to undo the January 2000 takeover of Highland Park Hospital by Evanston Northwestern Healthcare Corp. The FTC accused Evanston Northwestern of antitrust violations by using its post-merger market power in the Evanston hospital market to impose $40 \%$ to $60 \%$ price increases (Bernard Wysocki, Jr., "FTC Targets Hospital Merger in Antitrust Case," Wall Street Journal, January 17, 2005, A1). Hospitals, even within the same community, are geographically differentiated as well as possibly quality differentiated. Suppose that the demand for an appendectomy at Highland Park Hospital is a function of the price of the procedure at Highland Park and Evanston Northwestern Hospital: $q_H=50-0.01 p_H+0.005 p_{N^*}$. The comparable demand function at Evanston Northwestern is $q_{\mathrm{N}}=500-0.01 p_{\mathrm{N}}+0.005 p_H$. At each hospital, the fixed cost of the procedure is $\$ 20,000$ and the marginal cost is $\$ 2,000$.
a. Use the product-differentiated Bertrand model to analyze the prices the hospitals set before the merger. Find the Nash equilibrium prices of the procedure at the two hospitals.
b. After the merger, find the profit-maximizing monopoly prices of the procedure at each hospital. Include the effect of each hospital's price on the profit of the other hospital.
c. Does the merger result in increased prices? Explain.

Doris Bennett
Doris Bennett
Numerade Educator
05:33

Problem 9

Two pizza parlors are located within a few feet of each other on the Avenue of the Americas in New York City. Both were selling a slice of pizza for $$\$ 11^{32}$$ Then, Bombay Fast Food/6th Ave. Pizza lowered its price to 79 . The next morning, 2 Bros. Pizza dropped its price to $$75 \phi$$, which Bombay quickly matched. These price cuts led to long lines of customers. However, both firms claimed that they were losing money. The two proprietors had a meeting on the sidewalk. According to one, they reached an agreement and raised their prices back to a dollar. Can the identicalgoods, Bertrand, or cartel models be used to explain this series of events? Why or why not?

ED
Ethan Dee
Numerade Educator

Problem 9

Consider the Cournot model with $n$ firms. The inverse linear market demand function is $p=a-b Q$. Each of the $n$ identical firms has the same cost function $C(q)=A q_i+\frac{1}{2} B q_i^2$, where $a>A$. In terms of $n$, what is each firm's Nash equilibrium output and profit and the equilibrium price? As $n$ gets very large (approaches infinity), does each firm's equilibrium profit approach zero? Why? M

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04:47

Problem 10

Using Table 14.2 and other information from the chapter, show how the deadweight loss varies in the airline market as the number of firms increases from one to three. $\mathbf{M}$

KM
Kanishk Mishra
Numerade Educator

Problem 10

Firms use marketing to differentiate their bottled water products (see the Application "Differentiating Bottled Water Through Marketing"). If the firms in this market engage in a Bertrand game, what is the effect of this differentiation on prices? What is the effect on welfare?

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Problem 11

The viatical settlement industry enables terminally ill consumers, typically HIV patients, to borrow against equity in their existing life insurance contracts to finance their consumption and medical expenses. The introduction and dissemination of effective anti-HIV medication in 1996 reduced AIDS mortality, extending patients' lives, and hence delayed when the viatical settlement industry would receive the insurance payments. However, viatical settlement payments (what patients can borrow) fell more than can be explained by greater life expectancy. The number of viatical settlement firms dropped from 44 in 1995 to 24 in 2001. Sood, Alpert, and Bhattacharya (2005) found that an increase in market power of viatical settlement firms reduced the value of life insurance holdings of HIV-positive persons by about $$\$ 1$$ billion. When marginal cost rises and the number of firms falls, what happens to the Nash-Cournot equilibrium price? Use graphs or math to illustrate your answer. (Hint: If you use math, it may be helpful to assume that the market demand curve has a constant elasticity throughout.) $\mathbf{M}$

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Problem 11

A Bertrand duopoly produces differentiated products. The firms face demand curves: $q_i=q\left(p_1, p_2\right)$. Each firm has a marginal cost of $m$. What are the firms' best-response functions? Describe how to determine the Nash-Bertrand equilibrium. M

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00:48

Problem 12

Why does differentiating its product allow an oligopoly to charge a higher price?

Kaylee Mcclellan
Kaylee Mcclellan
Numerade Educator

Problem 13

A duopoly faces an inverse market demand function of $p=120-Q$. Firm 1 has a constant marginal cost of 20. Firm 2's constant marginal cost is 40. Calculate the output of each firm, market output, and price in (a) a collusive equilibrium or (b) a Nash-Cournot equilibrium. (Hint: See Solved Problem 14.1.) $\mathbf{M}$

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Problem 14

Graph the best-response curve of the second firm in Solved Problem 14.1 if its marginal cost is $m$ and if it is $m+x$. Add the first firm's best-response curve and show how the Nash-Cournot equilibrium changes as its marginal cost increases.

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01:54

Problem 15

In 2015, Spirit reported that its "average cost per available seat mile excluding special items and fuel" was $5.7 €$ compared to $8.5 \notin$ for Southwest. Assuming that Spirit and Southwest compete on a single route, use a graph to show that their equilibrium quantities differ.

Cerys Evans
Cerys Evans
Numerade Educator
05:44

Problem 16

How would the Nash-Cournot equilibrium change in the airline example if United's marginal cost were $$\$ 100$$ and American's were $$\$200$$?

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
07:50

Problem 17

To examine the trade-off between efficiency and market power from a merger, consider a market with two firms that sell identical products. Firm 1 has a constant marginal cost of 1 , and Firm 2 has a constant marginal cost of 2 . The market demand is $Q=15-p$.
a. Solve for the Nash-Cournot equilibrium price, quantities, profits, consumer surplus, and deadweight loss.
b. If the firms merge and produce at the lower marginal cost, how do the equilibrium values change?
c. Discuss the change in efficiency (average cost of producing the output) and welfare-consumer surplus, producer surplus (or profit), and deadweight loss. M

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator

Problem 18

The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is $p_1=52-q_1-0.5 q_2$. The inverse demand for Firm 2 is $p_2=40-q_2-0.5 q_1$. Each firm has a marginal cost of $m=1$. Solve for the Nash-Cournot equilibrium quantities.

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03:14

Problem 19

An incumbent firm, Firm 1, faces a potential entrant, Firm 2, that has a lower marginal cost. The market demand curve is $p=120-q_1-q_2$. Firm 1 has a constant marginal cost of $$\$ 20$$, while Firm 2's is $$\$ 10$$.
a. What are the Nash-Cournot equilibrium price, quantities, and profits without government intervention?
b. To block entry, the incumbent appeals to the government to require that the entrant incur extra
costs. What happens to the Nash-Cournot equilibrium if the legal requirement causes the marginal cost of the second firm to rise to that of the first firm, $$\$20$$?
c. Now suppose that the barrier leaves the marginal cost alone but imposes a fixed cost. What is the minimal fixed cost that will prevent entry?

Breanna Ollech
Breanna Ollech
Numerade Educator