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Liveblogging World War II: October 17, 1940

Econ 1: First Very Rough Draft of Problem Set 5

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In the central part of the state of Euphoria there is a small city, the home of Euphoric State University, called Avicenna--the word is a corruption of the Arabic Ibn Sina, the byname of the great eleventh century Iranian Abu Ali al-Husayn ibn Abd Allah ibn Sina: academic administrator, Quran reciter, astronomer, chemist, geologist, psychologist, theologian, mathematician, physicist, physician, poet, and paleontologist. For the next several questions, we will look at the daily market for espresso-based drinks in Avicenna. Suppose that the demand for espresso drinks is: Q = 10000 - 1000P, where P is the price of an espresso-based drink in dollars. Suppose that the supply is: Q = -5000 + 4000P, where P is the price of an espresso-based drink in dollars.

1) Calculate the market equilibrium

a) What is the market equilibrium price?
b) What is the market equilibrium quantity?
c) What is the producer surplus?
d) What is the consumer surplus?

2) Now suppose that PDC becomes alarmed at the number of strokes that are being treated at the public hospitals of Euphoria, and becomes aware of the link between caffeine consumption and blood pressure on the one hand and between blood pressure and strokes on the other. They decide to impose on consumers a $1/drink tax on espresso drinks and devote the money to hospital stroke-care units.

a) What is the equilibrium price that consumers pay?
b) What is the equilibrium price that producers receive?
c) What is the equilibrium quantity?
d) How much money is raised for hospital stroke care units?
e) What is the producer surplus?
f) What is the consumer surplus?
g) What is the change in the producer surplus relative to the market equilibrium?
h) What is the change in the consumer surplus relative to the market equilibrium?
i) What are the arguments that this tax on espresso drinks is a good idea?
j) What are the arguments that this tax on espresso drinks is a bad idea?

3) Now let us return to the market equilibrium. PDC now notes that baristas have low security of employment and often suffer from spells of unemployment. They decide to impose on producers a $1/drink tax to establish a social welfare fund for baristas.

a) What is the equilibrium price that consumers pay?
b) What is the equilibrium price that producers receive?
c) What is the equilibrium quantity?
d) How much money is raised for barista social welfare?
e) What is the producer surplus?
f) What is the consumer surplus?
g) What is the change in the producer surplus relative to the market equilibrium?
h) What is the change in the consumer surplus relative to the market equilibrium?
i) What are the arguments that this tax on espresso drinks is a good idea?
j) What are the arguments that this tax on espresso drinks is a bad idea?

4) What are the differences between your answer to (2) and your answer to (3)?

5) Return to the market equilibrium. Suppose that all the producers--and we know they are all the producers because they own all the espresso machines in Avicenna--decide that they don't want to work as hard, and that they will make their supply "inelastic": they will share demand equally among themselves and simply go home for the day when the total number of espresso drinks served hits 4000.

a) What is the equilibrium price?
b) What is the equilibrium quantity?
c) What is the producer surplus?
d) What is the consumer surplus?
e) What is the change in the producer surplus relative to the market equilibrium?
f) What is the change in the consumer surplus relative to the market equilibrium?

For the next several questions, let us remain in Avicenna but return to our yoga-lessons example. To simplify the math let's ignore the granularity in lesson supply, and say that the supply curve is simply: Q = 2 x P, where P is the price of a lesson in dollars and Q is the number of slots for yoga students in the classes that the yoga instructors teach. And to simplify the math let's write the daily demand curve as: Q = 126 - 5P, where P is the price of a lesson in dollars and Q is the number of students taking lessons.

6) Calculate the market equilibrium:

a) What is the market equilibrium price?
b) What is the market equilibrium quantity?
c) What is the producer surplus?
d) What is the consumer surplus?

7) Now suppose PDC--Production Distribution Coordination--gets into the act. Somebody gives an eloquent speech about how it is unfair that people are charged as much as $18/lesson for yoga, and PDC enacts a price ceiling: nobody is allowed to charge more than $10/lesson for yoga classes--and the lessons will be taken by those who are the first to sign up.

a) What quantity are suppliers willing to provide at a price of $10/lesson?
b) How many people will want to sign up for yoga lessons?
c) What is the average valuation the people who want to sign up place on yoga lessons?
d) Suppose that the average person who succeeds in signing up has the average valuation among all those who wish to sign up. What, then is the consumer surplus?
e) What is the producer surplus?
f) Who has gained and who has lost from this decree relative to the market equilibrium, and how much?
g) Can you think of a reason why this decree from the PDC might be popular?
h) Suppose it is your job to argue that the decree should be repealed. What would you say?
i) In ancient Athens there was a crime--punishable by death or fine--of having convinced the Assembly of Athens to pass an unjust decree: γραφὴ παρανόμων. Do you think those who persuaded PDC to pass this decree should be tried and punished for this crime? Why or why not?

8) Now suppose that somebody stands up at PDC and gives a persuasive speech that yoga is an alien fitness discipline and that we should be encouraging all-American forms of exercise--like hot-dog eating contests. As a result, PDC passes a decree that no more than 20 people should take yoga lessons a day. However, they do not restrict the price that those lucky enough to be allowed to offer the 20 lessons can charge.

a) To what price will consumers bid up the price of yoga lessons?
b) What will the consumer surplus be?
c) What is the average reservation price that the people who want to sign up to teach yoga will place on yoga lessons?
d) Suppose that the average teacher who succeeds in signing up to give the 20 lesson slots has the average valuation among all those who wish to sign up. What, then, is the producer surplus?
e) Who has gained and who has lost from this decree relative to the market equilibrium, and how much?
f) Can you think of a reason why this decree from the PDC might be popular?
g) Suppose it is your job to argue that the decree should be repealed. What would you say?
h) In ancient Athens there was a crime--punishable by death or fine--of having convinced the Assembly of Athens to pass an unjust decree: γραφὴ παρανόμων. Do you think those who persuaded PDC to pass this decree should be tried and punished for this crime? Why or why not?

9) In the far north of the state of Euphoria there is a small town called Ihavefoundit. There is one theater in Ihavefoundit--and there is no connectivity to the outside world whatsoever. This means that the 1000 or so residents of Ihavefoundit who have a fondness for watching classic Japanese cinema with subtitles have only one way to do so: somebody has to rent a copy of a movie and rent the theater--paying $1000 to do both of those things--and then show the movie, charging admission. No matter how many people show up to the theater the cost of showing the movie remains the same: $1000. And the reservation prices of the Japanese cinema-loving residents are given by the demand curve: Q = 1000 - 100P, where P is the price charged to see the movie in dollars.

a) Suppose that the profit-making Entrepreneurial Company enters the business and is the only--the monopoly--seller of opportunities to see classic Japanese cinema in the benighted, fog-bound, and redwood-infested town of Ihavefoundit. For each price between $10/ticket and $0/ticket, counting down by $1/ticket each time, what are the profits earned by Entrepreneurial Company?
b) What price maximizes profits for the monopolist Entrepreneurial Company?
c) What is the consumer surplus for that price?
d) What is the total social surplus for that price?

10) Let us remain in the far north of Euphoria, but this time classic Japanese cinema is going to be shown by the Redwood Collective for Culture. The RCC is--let us suppose--an efficient organization, able to actually rent a theater, rent a print of the movie, collect money, and not have it stolen. The only constraint on the RCC is that it has to break even.

a) At what price charged per ticket does the RCC break even--collect the $1000 it needs to run its operations?
b) What is the consumer surplus when the RCC breaks even?
c) How does that compare to the consumer surplus in problem (9), when the profit-maximizing Entrepreneurial Company showed the movies?
d) How does that compare to the sum of the consumer and producer surplus in problem (9), when the profit-maximizing Entrepreneurial Company showed the movies?
e) Which comparison--that of consumer surplus with the RCC to consumer surplus with the profit-making EC in part (c), or that of consumer surplus with the RCC to consumer plus producer surplus with the profit-making EC in part (d)--is the best one to keep in mind in guiding your analysis of whether classic Japanese cinema in Ihavefoundit should be shown by a private company or by a nonprofit organization?

11) Suppose that the government of the state of Euphoria gives the RCC a $500 grant to show a movie.

a) At what price now charged per ticket does the RCC break even?
b) What is the consumer surplus now when the RCC breaks even?
c) By how much has consumer surplus increased as a result of this $500 grant?
d) What are the arguments that this $500 grant is a good use of the government's money?
e) What are the arguments that this $500 grant is a bad use of the government's money?

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