4.1

1. Suppose the following table shows the quantity of laundry detergent that is demanded and supplied at various prices in Country 1.

P ($)

Quantity Demanded (million oz.)

Quantity Supplied (million oz.)

2 65 354 60 406 55 458 50 5010 45 5512 40 6014 35 65

a. Use the data in the table to draw the demand and supply curves in the market for laundry detergent.

b. What is the equilibrium price and quantity in the market?

c. The following tables give the demand and supply schedules for two of its neighboring countries, Country 2 and Country 3. Suppose these three countries decide to form an economic union and integrate their markets. Use the data in the table to plot the market demand and supply curves in the newly formed economic union. What is the equilibrium price and quantity in the market?

Country 2:

P ($) Quantity Demanded (million oz.)

Quantity Supplied (million oz.)

2 35 54 30 106 25 158 20 20

10 15 2512 10 3014 5 35

Country 3:

P ($)Quantity Demanded

(million oz.)Quantity Supplied

(million oz.)2 40 104 35 156 30 208 25 25

10 20 3012 15 3514 10 40

Answers:

a. The following figure shows the domestic market for laundry detergent:

b. The equilibrium price in the market is $8 and the equilibrium quantity is 50,000,000 oz.

c. If the three countries decide to integrate, the individual country demand and supply curves need to be aggregated to arrive at the demand and supply curves in the economic union. The following figure shows the demand (DM) and supply (SM) curves in the economic union:

As can be seen in the figure, the equilibrium price remains $8 while the total quantity sold is equal to 95 million oz.

5.1

1. Each school-week night you can play video games, talk on the phone, or watch a movie. You have a total of five nights to spend doing one of these three things.

Play Video Games Talk on Phone Watch a Movie

Quantity (nights): TotalBenefit

MarginalBenefit

TotalBenefit

MarginalBenefit

TotalBenefit

MarginalBenefit

0 0 -- 0 -- 0 --

1 20 5 3

2 22 10 6

3 23 12 9

4 23 14 12

5 23 15 15

a. Fill out the marginal benefit column.

b. Your friend tells you to play video games for two nights and talk on the phone for the other three nights. What will be your total benefit of this plan?

c. Use marginal benefit column to argue why your total benefit will increase if you play video games less and watch one movie instead.

d. What is the best way to use your five nights? What is the total benefit? Use the marginal benefits column to find the answer more easily.

Answers:

a. To calculate marginal benefit, look at the different in total benefit between each row. For example, the marginal benefit of a third night of playing video games is 23 - 22 = 1.

Play Video Games Talk on Phone Watch a Movie

Quantity (nights): TotalBenefit

MarginalBenefit

TotalBenefit

MarginalBenefit

TotalBenefit

MarginalBenefit

0 0 -- 0 -- 0 --

1 20 20 5 5 3 3

2 22 2 10 5 6 3

3 23 1 12 2 9 3

4 23 0 14 2 12 3

5 23 0 15 1 15 3

b. 22 + 12 + 0 = 34 (See underlined numbers in the table above.)

c. The marginal benefit of the second night of video games is only 2, which is less than the marginal benefit of 3 of one movie. Thus, you should play video games less and watch a movie instead. This will increase your total benefit to 20 + 12 + 3 = 35 > 34.

You can guess and check to find the right answer. However, the easiest way is to find the five highest marginal benefits: 20, 5, 5, 3, and 3 (bolded). Thus, you should play video games one night, talk on the phone for two nights, and watch movies for two nights. Total benefit is 20 + 10 + 6 = 36. It is not possible to get a higher total than this.

6.3

1. The following table gives you information on the total cost of Mac’s ice cream production:

Quantity of Ice Cream (liter) Total Cost

0 $50

10 $90

20 $110

30 $140

40 $190

50 $260

60 $350

a. Is Mac producing ice cream in the short run or the long run? Explain.

b. Compute the average total cost at each level of output.

c. Compute the marginal cost at each level of output.

d. At which level of output does the average total cost start increasing? Explain the increasing average total cost and its relationship with the marginal cost.

Answer:

d. As the quantity of ice cream is zero, the total cost is $50, which comes from the fixed costs. Since there is at least one fixed input, Mac is producing in the short run.

e.Quantity of Ice Cream (liter) Average Total Cost

0 $010 $920 $5.530 $4.6740 $4.7550 $5.260 $5.83

f.

Quantity of Ice Cream (liter) Marginal Cost

0 -10 $420 $230 $340 $550 $760 $9

The average total cost starts increasing at the output level of 40. The average total cost increases because the marginal cost is higher than the average total cost at the output level of 40 and above.

7.8

1. The following tables show a small firm’s long-run average cost of manufacturing a good at two different plants:

Plant 1Quantit

yTotal Cost

Average Cost

Marginal Cost

1 502 1063 1644 2245 2876 3557 4308 5209 618

Plant 2Quantit

yTotal Cost

Average Cost

Marginal Cost

1 202 523 904 1305 1756 2277 2858 3459 407

a. Complete the third and fourth columns of each table.

b. Suppose the price of the good is $60. How much should the firm produce in each plant in order to maximize the firm’s profit? Find the firm’s profit.

c. A new manager is assigned to the production department. He thinks that the firm can profitably move all production to Plant 2 since the average cost of production is lower in Plant 2 than in Plant 1. If the firm only uses Plant 2, how much should it produce in order to maximize profits? Find the firm’s profit. Assume zero fixed cost.

Answer:

a.

Plant 1Quantity Total

CostAverage

CostMarginal

Cost1 50 50.00 502 106 53.00 563 164 54.67 584 224 56.00 605 287 57.40 636 355 59.17 687 430 61.43 758 520 65.00 909 618 68.67 98

Plant 2Quantity Total

CostAverage

CostMarginal

Cost1 20 20.00 202 52 26.00 323 90 30.00 384 130 32.50 405 175 35.00 456 227 37.83 527 285 40.71 588 345 43.13 609 407 45.22 62

b. Since the price of the good is $60, profits are maximized when marginal cost of production is equal to $60 at both plants. This occurs when 4 units are produced at Plant 1 and 8 units are produced at Plant 2. The firm’s revenue will be 12 x $60 = $720, its total costs will be $224 + $345 = $569, and it will earn a profit of $720 - $569 = $151.

If the firm uses just Plant 2 it would maximize profits by producing just 8 units (since price equals marginal cost in Plant 2 at 8 units). Its revenue will be 8 x $60 = $480, its cost will be $345, and its profit will be $480 - $345 = $135.

8.5

1. Julia is a dressmaker and runs her own business. She has 10 employees working 8 hours a day. Now assume that Julia is enters into an agreement to make 25 shirts and 25 skirts for a company in

2 weeks. The following table shows the number of dresses her employees can sew in a given number of hours:

Hours spent on sewing Shirts

Hours spent on sewing Skirts

1 0.5 1 12 1 2 23 1.25 3 2.54 1.5 4 35 1.75 5 3.56 2 6 47 2.25 7 4.58 2.5 8 5

a. Sketch Julia’s PPC.

b. What is her opportunity cost of sewing one shirt?

c. Can you determine her terms of trade? Why or why not?

Answer:

a. The PPC for Julia:

b. The opportunity cost of sewing one shirt is 1/0.5 = 2 skirts.

We cannot discuss her terms of trade as we do not have any information regarding the negotiated exchange rate of her goods for other goods.

8.7

2. The remote island nations of Nearway and Farway produce fish and coconuts and have recently decided to trade with one another. Use the table to answer the following questions:

Coconuts FishNearway Farwa

yNearway Farway

Optimal Production without Trade 200 300 100 200

Specialization: Optimal Production with Trade 600 500

Traded Goods 250 250Post-Trade AllocationGains for Trade

a. Calculate the opportunity costs of producing fish and coconuts in Nearway and Farway, and then determine who has an absolute advantage and comparative advantage in the production of each good.

b. Using what you learned in part (a), fill in the blanks in the table above.

c. Which nation received the better deal in this trade? Explain using the exchange rate range.

d. Would Nearway and Farway ever trade 60 coconuts for 20 fish? Why or why not?

Answer:

a. Consider the opportunity cost of fish in Nearway. We know that Nearway could produce either (i) 200 coconuts and 100 fish, or (ii) 0 coconuts and 500 fish. So in Nearway increasing fish production by 500 – 100 = 400 means that coconut production falls by 200. This is equivalent to saying that increasing fish production by 1 means that coconut production falls by 200 / 400 = .5, and so the opportunity cost of fish in Nearway is .5

Now consider the opportunity cost of fish in Farway. We know that Farway could produce either (i) 300 coconuts and 200 fish, or (ii) 600 coconuts and 0 fish. So in Farway increasing fish production by 200 would mean that coconut production would fall by 600 – 300 = 300. This is equivalent to saying that increasing fish production by 1 means that coconut production falls 300 / 200 = 1.5, and so the opportunity cost of fish in Farway is 1.5

Similar calculations would show that the opportunity cost of coconuts is 2 in Nearway and .67 in Farway. The following table shows the opportunity costs of producing fish and coconuts in the two countries:

 

Opportunity cost

Fish Coconut

Nearway

.5 coconuts 2.0 fish

Farway1.5

coconuts 0.67 fish

Nearway’s opportunity cost of fish is less than Farway’s opportunity cost of fish (.5 < 1.5) and therefore Nearway has a comparative advantage in fish. Farway’s opportunity cost of coconuts is less than Nearway’s opportunity cost of coconuts (.67 < 2.0) and therefore Farway has a comparative advantage in coconuts.

b. We found in the first part of this problem that Nearway has a comparative advantage in the production of fish and that Farway has a comparative advantage in the production of coconuts. Suppose Farway produced 600 coconuts and Nearway produced 500 fish as shown in the table. Farway trades 250 coconuts for 250 fish with Nearway. This means that after the trade Farway consumes 600 – 250 = 350 coconuts and 250 fish, while Nearway consumes 250 coconuts and 500 – 250 = 250 fish. The last row in the table shows the gains from trade. After trading with Farway, Nearway consumed 50 more coconuts and 150 more fish than it had before specialization and trade. After trading with Nearway, Farway consumed 50 more coconuts and 50 more fish than it had before specialization and trade.

Coconuts Fish

Nearway Farway Nearway Farway

Optimal Production without Trade 200 300 100 200

Specialization: Optimal Production with Trade 0 600 500 0

Traded Goods 250 -250 -250 250

Post-Trade Allocation 250 350 250 250

Gains for Trade 50 50 150 50

c. Nearway and Farway are trading one coconut for one fish. The terms of trade lie between Nearway and Farway’s opportunity costs.

.5 coconuts per fish ≤ terms of trade ≤ 1.5 coconuts per fish

0.67 fish per coconut ≤ terms of trade ≤ 2.0 fish per coconut

Since the terms of trade of 1 fish per coconut is closer to Farway’s opportunity cost of coconuts, Nearway received much of the benefit from trade.

Nearway and Farway would never trade 60 coconuts for 20 fish. If they did, the terms of trade would be 3 coconuts per fish. Trade can occur only if the terms of trade are between the two countries’ opportunity costs; the opportunity cost of fish is less than 3 coconuts in both Nearway and Farway.

9.11

5. Three roommates Tinker, Evers, and Chance share an apartment. It is really cold outside and they are considering turning up the thermostat in the apartment up by 1, 2, 3, or 4 degrees. Their individual marginal benefits from making it warmer in the apartment are as follows:

Tinker Evers Chance1 degree $5 $4 $32 degrees $4 $3 $23 degrees $3 $2 $14 degrees $2 $1 $0

They know that each time they raise the temperature by one degree, their heating bill goes up by $8.

a. Find the marginal social benefit from making it 1, 2, 3, or 4 degrees warmer.

b. By how many degrees should they raise the temperature?

Answer:

a. Heat in the apartment is a public good; all three enjoy the benefits from turning up the thermostat. The marginal social benefit is therefore the sum of their individual marginal benefits.

Tinker Evers ChanceMarginal

Social Benefit

1 degree $5 $4 $3 $12

2 degrees $4 $3 $2 $9

3 degrees $3 $2 $1 $6

4 degrees $2 $1 $0 $3They should continue to turn up the thermostat as the long as the marginal social benefit from making it warmer is at least as great as the marginal cost of making it warmer (which we are told is $8). They should therefore raise the temperature by two degrees. The marginal social benefit of raising the temperature a third degree is $6, which is less than marginal cost.

10.5

1. Consider the following demand and supply schedules in the market for basketballs in country A.

Demand Supply Price700 0 $2.00600 0 $2.50500 100 $3.00400 200 $3.50300 300 $4.00200 400 $4.50100 500 $5.00

a. Find the initial equilibrium price and quantity and draw the graph.

b. Suppose the government imposes a $0.5/unit tax on the producers of basketballs. Find the new equilibrium price and quantity. Draw the graph.

c. Suppose the government changes the tax by switching it from the producer to the consumer. What will be the new equilibrium price and quantity? Draw the graph.

Answers:

a. The initial equilibrium price is $4.00 and the initial equilibrium quantity is 300.

b. A tax on suppliers shifts the supply schedule by the amount of the tax. Therefore, for example, firms supplied 100 units at the price of $3.00 without the tax, but with the tax, they would supply 100 units at the price of $3.50. Quantity supplied is equal to the quantity demanded at a price of $4.50. The new equilibrium quantity is 200. Suppliers keep $4.50 – $0.5 = $4.00 after paying the tax.

c. tax on the consumer shifts the demand schedule by the amount of the tax. Therefore, for example, consumers were willing to buy 500 units at the price of $5.00 without the tax, but with the tax, they would demand 500 units at the price of $4.50. The new equilibrium price is $3.50 and the new equilibrium quantity is 200. Consumers pay a total of $3.50 + $0.5 = $4.00.

11.1

1. Suppose that, at your firm, the relationship between output produced and the number of workers you hire is as follows:

LaborTotal

Product 0 01 122 233 324 385 426 45

a. Find the marginal product of labor for each worker.

b. Is the relationship between output and labor consistent with the Law of Diminishing Returns?

c. Suppose your firm is a perfect competitor in the output market and the labor market. If the price of output is $9 and the wage rate is $27, how many workers should your firm hire?

d. If the price of output falls to $3 and the wage remains $27, how many workers should your firm hire?

Answers:

a. Column (3) in the following table shows the marginal product of labor. The marginal product of labor is the increase in output from hiring one more worker. So, for example, the marginal product of the second worker is 23 – 12 = 9. The value of the marginal product of labor equals the price of output times the marginal product of labor. We showed that the marginal product of the second worker is 9. If the price of output is $9 then the value of the marginal product of the second worker is $9 x 9 = $81.

(1)Labor

(2)Total

Product

(3)Marginal Product

(4)Value of the Marginal Product

(Price = $9)

(5)Value of the Marginal

Product(Price = $3)

0 0 -- -- --1 12 12 $108 $362 23 11 99 333 32 9 81 274 38 6 54 185 42 4 36 126 45 3 27 9

b. The law of diminishing returns says that the marginal product of labor becomes smaller as the number of workers increases. This is true in this example. The marginal product of labor, for example, of the first worker is 12 but the marginal product of the sixth worker is just 3.

c. The profit-maximizing firm hires the number of workers such that the wage rate is equal to the value of the marginal product of labor. If the price of output is $9 and the wage is $27, the firm will hire up to 6 workers (see the fourth column in the table above).

As in part (b), the profit-maximizing firm hires the number of workers such that the wage rate is equal to the value of the marginal product of labor. If the price is $3, this implies the firm will hire 3 workers (see the fifth column in the table above).