Questions Solutions

ECON 122 Principles of Macroeconomics Macroeconomics – – Sections Sections A, B

Fall 2017

Problem Set 1 – Solution Solution Instructor: Gayane Barseghyan

Chapter 23. 

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Quick Check Multiple Choice : 1-6 (see the textbook) Answers: 1. b 2. c 3. d 4. c 5. a 6. b

Problems and Applications Problem 2:

The government purchases component of GDP does not include spending on transfer payments such as Social Security. Thinking about the definition of GDP, explain why transfer payments are excluded Solution: With transfer payments, nothing is produced, so there is no contribution to GDP. Problem 3:

As the chapter states, GDP does not include the value of used goods that are resold. Why would including such transactions make GDP a less informative measure of economic well-being? Solution: If GDP included goods that are resold, it would be counting output of that particular year, plus sales of goods produced in a previous year. It would double-count goods that were sold more than once. This double-counting would make GDP a less informative measure of economic well-being because it would overstate the value of production. Problem 4: Below are some data from the land of milk and honey. Year 2013 2014 2015

Price of Milk $1 $1 $2

Quantity of Milk 100 quarts 200 200

Price of Honey $2 $2 $4

Quantity of Honey 50 quarts 100 100

a. Compute nominal GDP, real GDP, and the GDP deflator for each year, using 2013 as the base year. 1


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b. Compute the percentage change in nominal nominal GDP, real GDP, and the GDP deflator deflator in 2014 and 2015 from from the preceding year. For each year, identify the variable that does not change. Explain why your answer makes sense. c. Did economic well-being rise more in 2014 or 2015? Explain

Solution: a.

Calculating nominal GDP: 2013: ($1 per qt. of milk  100 qts. milk) + ($2 per qt. of honey  50 qts. honey) = $200 2014: ($1 per qt. of milk  200 qts. milk) + ($2 per qt. of honey  100 qts. honey) = $400 2015: ($2 per qt. of milk  200 qts. milk) + ($4 per qt. of honey  100 qts. honey) = $800 Calculating real GDP (base year 2013): 2013: ($1 per qt. of milk  100 qts. milk) + ($2 per qt. of honey  50 qts. honey) = $200 2014: ($1 per qt. of milk  200 qts. milk) + ($2 per qt. of honey  100 qts. honey) = $400 2015: ($1 per qt. of milk  200 qts. milk) + ($2 per qt. of honey  100 qts. honey) = $400 Calculating the GDP deflator: 2013: ($200/$200)  100 = 100 2014: ($400/$400)  100 = 100 2015: ($800/$400)  100 = 200 b.

Calculating the percentage change in nominal GDP:

Percentage change in nominal GDP in 2014 = [($400 – [($400 – $200)/$200] $200)/$200]  100 = 100%. Percentage change in nominal GDP in 2015 = [($800 – [($800 – $400)/$400] $400)/$400]  100 = 100%. Calculating the percentage change in real GDP: Percentage change in real GDP in 2014 = [($400 – [($400 – $200)/$200] $200)/$200]  100 = 100%. Percentage change in real GDP in 2015 = [($400 – [($400 – $400)/$400] $400)/$400]  100 = 0%. Calculating the percentage change in GDP deflator: Percentage change in the GDP deflator in 2014 = [(100 – 100)/100] 100)/100]  100 = 0%. Percentage change in the GDP deflator in 2015 = [(200 – 100)/100] 100)/100]  100 = 100%. Prices did not change from 2013 to 2014. Thus, the percentage change in the GDP deflator is zero. Likewise, output levels did not change from 2014 to 2015. This means that the percentage change in real GDP is zero. c.

Economic well-being rose more in 2014 than than in 2015, since real GDP rose rose in 2014 but not in 2015. In 2014, real GDP rose but prices did not. In 2015, real GDP did not rise but prices did.

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Problem 5:

Consider an economy that produces only chocolate bars. In year 1, the quantity produced is 3 bars and the price is $4. In year 2, the quantity produced is 4 bars and the price is $5. In year 3, the quantity produced is 5 bars and the price is $6. Year 1 is the base year. a. What is nominal GDP for each of these three years? b. What is real GDP for each of these years? c. What is the GDP deflator for each of these years? d. What is the percentage growth rate of real GDP from year 2 to year 3? e. What is the inflation rate as measured by b y the GDP deflator from year 2 to year 3? f. In this one-good economy, how might you have answered parts (d) and (e) without first answering parts (b) and (c)? Solution: a.

Calculating Nominal GDP: Year 1: (3 bars  $4) = $12 Year 2: (4 bars  $5) = $20 Year 3: (5 bars  $6) = $30 b. Calculating Real GDP: Year 1: (3 bars  $4) = $12 Year 2: (4 bars  $4) = $16 Year 3: (5 bars  $4) = $20 c. Calculating the GDP deflator: Year 1: $12/$12  100 = 100 Year 2: $20/$16  100 = 125 Year 3: $30/$20  100 = 150 d. The growth rate of real GDP from Year 2 to Year 3 = (20 – (20 – 16)/16 16)/16  100 = 25% e.

The inflation inflation rate from Year 2 to Year Year 3 = (150 – (150 – 125)/125 125)/125  100 = 20%.

f.

To calculate the growth rate of real GDP, we could simply calculate the percentage change in the quantity of bars. To calculate the inflation rate, we could measure the percentage change in the price of bars.

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Problem 6:

Consider the following data on U.S. GDP: Year 2012 2002

Nominal GDP (in billions billions of dollars) 15,676 10,642

GDP Deflator (base year 2005) 115.4 92.2

a. What was the growth rate of nominal GDP between 2002 and 2012? (Hint: The growth rate of a variable X over an N-year period is calculated as 100 × [(Xfinal/Xinitial ) 1/N − 1].) b. What was the growth rate of the GDP deflator between 2002 and 2012? c. What was real GDP in 2002 measured in 2005 prices? d. What was real GDP in 2012 measured in 2005 prices? e. What was the growth rate of real GDP between 2002 and 2012? f. Was the growth rate of nominal GDP higher or lower than the growth rate of real GDP? Explain Solution: a. b. c. d. e. f.

The growth rate of nominal GDP = 100  [($15,676/$10,64 [ ($15,676/$10,642) 2) 0.10 – 1] 1] = 3.9% 0.10 The growth rate of the deflator = 100  [(115.4/92.2) – 1] 1] = 2.3% Real GDP in 2002 (in 2005 prices) is $10,642/(92.2/100) $10,642/(92.2/100) = $11,542.30. Real GDP in 2012 (in 2005 prices) is $15,676/(115.4/100) $15,676/(115.4/100) = $13,584.06. The growth rate of real GDP = 100  [($13584.06/$11,542.30) [($13584.06/$11,542.30) 0.10 – 1] 1] = 1.6% The growth rate of nominal GDP was higher than the growth rate of real GDP because of inflation.

Problem 8:

A farmer grows wheat, which she sells to a miller for $100. The miller turns the wheat into flour, which she sells to a baker for $150. The baker turns the wheat into bread, which she sells to consumers for $180. Consumers eat the bread. a. What is GDP in this economy? Explain. b. Value added is defined as the value of a producer’s output minus the value of the intermediate goods that the producer buys to make the output. Assuming there are no intermediate goods beyond those described above, calculate the value added of each of the three producers. c. What is total value added of o f the three producers in this economy? econom y? How does it compare to the economy’s GDP? Does this example suggest another anoth er way of calculating GDP? Solution: a.

GDP is the market value of the final good sold, $180.

b. Value added for the farmer: $100.

Value added for the miller: $150 – $150 – $100 $100 = $50. 4


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Value added for the baker: $180 – $180 – $150 $150 = $30. c. Together, the value added for the three three producers is $100 + $50 + $30 = $180. $180. This is the value of GDP. This example suggests that GDP could be calculated as the sum of the value added by all producers.

Problem 10:

The participation of women in the U.S. labor force has risen dramatically since 1970. a. How do you think this rise affected GDP? b. Now imagine a measure of well-being that includes time spent working in the home and taking leisure. How would the change in this measure of wellbeing compare to the change in GDP? c. Can you think of other aspects of well- being being that are associated with the rise in women’s labor force participation? Would it be practical to construct a measure of well-being that includes these aspects? Solution: a.

The increased labor-force participation participation of women has increased GDP in the United United States, because it means more people are working working and production has increased. b. If our measure of well-being included included time spent working working in the home and taking leisure, leisure, it would not rise as much as GDP, because the rise in women's labor-force participation has reduced time spent working in the home and taking leisure. c. Other aspects of well-being that are associated associated with the rise in women's increased increased labor-force participation include include increased self-esteem and prestige prestige for women in the workforce, especially at managerial levels, but decreased quality time spent with children, whose pare nts have less time to spend with them. Such aspects would be quite difficult to measure.

Problem 11:

One day, Barry the Barber, Inc., collects $400 for haircuts. Over this day, his equipment depreciates in value by $50. Of the remaining $350, Barry sends $30 to the government in sales taxes, takes home $220 in wages, and retains $100 in his business to add new equipment in the future. From the $220 that Barry takes home, he pays $70 in income taxes. Based on this information, compute Barry’s contribution to the following measures of income. a. gross domestic product b. net national product c. national income d. personal income e. disposable personal income 5


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Solution: a. b. c. d.

GDP equals the dollar dollar amount Barry collects, collects, which is $400. NNP = GDP – GDP – depreciation depreciation = $400 – $400 – $50 $50 = $350. National income = NNP = $350. Personal income = national income – income – retained retained earnings – earnings – indirect indirect business taxes = $350 – $100 – $100 – $30 $30 = $220. e. Disposable personal income = personal income – income – personal personal income tax = $220 – $220 – $70 $70 = $150.

Chapter 24. 

Quick Check Multiple Choice : 1-6 (see the textbook) Answers: 1. c 2. b 3. d 4. a 5. d 6. d

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Suppose that people consume only three goods, as shown in this table: 2014 price 2014 quantity 2015 price 2015 quantity

Tennis Balls $2

Golf Balls $4

Bottles of Gatorade $1

100

100

200

$2

$6

$2

100

100

200

a. What is the percentage change in the price of each of the three goods? b. Using a method similar to the consumer price index, compute the percentage change in the overall price level. c. If you were to learn that a bottle of Gatorade increased in size from 2014 to 2015, should that information affect your calculation of the inflation rate? If so, how? d. If you were to learn that Gatorade Gatorad e introduced new flavors in 2015, should shoul d that information affect your calculation of the inflation rate? If so, how? Solution: a.

The percentage change in the price of tennis balls is ($2 – $2)/$2 $2)/$2 × 100 = 0%. The percentage change in the price of golf balls is ($6 – $4)/$4 $4)/$4 × 100 = 50%. The percentage change in the price of Gatorade is ($2 – ($2 – $1)/$1 $1)/$1 × 100 = 100%. 6


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b. The cost of the market basket in 2014 2014 is (100 x $2) + (100 x $4) $4) + (200 x $1) = $800. The cost of the market basket in 2015 is (100 x $2) + (100 x $6) + (200 x $2) = $1,200. Using 2014 as the base year, we can compute the CPI in each year: 2014 = ($800/$800) x 100 = 100 2015 = ($1,200/$800) x 100 = 150 We can use the CPI values to compute the percentage change in the overall price level: (150-100)/100 x 100 = 50%. c.

This would lower the estimation estimation of the inflation inflation rate because because the value value of a bottle bottle of Gatorade is now greater than before. The comparison should be made on a per-ounce basis.

d. More flavors enhance consumers’ consumers’ well-being. well-being. Thus, this would be considered a change in quality and would also lower the estimate of the inflation rate.

Problem 5:

A small nation of ten people idolizes the TV show American Idol. All they produce and consume are karaoke machines and CDs, in the following amounts:

Karaoke Machines Quantity Price

2014 2015

10 12

$40 $60

CDs Quantity

30 50

Price

$10 $12

a. Using a method similar to the consumer price index, compute the percentage change in the overall price level. Use 2014 as the base year and fix the basket at 1 karaoke machine and 3 CDs. b. Using a method similar to the GDP deflator, compute the percentage change in the overall price level. Also use 2014 as the base year. c. Is the inflation rate in 2015 the same using the two methods? Explain why or why not. Solution: a.

The cost of the market market basket in in 2014 is (1 × $40) + (3 × $10) = $70. The cost of the market basket in 2015 is (1 × $60) + (3 × $12) = $96. Using 2014 as the base year, we can compute the CPI in each year: 2014: $70/$70 × 100 = 100 2015: $96/$70 × 100 = 137.14 We can use the CPI to compute the inflation rate for 2015: (137.14 – (137.14 – 100)/100 100)/100 × 100 = 37.14% 7


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b. Nominal GDP for 2014 = (10 × $40) $40) + (30 × $10) = $400 + $300 = $700. $700. Nominal GDP for 2015 = (12 × $60) $60) + (50 × $12) = $720 + $600 = $1,320. $1,320. Real GDP for 2014 = (10 × $40) + (30 × $10) = $400 + $300 = $700. Real GDP for 2015 = (12 × $40) + (50 × $10) = $480 + $500 = $980. The GDP deflator for 2014 = ($700/$700) × 100 = 100. The GDP deflator for 2015 = ($1,320/$980) × 100 = 134.69. The rate of inflation for 2015 = (134.69 – (134.69 – 100)/100 100)/100 × 100 = 34.69%. c. No, it is not the same. The rate of inflation calculated by the CPI holds holds the basket basket of goods goods and services constant, while the one calculated ca lculated by the GDP deflator allows it to change.

Problem 6:

Which of the problems in the construction of the CPI might be illustrated by each of the following situations? Explain. a. the invention of the cell phone b. the introduction of air bags in cars c. increased personal computer purchases in response to a decline in their price d. more scoops of raisins in each package of Raisin Bran e. greater use of fuel-efficient cars after gasoline prices increase Solution: a. introduction of new goods; b. unmeasured quality change; c. substitution bias; d. unmeasured quality change; e. substitution bias

Problem 7:

The New York Times cost $0.15 in 1970 and $2.00 in 2011. The average wage in manufacturing was $3.36 per hour in 1970 and $23.09 in 2011. a. By what percentage did the price of a newspaper rise? b. By what percentage did the wage rise? c. In each year, how many minutes did a worker have to work to earn enough to buy a newspaper? d. Did workers’ purchasing power in terms of newspapers rise or fall? 8


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Solution: a.

($2.00 – ($2.00 – $0.15)/$0.15 $0.15)/$0.15 × 100 = 1,233%.

b. ($23.09 – ($23.09 – $3.36)/$3.36 $3.36)/$3.36 × 100 = 587%. c. In 1970: $0.15/($3.36/60) = 2.7 minutes. In 2011: $2.00/($23.09/60) = 5.2 minutes. d. Workers' purchasing power in terms terms of newspapers fell.

Problem 8:

The chapter explains that Social Security S ecurity benefits are increased each year in proportion to the increase in the CPI, even though most economists believe that the CPI CP I overstates actual inflation. a. If the elderly consume the same market basket as other people, does Social S ocial Security provide the elderly with an improvement in their standard of living each ea ch year? Explain. b. In fact, the elderly consume more healthcare compared to younger people, and healthcare costs have risen faster than overall inflation. What would you do to determine whether the elderly are actually better off from year to year? Solution: a.

If the elderly consume the same market basket as other people, Social Security would provide the elderly with an improvement in their standard of living each year because the CPI overstates inflation and Social Security payments are tied to the CPI.

b. Because the elderly consume more health care than younger people do, and because health care costs have risen faster than overall inflation, it is possible that the elderly are worse off. To investigate this, you would need to put together a market basket for the elderly, which would have a higher weight on health care. You would then compare the rise in the cost of the "elderly" basket with that of the the general basket for CPI.

Problem 9:

Suppose that a borrower and a lender agree on the nominal interest rate to be paid on a loan. Then inflation turns out to be higher than they both expected. a. Is the real interest rate on this loan higher or lower than expected? b. Does the lender gain or lose from this unexpectedly high inflation? Does the borrower gain or lose? c. Inflation during the 1970s was much higher than most people had expected when the decade began. How did this affect homeowners who obtained fixed-rate mortgages during the 1960s? How did it affect the banks that lent the money? 9


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Solution: a.

When inflation is higher than was expected, the real r eal interest rate is lower than expected. For example, suppose the market equilibrium has an expected real interest rate of 3% and people expect inflation to be 4%, so the nominal interest rate is 7%. If inflation turns out to be 5%, the real interest rate is 7% minus 5% equals 2%, which is less than the 3% that was expected.

b. Because the real interest rate is lower than was expected, the lender loses and the borrower gains. The borrower is repaying the loan with dollars that are worth less than was expected. c.

Homeowners in the 1970s who had fixed-rate mortgages from the 1960s benefited from the unexpected inflation, while the banks that made the mortgage loans were harmed.

Chapter 25. 

Quick Check Multiple Choice : 1-6 (see the textbook) Answers:

1. b 2. c 3. d 4. c 5. c 6. a 


Suppose that society decided to reduce consumption and increase investment. a. How would this change affect economic growth? b. What groups in society would benefit from this change? What groups might be hurt? Solution: a.

More investment investment would lead to faster economic economic growth in the short run. run.

b. The change would benefit many people in society who who would have higher incomes incomes as the result of faster economic growth. However, there might be a transition period in which workers and owners in consumption-good industries would get lower incomes, and workers and owners in investment-good industries industries would get higher incomes. In addition, some group would have to reduce their spending for some time so that investment could rise.

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Problem 4:

What is the opportunity cost of investing in capital? Do you think a country country can “overinvest” in capital? What is the opportunity cost of investing in h uman capital? Do you think a country can “overinvest” in human capital? Explain. Solution: The opportunity cost of investing in capital is the loss of consumption that results from redirecting resources toward investment. Over-investment in capital is possible because of diminishing marginal returns. A country can "over-invest" in capital if people would prefer to have higher consumption spending and less future growth. The opportunity cost of investing in human capital is also the loss of consumption that is needed to provide the resources for investment. A country could "over-invest" in human capital if people were too highly educated for the jobs they could get  for for example, if the best job a Ph.D. in philosophy could find is managing a restaurant. Problem 5:

In the 1990s and the first decade of the 2000s, investors from the Asian economies eco nomies of Japan and China made significant direct and portfolio investments in the United States. At the time, many man y Americans were unhappy that this investment was occurring. a. In what way was it better for the United States to receive this foreign investment than no t to receive it? b. In what way would it have been better still for Americans to have made this investment? Solution: a.

The United States benefited benefited from the Chinese and Japanese investment investment because it it made United States capital stock larger, increasing the economic growth.

b. It would have been better for for Americans to make the investments investments because then they would would have received all of the returns on the investments, instead of the returns going to China and Japan.

Problem 6:

In many developing nations, young women have lower enrollment rates in secondary school than do young men. Describe several ways in which greater educational opportunities opp ortunities for young women could lead to faster economic growth g rowth in these countries. Solution: Greater educational opportunities for women could lead to faster economic growth in these developing countries because increased human capital would increase productivity and there would be external effects from greater knowledge in the country. Sec ond, increased educational opportunities for young women may lower the population growth rate because such opportunities raise the opportunity cost of having a child. 11


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Problem 7:

International data show a positive correlation between income p er person and the health of of the population. a. Explain how higher income might cause better health outcomes. b. Explain how better health outcomes might cause higher income. c. How might the relative importance of your two hypotheses be relevant for public policy? Solution: a.

Individuals with higher higher incomes have better access access to clean water, medical medical care, and good nutrition.

b. Healthier individuals individuals are likely to be more productive. productive. c.

Understanding the direction of causation will help policymakers place place proper emphasis emphasis on the programs that will achieve achieve both greater health and higher higher incomes.

Chapter 26. 

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Quick Check Multiple Choice : 1-6 (see the textbook) Answers: 1. d 2. d 3. c 4. b 5. c 6. a Problems and Applications- Solutions Problem 1:

For each of the following pairs, which bond would you expect to pay a higher interest rate? Explain. a. a bond of the U.S. government or a bond of an Eastern European government b. a bond that repays the principal in year 2020 or a bond that repays the principal in year 2040 c. a bond from Coca-Cola or a bond from a software company you run in your garage Solution: a. The bond of an eastern European government would pay a higher interest rate than the bond of the U.S. government because there would be a greater risk of default. 12


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b. A bond that repays the principal in 2040 would pay a higher interest rate than a bond that repays the principal in 2020 because it has a longer term to maturity, so there is more risk to the principal. c. A bond from from a software company you you run in in your garage would pay a higher interest interest rate than a bond from Coca-Cola because your software company has more credit risk. Problem 2:

Many workers hold large amounts of stock issued by b y the firms at which they work. Why do you suppose companies encourage this behavior? Why might a person not want to hold stock in the company where he works? Solution: Companies encourage their employees to hold stock in the company because it gives the employees the incentive to care about the firm’s profits, not just their own salaries. Then, if employees see waste or see areas in which the th e firm can improve, they will take actions that benefit the company because they know the value of their stock will rise as a result. It also gives employees an additional incentive to work hard, knowing that if the firm does well, they will profit. But from an employee’s point of view, view, owning stock in the company for which she or he works can be risky. The employee’s emplo yee’s wages or salary is already tied to how well the firm performs. If the firm has trouble, trouble, the employee could be laid off or have her or his salary reduced. If the employee owns stock in the firm, then there is a double whammy  the the employee is unemployed or gets a lower salary and the value of the stock falls as well. So owning stock in your own company compan y is a very risky proposition. Most employees would be better off diversifying  owning owning stock or bonds in other companies comp anies  so so their fortunes would not depend so much on the firm for which they work.

Problem 3:

Explain the difference between saving and investment as defined by a macroeconomist. mac roeconomist. Which of the following situations represent investment? Saving? Explain. a. Your family takes out a mortgage and buys a new house. b. You use your $200 paycheck to buy stock in AT&T. c. Your roommate earns $100 and deposits it in his account at a bank. d. You borrow $1,000 from a bank to buy a car to use in your pizza delivery business.

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Solution: To a macroeconomist, saving occurs when a person’s income exceeds his consumption, while investment occurs when a person or firm purchases new capital, such as a house or business equipment. a.

When your family takes takes out a mortgage mortgage and buys buys a new house, that is investment because because it is a purchase of new capital.

b. When you use your $200 paycheck paycheck to buy stock in AT&T, AT&T, that is saving because because your income of $200 is not being spent on consumption goods. c.

When your roommate earns $100 and deposits it in his account at a bank, that is is saving because the money is not spent spent on consumption goods. goods.

d. When you borrow $1,000 from a bank to buy a car to use in your pizza-delivery business, business, that is investment because because the car is a capital good.

Problem 4:

Suppose GDP is $8 trillion, taxes are $1.5 trillion, private saving is $0.5 trillion, and public saving is $0.2 trillion. Assuming this economy is closed, calculate con sumption, government purchases, national saving, and investment Solution: Given that Y = = 8, T = = 1.5, S private = 0.5 = Y – T – C C , S public = 0.2 = T – G G. Because S private = Y – T = Y – T 8 – 1.5 – 1.5 – 0.5 0.5 = 6. T – C C , then rearranging gives C = T – S private = 8 – Because S public = T – G 1.5 – 0.2 0.2 = 1.3. G, then rearranging gives G = T – S S public = 1.5 – Because S = national saving = S private + S public = 0.5 + 0.2 = 0.7. Finally, because I = investment = S , I = 0.7. Problem 5:

Economists in Funlandia, a closed economy, have collected the following information about the economy for a particular year: Y = 10,000 C = 6,000 T = 1,500 G = 1,700 The economists also estimate that the investment function is: I = 3,300 - 100r,

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where r is the country’s real interest rate, expressed as a percentage. Calculate private saving, public saving, national saving, investment, and the equilibrium real interest rate. Solution: Private saving is equal to ( Y – T 10,000 – 1,500 1,500 - 6,000 = 2,500. T – C C ) = 10,000 – Public saving is equal to ( T – G 1,500 – 1,700 1,700 = -200. G) = 1,500 – National saving is equal equal to ( Y – C 10,000 – 6,000 – 6,000 – 1,700 1,700 = 2,300. C – G G) = 10,000 – Investment is equal to saving = 2,300. The equilibrium interest rate is found by setting investment equal to 2,300 and solving for r :

3,300 – 3,300 – 100 100r = = 2,300. 100r = = 1,000. = 10%. r = Problem 6:

Suppose that Intel is considering building a new chipmaking factory. a. Assuming that Intel needs to borrow money mone y in the bond market, why wh y would an increase in interest rates affect Intel’s decision about whether to build the factory? b. If Intel has enough of its own funds to finance the new factory without borrowing, would an increase in interest rates still affect Intel’s decision about whether to build the factory? Ex plain. Solution: a.

If interest rates increase, the costs of borrowing money to build the factory become higher, so the returns from building the new plant may not be sufficient to cover the costs. Thus, higher interest rates make it less likely that Intel will build the new factory.

b. Even if Intel uses its own funds to finance the factory, the rise in interest rates still matters. There is an opportunity cost on the use of the funds. Instead of investing in the factory, f actory, Intel could use the money to purchase bonds and earn the higher interest rate available there. Intel will compare its potential returns from building the factory to the potential returns from the bond market. If interest rates rise, so that bond market returns ret urns rise, Intel is again less likely to invest in the factory.

Problem 7:

Three students have each saved $1,000. Each has an investment opportunity in which he or she can invest up to $2,000. $2,0 00. Here are the rates of return on o n the students’ investment projects: Harry

5 percent

Ron

8 percent

Hermione

20 percent 15


Fall 2017

a. If borrowing and lending is prohibited, so each student uses only personal saving to finance his or her own investment project, how much will each student have a year later when the project pays its return? b. Now suppose their school opens up a market for loanable funds in which students can borrow and lend among themselves at an interest rate r. What would determine whether a student would choose to be a borrower or lender in this market? c. Among these three students, what would be the quantity of loanable funds supplied and quantity demanded at an interest rate of 7 percent? At 10 percent? d. At what interest rate would the loanable funds market among these three students be in equilibrium? At this interest rate, which student(s) would borrow and which student(s) would lend? e. At the equilibrium interest rate, how much does each student have a year later after the investment projects pay their return and loans have been repaid? Compare your answers to those you gave in part (a). Who benefits from the existence of the loanable funds market — — the the borrowers or the lenders? Is anyone worse off? Solution: a.

Harry will have $1,000(1 + 0.05) = $1,050. Ron will have have $1,000(1 + 0.08) = $1,080. $1,080. Hermione will have $1,000(1 + 0.20) = $1,200. b. Each student would compare compare the expected rate of return on his or her her own project with the market rate of interest ( r ). ). If the expected rate of return is greater than r , the student would borrow. If the expected rate of return is less less than r , the student would lend. c. If r = = 7%, Harry would want to lend while Ron and Hermione would want to borrow. The quantity of funds demanded would be $2,000, while the quantity supplied would be $1,000. If r = = 10%, only Hermione would want to borrow. The quantity of funds demanded would be $1,000, while the quantity supplied would be $2,000. d. The loanable funds market would be in equilibrium equilibrium at an interest rate of 8%. Harry Harry would want to lend and Hermione would want to borrow. Ron would use his own savings for his project, but would want to neither borrow nor lend. Thus Thus quantity demanded = quantity quantity supplied = $1,000. e. Harry will have $1,000(1 + 0.08) = $1,080. Ron will have have $1,000(1 + 0.08) = $1,080. Hermione will have $2,000(1 + 0.20) – $1,000(1 $1,000(1 + 0.08) = $2,400 – $2,400 – $1,080 $1,080 = $1,320. Both borrowers and lenders are better better off. No one is worse off.

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