Chapter 6: An Introduction to Macroeconomics

Practice Problems

Warm-Up: Quick Concept and Calculation Checks

1. A town’s population grows from 8,000 to 8,400 in one year. What is the population growth rate?
2. A country’s real GDP is $50 million and its population is 25,000. What is real GDP per capita?
3. A household saves $500 per month. How much total saving does that household contribute in one year?
4. A $10,000 investment is expected to generate $800 per year in profit. What is the expected rate of return?
5. A retiree buys 10 shares of an existing company’s stock on the stock market. Does this count as Investment in the economic sense? Why or why not?
6. A bakery purchases a new industrial oven to expand production. Does this count as Investment in the economic sense? Why or why not?
7. A landlord signs a 12-month apartment lease with tenants at a fixed monthly rent. Is this price sticky or flexible?
8. The price of Bitcoin on a cryptocurrency exchange. Is this price sticky or flexible?

Show Answer

1. \((8{,}400 - 8{,}000)/8{,}000 = 5\) percent.
2. \(\$50{,}000{,}000 / 25{,}000 = \$2{,}000\) per person.
3. \(\$500 \times 12 = \$6{,}000\) per year.
4. \(\$800 / \$10{,}000 = 8\) percent.
5. No. Buying existing shares just transfers ownership of an already-existing asset from one person to another, it does not create any new capital.
6. Yes. A new oven is new capital equipment that expands the firm’s ability to produce, exactly what economic Investment means.
7. Sticky. The rent is locked in by a 12-month lease regardless of changing market conditions.
8. Flexible. Cryptocurrency prices trade continuously on an exchange and adjust to new information almost instantly.

Problem 1: Total Growth vs. Per-Capita Growth

A country’s real GDP grows from $18.0 trillion to $18.9 trillion over one year. Over that same year, the country’s population grows from 300 million to 306 million people.

1. What is the percentage growth rate of total real GDP?
2. What is real GDP per capita in each year?
3. What is the percentage growth rate of real GDP per capita?
4. Why is the answer to (c) smaller than the answer to (a)?

Show Answer

1. Growth rate of total real GDP = ($18.9 trillion minus $18.0 trillion) divided by $18.0 trillion = $0.9 trillion divided by $18.0 trillion = 5.0 percent.
2. Real GDP per capita, year 1: $18.0 trillion divided by 300 million = $60,000. Year 2: $18.9 trillion divided by 306 million = $61,765 (rounded).
3. Growth rate of real GDP per capita = ($61,765 minus $60,000) divided by $60,000 = about 2.9 percent.
4. Total output grew 5.0 percent, but population also grew (from 300 million to 306 million, a 2.0 percent increase). Since that larger output has to be divided among more people, the increase in living standards per person is smaller than the increase in total output. This is why economists track GDP per capita, not just total GDP, when asking whether people are actually getting better off.

Problem 2: Saving, Investment, and Expected Returns

A firm is deciding whether to build a new factory that costs $5 million. The firm forecasts the factory would generate $600,000 in additional profit per year.

1. What annual rate of return does the firm expect on this $5 million investment?
2. If interest rates rise and the firm could instead earn a guaranteed 8 percent per year by simply depositing that $5 million in a bank, should the firm still build the factory? Explain using the idea of expected returns.
3. Explain, in one or two sentences, why a general rise in interest rates throughout the economy tends to reduce the total amount of economic investment.

Show Answer

1. Expected rate of return = $600,000 divided by $5,000,000 = 12 percent per year.
2. The factory still expected to return 12 percent, comfortably more than the guaranteed 8 percent from a bank deposit, so the firm should still build it. The factory return does carry more risk than a bank deposit, but as long as the firm believes 12 percent is the fair expected return for that risk, it remains the better choice.
3. Investment projects only get funded when the expected return on the project beats the return available elsewhere, such as a bank deposit or bond. When interest rates rise economy-wide, the bar an investment project has to clear rises too, so fewer projects have an expected return high enough to be worth funding, and total investment falls.

Problem 3: When the Average Isn’t the Typical Household

A small country has exactly 5 households. Their annual incomes in Year 1 and Year 2 are:

Household	Year 1 Income	Year 2 Income
1	$30,000	$31,000
2	$32,000	$33,000
3	$35,000	$36,000
4	$38,000	$39,000
5	$65,000	$111,000

1. Compute the mean (average) household income in Year 1 and in Year 2, and the growth rate of the mean.
2. Compute the median household income in Year 1 and in Year 2 (the income of the middle household when incomes are sorted low to high), and the growth rate of the median.
3. A news report says “average income in this country grew 25 percent this year.” Is that statement misleading? Why or why not?
4. Relate this example back to the GDP per capita versus median household income discussion from the slides. Why might a country with healthy GDP-per-capita growth still have a lot of unhappy citizens?

Show Answer

1. Mean, Year 1: \((30{,}000+32{,}000+35{,}000+38{,}000+65{,}000)/5 = 200{,}000/5 = \$40{,}000\). Mean, Year 2: \((31{,}000+33{,}000+36{,}000+39{,}000+111{,}000)/5 = 250{,}000/5 = \$50{,}000\). Growth rate of the mean: \((50{,}000-40{,}000)/40{,}000 = 25\) percent.
2. Median, Year 1 (middle of 30, 32, 35, 38, 65): $35,000. Median, Year 2 (middle of 31, 33, 36, 39, 111): $36,000. Growth rate of the median: \((36{,}000-35{,}000)/35{,}000 \approx 2.9\) percent.
3. It is technically true but misleading. The 25 percent figure is entirely driven by Household 5, whose income nearly doubled, while the other four households, four out of five people in this economy, saw incomes rise only about 3 percent. The “average person” implied by the mean does not resemble any actual household here.
4. GDP per capita is a mean, just like average income in this example. When growth is concentrated among a relatively small share of the population, GDP per capita can rise substantially even while the typical (median) household’s living standard barely improves. That gap between a healthy aggregate statistic and a stagnant typical experience is exactly the kind of thing that can make official “the economy is growing” headlines feel disconnected from how most people actually feel.

Problem 4: The Market for Loanable Funds

Chapter 3 introduced supply and demand for goods, like soybeans or textbooks. The same model can describe the market where saving meets investment, called the market for loanable funds. Savers supply funds to this market (depositing money in banks, buying bonds), hoping to earn interest. Borrowers, often firms that want to invest, demand funds from this market, and have to pay interest to get them.

The table below shows the (hypothetical) market for loanable funds in a country.

Interest Rate	Quantity of Saving Supplied	Quantity of Investment Demanded
2%	$100 billion	$400 billion
3%	$150 billion	$350 billion
4%	$200 billion	$300 billion
5%	$250 billion	$250 billion
6%	$300 billion	$200 billion
7%	$350 billion	$150 billion

1. Why does it make sense to treat saving as a supply curve and investment as a demand curve in this market? What plays the role of “price”?
2. Using the table, what is the equilibrium interest rate, and what quantity of funds gets loaned at that rate?
3. Suppose the interest rate is temporarily stuck at 3 percent. Is there a shortage or surplus of loanable funds at that rate, and how large? Which direction would you expect the interest rate to move to restore equilibrium?
4. Using what you learned about supply and demand shifts in Chapter 3: if a new government policy encourages people to save more at every interest rate (the saving curve shifts right), what happens to the equilibrium interest rate and the equilibrium quantity of loanable funds?

Show Answer

1. Savers act like sellers, they supply more funds to the market as the reward for doing so (the interest rate) rises, just like a seller offers more of a good as its price rises. Borrowers act like buyers, they demand fewer funds as the cost of borrowing (the interest rate) rises, just like a buyer demands less of a good as its price rises. The interest rate plays the role of price in this market.
2. Equilibrium interest rate is 5 percent, where quantity of saving supplied equals quantity of investment demanded, both equal $250 billion.
3. At 3 percent, quantity of saving supplied is $150 billion but quantity of investment demanded is $350 billion. That is a shortage of loanable funds of $200 billion, borrowers want far more funds than savers are offering at that low rate. Just like a shortage in a goods market, this pushes the interest rate up toward the \(5\) percent equilibrium, as borrowers compete for the scarce funds available.
4. This is exactly the same logic as a rightward supply shift in Chapter 3: more funds supplied at every interest rate pushes the equilibrium interest rate down and the equilibrium quantity of loanable funds up. Cheaper borrowing (a lower interest rate) is also exactly the kind of change that, from the investment decisions slide, would encourage firms to invest more.