Chapter 24, Externalities: The Free Market–Interventionist Battle Continues Video Solutions, Microeconomics: A Modern Approach (with InfoApps 2-Semester Printed Access Card)

Problem 1

Let us say that there is a class in which a weekly exam is given. The class has one genius, who always scores $100 \%$, and 19 "regular" students, who always score $85 \%$. The teacher grades the exam on a curve by taking the difference between the highest score and 100 and adding the result to each student's score. For example, if the highest score is 78 , each student will have 22 points added to his or her score. The parents of these students pay them \$1 for each point scored on the exam.
a) Does the genius impose externalities on the rest of the class? If so, what is the value of the marginal externality for each exam?
b) What is the Pareto-optimal configuration of grades?
c) If the highest scoring student on each exam could be taxed for each point he or she scores above the second-highest scoring student, what marginal tax would result in the Pareto-optimal distribution of grades?
d) If the 19 "regular" students were to bribe the genius to start scoring 85 instead of 100 , what is the maximum amount of money they could offer?

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01:12

Problem 2

A soot-spewing factory that produces steel windows is next to a laundry. We will assume that the factory faces a prevailing market price of $$P=\$ 40$$. Its cost function is $C=X^2$, where $X$ is window output, so the factory's marginal cost is $M C=2 X$. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so the laundry has to clean it again. This increases the laundry's costs. In fact, the cost function of the laundry is $C=Y^2+0.05 X$, where $Y$ is pounds of laundry washed. The demand curve faced by the laundry is perfectly horizontal at a price of $$\$ 10$$ per pound.
a) What outputs $X$ and $Y$ would maximize the sum of the profits of these two firms?
b) Will those outputs be set by a competitive market?
c) What per-unit tax would we need to set on window production to obtain the outputs found in part a of this problem?

Carson Merrill

Numerade Educator

05:00

Problem 3

Suppose that the speed limit on a four-lane highway is 60 miles per hour. An accident has occurred in the southbound lanes, and people in the northbound lanes tend to slow down and look at it. This reduces the speed in the northbound lanes from 60 to 40 miles per hour. All the people in the northbound lanes are on their way to work and are driving 40 miles. If they agree not to slow down, they can get to work in 40 minutes. However, if they slow down, the trip will take 60 minutes. The people in the northbound lanes all obtain private satisfaction from slowing down and looking at the accident.
a) Will an informal agreement not to slow down be stable?
b) What is the externality in this situation?

Vishal Gupta

Numerade Educator

09:35

Problem 4

Assume that a society has three firms, A, B, and C, situated in a row. The society faces the following problem. Every unit of output that firm A produces creates a benefit for firm B of $$\$7$$ and a cost to firm C of $$\$3$$. The marginal cost of production for firm A is $M C=4 q^d$, where $q^a$ is firm A's output. The market price for the output of firm $\mathrm{A}$ is $$\$ 16$$. (Assume that this is the marginal benefit to society of consuming each unit.)
a) What total amount of output will firm A produce in a competitive market?
b) What output is the optimal output for society?
c) Suppose that firms A and B merge and then set the output that is best for them. What would that output be? Would it be the socially optimal output?

Yang Su

Numerade Educator

04:25

Problem 5

Let's say that there are three firms in a community that pollute the environment. The government has decided that 21 units of pollution must be abated and that each firm must cut pollution by 7 units. The marginal cost of pollution abatement is $M C^A=\frac{1}{3} q$ for firm $A, M C^B=\frac{1}{2} q$ for firm $B$, and $M C^C=\frac{1}{4} q$ for firm $C$, where $q$ is the quantity of abatement. The government wants the total amount of pollution to be reduced by 21 units and demands that each firm reduce its pollution by 7 units.
a) Is this solution efficient? Explain why or why not.
b) If the solution is not efficient, how much pollution should each firm reduce at the efficient outcome?
c) If each firm must abate 7 units of pollution, what is the maximum firm $\mathrm{A}$ would be willing to pay firm $\mathrm{C}$ to cut 2 additional units of pollution so that firm $\mathrm{A}$ could cut its pollution by only 5 units?

Kaylee Mcclellan

Numerade Educator