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**Chapter 7 Efficiency and Exchange**

Odd-numbered Qs. And Q.10

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Problem #1, Chapter 7 (1) Suppose the weekly demand and supply curves for used DVDs in Lincoln, Nebraska, are as shown in the diagram. Calculate The weekly consumer surplus The weekly producer surplus The maximum weekly amount that producers and consumers in Lincoln would be willing to pay to be able to buy and sell used DVDs in any given week

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**Problem #1, Chapter 7 (2) S 12 10.50 7.5 Price ($/DVD) 6 D 2 6 18 48**

2 6 18 48 Quantity (DVDs/week)

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**Solution to Problem #1 (1)**

The weekly consumer surplus Recall consumer surplus refers to the difference between consumer’s reservation price and the actual market price Graphically, it is the area under the demand curve but above the actual market price In this problem, the equilibrium is achieved at a a price where Q(D) = Q(S) The equilibrium price is $10.50 per DVD At an equilibrium price of $10.50 the corresponding equilibrium quantity is 6 units of DVD per week

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**Solution to Problem #1 (2)**

The weekly consumer surplus (1/2) (Highest consumer’s reservation price – actual market price) * actual market quantity (1/2) ($12 - $10.50) * 6 = $4.5 The weekly producer surplus Recall producer surplus refers to the difference between producer’s reservation price and the actual market price Graphically, it is the area above the supply curve but under the actual market price

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**Solution to Problem #1 (3)**

The weekly producer surplus (1/2) (Actual market price – lowest producer’s reservation price) * actual market quantity (1/2) ($ $6) * 6 = $13.5 The maximum weekly amount that producers and consumers in Lincoln would be willing to pay in a week In other words, it refers to the total gains from trading in used DVDs- the total economic surplus Total economic surplus = consumer surplus + producer surplus Total economic surplus = $4.5 + $13.5 = $18 per week

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Problem #3, Chapter 7 (1) The Kubak crystal caves are renowned for their stalactites and stalagmites. The warden of the caves offers a tour each afternoon at 2pm sharp. The cave can be shown to only four people per day without disturbing their fragile ecology. Occasionally, however, more than four people want to see the caves on the same day. The following table lists the people who wanted to see the caves on September 24, 2003, together with their respective times of arrival and reservation prices for taking that day.

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**Problem #3, Chapter 7 (2) Arrival Time Reservation Price ($) Herman**

Arrival Time Reservation Price ($) Herman 1:48 20 Jon 1:50 14 Kate 1:53 30 Jack 1:56 15 Penny 1:57 40 Fran 1:59 12 Faith 2:00 17

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**Solution to Problem #3 (1)**

A) If the tour is “free” and the warden operates it on a first-come, first served basis, what will the total consumer surplus be for the four people who get to go on the tour on that day? Note that the capacity is only 4 people per day If it serves on a first-come, first served basis, only Herman, Jon, Kate and Jack are able to see the caves Since the tour is free, assume both the production cost and actual market price are zero The consumer surplus is thus exactly to consumer’s reservation price

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**Solution to Problem #3 (2)**

The total consumer surplus Sum of visitors’ reservation prices = $20 + $14 + $30 + $15 = $79 per day B) Suppose the warden solicits volunteers to postpone their tour by offering increasing amounts of cash compensation until four people still wish to see the caves that day. If he gives each volunteer the same compensation payment, how much money will he have to offer to generate the required number of volunteers? What is the total economic surplus under this policy?

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**Solution to Problem #3 (3)**

Recall reservation price refers to the maximum price that a consumer is willing to pay for a good or service It reflects how much does a consumer value on that good or service Based on the reservation prices, an offer of $15 compensation will attract Jon, Jack and Fran to postpone their visit to the caves After the proposal of this offer, Herman, Kate, Penny and Faith are able to visit the caves without having to watch out their arrival time

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**Solution to Problem #3 (4)**

As a result, the total economic surplus: = $20 + $30 + $ = $107 per day However, all the four visitors have to pay a total of $45 ($15*3) cash compensation On the whole, the total of $45 cash compensation is not actually cost, as the compensation represents the gains of the non-visitors (Jon, Jack and Faith) The cash compensation is simply a TRANSFER from the visitors to non-visitors; it neither increases or decreases the total economic surplus Hence, the new total economic surplus is $107 per day

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**Solution to Problem #3 (5)**

C) Why is the compensation policy more efficient than the first-come, first served policy? It is more efficient as the compensation policy generates a higher total economic surplus ($107 per day) rather than just $79 per day under the first-come, first served policy It creates a market trading the rights on the visit to the caves. Non-visitors’ reservation prices are compensated by the visitors Visitors pay an opportunity cost of $15 to ensure the visit to the cave, and thus only those who value the visit more than $15 will actually accept the deal

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**Solution to Problem #3 (6)**

D) Describe a way of financing the warden’s compensation payments that will make everyone, including the warden, either better off or no worse off than under the first-come, first-served approach Auction Suppose the warden auctions off the admission rights Starting zero, the auction price steadily goes up by $1 increment until only 4 people are willing to visit the caves It will stop when the auction price reaches $16 Faith, Penny, Herman and Kate will be the four visitors As a result, the warden will collect $64 from the auction

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**Solution to Problem #3 (7)**

The warden will give a refund to Herman and Kate, who would have gotten to go for free under the first-come, first-served policy- they will be just as well off as before The warden will then give $16 to Jack which is $1 more than enough to compensate him for not visiting The warden will also give $15 to Jon, which is again $1 more than enough to compensate him for not visiting Thus, both Jon and Jack gain $1 from the auction Faith is $1 better off than before ($17 reservation -$16 auction fee); Penny is $24 better off ($40 reservation - $16 auction fee) All others are same as well off as before

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Problem #5, Chapter 7 Is a company’s producer surplus the same as its profit? (Hint: A company’s total cost is equal to the sum of all marginal costs incurred in producing its output, plus any fixed costs.)

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**Solution to Problem #5 (1)**

Producer surplus refers to the total difference between the actual market price and the producer’s reservation price Producer’s reservation price refers to the lowest price that he or she is willing to produce A perfectly competitive firm charges a price =MC As a result, producer’s reservation price = marginal cost In other words, producer surplus is the difference between the total revenue and the sum of all marginal costs incurred

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**Solution to Problem #5 (2)**

Total profit = Total revenue – total cost Total revenue = Price * Quantity Total cost = given in the hint – sum of all the marginal costs plus fixed costs Since producer surplus does not cover any of fixed costs, it is thus not equal to profit

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Problem #7, Chapter 7 The municipal water works of Cortland draws water from two sources: an underground spring and a nearby lake. Water from the spring costs 2 cents per 100 gallons to deliver, and the spring has a capacity of 1 million gallons per day. Water from the lake costs 4 cents per 100 gallons to deliver and is available in unlimited quantities. The demand for water in the summer months in Cortland is P= Q, where P is the price of water in cents per 100 gallons and Q is the quantity demanded in hundreds of gallons per day. The demand curve for water in the winter months is P= 10 – 0.001Q. If the water works wants to encourage efficient water use, how much should it charge for water in the summer months? In the winter months?

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**Solution to Problem #7 (1)**

Demand for summer months Demand for winter months 20 Price per 100 gallons Price per 100 gallons Ds 10 Dw Qw Qs 20,000 hundreds of gallons 10,000 hundreds of gallons

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**Solution to Problem #7 (2)**

The cost of water from underground spring is cheaper than that from lake Therefore, the municipal water works should always to try satisfy the demand by water from underground spring The application of Low-hanging Fruits Principle The relatively small demand for water in winter months can be served by underground spring alone Therefore, the price should be equal to the (marginal) cost of water from underground spring, which is 2 cents per 100 gallons in the winter months

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**Solution to Problem #7 (3)**

The relative large demand for water in summer months must be satisfied by extracting water from lake which has a larger supply than underground spring Again, the price should be equal to the (marginal) cost of water from lake, which is 4 cents per 100 gallons in the winter months

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Problem #9, Chapter 7 The government of Islandia, a small island nation, imports heating oil at a price of $2 per gallon and makes it available to citizens at a price of $1 per gallon. If Islandians’ demand curve for heating oil is given by P = 6-Q, where P is the price per gallon in dollars and Q is the quantity in millions of gallons per year, how much economic surplus is lost as a result of the government’s policy?

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**Solution to Problem #9 (1)**

P ($/gal) 6 2 1 Q (millions of gal/yr) 4 5 6

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**Solution to Problem #9 (2)**

At a per gallon price of $1, Islandians consume 5 million gallons of oil per year However, this level of consumption is attributed to the price control set of the government The true per unit cost is actually $2 per gallon If the government charges where P= MC, Islandians will only demand for 4 million gallons of oil per year Therefore, if Islandians consume 5 gallons of oil per year at the controlled price of $1, there will be an economic loss that is equal to the difference between the total cost of oil and Islandians’ reservation prices for oil

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**Solution to Problem #9 (3)**

P ($/gal) 6 Loss in total economic surplus 2 1 Q (millions of gal/yr) 4 5 6 That is (1/2) ($2 - $1) * (5 – 4) = $0.5 million gallon per year

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Problem #10, Chapter 7 Refer to problem 9. Suppose each of the 1million Islandian households has the same demand curve for heating oil. P ($/gal) 6 Loss in total economic surplus 2 1 Q (millions of gal/yr) 4 5

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**Solution to Problem #10 (1)**

What is the household demand curve? The household demand curve with be the same as in problem 9, instead, the only differences is the scaling. P ($/gal) 6 Loss in total economic surplus 2 1 Q (gal/yr) 4 5

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**Solution to Problem #10 (2)**

How much consumer surplus would each household lose if it had to pay $2 per gallon instead of $1 per gallon for heating oil, assuming there were no other changes in the household budget? P ($/gal) A 6 B C 2 E 1 D Q (gal/yr) 4 5

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**Solution to Problem #10 (3)**

With the subsidy, $1 per gallon, household’s consumer surplus: (Area of ADE) ($6/gal - $1/gal)(5gal/yr) (1/2) = $12.5/yr Without subsidy, $2 per gallon, household’s consumer surplus: (Area of ABC) ($6/gal - $2/gal)(4gal/yr) (1/2) = $8/yr The lost in Total Consumer surplus = $12.5/yr - $8/yr = $4.5/yr That is the area of BCED.

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**Solution to Problem #10 (4)**

With the money saved by not subsidizing oil, by how much could the Islandian government afford to cut each family’s annual taxes? Government’s oil subsidy to each household is ($1/gal)(5gal/yr) = $5/yr. If government imposes oil subsidy to subsidized the poor, the government needs to collect a higher tax from the taxpayers. Now, if the government not subsidizing oil, then the taxpayers, who were need to pay the higher tax, pay a lower tax than before, $5/yr less. Therefore, the government could cut each household’s taxes by $5/yr by not subsidizing oil.

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**Solution to Problem #10 (5)**

If the government abandoned its oil subsidy and implemented the tax cut, by how much would each family be better off? Implement the tax cut, household saves $5/yr on tax. Household’s net gain would be $5/yr - $4.5/yr it loses in consumer surplus from its heating oil purchases, $0.5/yr.

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**Solution to Problem #10 (6)**

How does the resulting gain for 1 million families compare with your calculation of the lost surplus in problem 9? The aggregate net gain from tax cut and removal of subsidy is $500,000/yr. Total Economic surplus lost resulting from oil subsidy is $500,000/yr. The gain from tax cut and removal of oil subsidy is the same as the loss in Economic Surplus. Therefore, it is better for the government not to use the oil subsidy to help the poor. Instead, government should find a more efficient solution.

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**Extra Question #1, Chapter 7**

Tax is always a distortion to a perfectly competitive market; it always works to decrease the total economic surplus True or False, and provide an explanation

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Solution to Extra #1 (1) Graphically, equilibrium is achieved at the intersection of demand curve and supply curve In general, total economic surplus is maximized at equilibrium P S CS P* PS D Q Q*

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**Solution to Extra #1 (2) However, there are exceptions!**

The demand curve does not fully capture the complete benefit (willingness to pay) The supply curve does not fully capture the complete production cost Thus, if there is positive or negative externality, the total economic surplus at equilibrium may be either overestimated or underestimated

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**Solution to Extra #1 (3) Example**

The supply curve of a manufacturing firm is often underrepresented the true production cost The supply curve often fails to take account of pollution cost which is then fully bared by society In other words, there is unaccounted negative externality in the market

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**Solution to Extra #1 (4) S with negative externality P S CS’**

Economic loss P*’ PS’ P* D Q Q*’ Q*

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Solution to Extra #1 (5) Any solution to correct the estimation of supply curve that renders a true production cost or a true willingness to produce? Imposition of tax may shed some light to elimination of negative externality If a per unit tax that is exactly equal to the per unit negative externality arising from the production is imposed, the introduction of pollution tax can help eliminate the economic loss

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**Solution to Extra #1 (6) S with a per unit tax P S CS’**

Economic loss eliminated P*’ PS’ P* D Q Q*’ Q*

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