Chapter 7: Measuring Domestic Output and National Income
Practice Problems
Warm-Up: Quick Concept and Calculation Checks
- A furniture maker buys $300 worth of lumber and uses it to build a table it sells for $750. How much value did the furniture maker add?
- Is the steel an automaker buys a final good or an intermediate good? What about the finished car a family buys?
- A student resells last year’s textbook to a classmate for $40. Does this sale count in this year’s GDP? Why or why not?
- A government agency mails $800 in food assistance benefits to a family. Does this count as government purchases (G) in GDP? Why or why not?
- For each purchase, name the GDP component (C, Ig, G, or Xn): (i) a family buys a new washing machine, (ii) a bakery buys a new delivery van, (iii) a city pays a contractor to repave a road, (iv) a foreign customer buys a U.S.-made tractor.
- A country exports $40 billion of goods and services and imports $55 billion. What are its net exports?
- Nominal GDP is $2,400 billion and the GDP price index is 120. What is real GDP?
- A neighbor volunteers 10 hours a week at a food bank. Does that work show up in GDP? Why or why not?
Show Answer
- \(\$750 - \$300 = \$450\) of value added.
- The steel is an intermediate good (it is used up making something else). The finished car is a final good (bought by its end user).
- No. The textbook was already counted in GDP in the year it was produced. Resale does not measure new production.
- No. Food assistance benefits are transfer payments, money moved from one person to another without a good or service being produced in exchange. Government purchases (G) count only spending on newly produced goods and services.
- C (a consumer durable good). (ii) Ig (new capital equipment for a business). (iii) G (a government purchase of a service). (iv) Xn (an export, which adds to net exports).
- \(\$40 - \$55 = -\$15\) billion. Net exports can be negative.
- Real GDP \(= \$2{,}400 / (120/100) = \$2{,}000\) billion.
- No. Volunteer work involves no market transaction, so it is not counted, even though it clearly produces something of value.
Problem 1: GDP by the Expenditures Approach
A small country reports the following figures for one year (in billions of dollars):
| Item | Amount |
|---|---|
| Personal consumption expenditures | $620 |
| Gross private domestic investment | $150 |
| Government purchases of goods and services | $210 |
| Exports | $95 |
| Imports | $120 |
| Unemployment benefits and other transfer payments | $80 |
| Purchases of existing stocks and bonds | $45 |
| Sales of secondhand goods | $12 |
| Depreciation (consumption of fixed capital) | $35 |
- What are net exports?
- Calculate GDP using the expenditures approach.
- Three of the items in the table should not be included in GDP. Which ones, and why?
- Calculate net domestic product (NDP) and net private domestic investment.
Show Answer
- Net exports \(= \$95 - \$120 = -\$25\) billion.
- GDP \(= C + I_g + G + X_n = 620 + 150 + 210 + (-25) = \$955\) billion.
- Transfer payments ($80): no good or service is produced in exchange. Purchases of existing stocks and bonds ($45): just a transfer of ownership of existing financial assets, not production. Sales of secondhand goods ($12): those goods were counted in GDP when they were first produced.
- NDP \(=\) GDP \(-\) depreciation \(= 955 - 35 = \$920\) billion. Net private domestic investment \(=\) gross investment \(-\) depreciation \(= 150 - 35 = \$115\) billion.
Problem 2: From GDP to Disposable Income
Another economy reports these national income figures (in billions of dollars). Assume the statistical discrepancy and net foreign factor income are both zero.
| Item | Amount |
|---|---|
| Compensation of employees | $560 |
| Rents | $20 |
| Interest | $30 |
| Proprietors’ income | $70 |
| Corporate profits | $110 |
| Taxes on production and imports | $65 |
| Depreciation (consumption of fixed capital) | $90 |
| Social Security contributions | $55 |
| Corporate income taxes | $35 |
| Undistributed corporate profits | $40 |
| Transfer payments | $85 |
| Personal taxes | $60 |
- Calculate national income (NI) by adding up the types of income and taxes on production and imports.
- Calculate GDP and NDP using the income approach.
- Calculate personal income (PI).
- Calculate disposable income (DI).
- What share of national income is compensation of employees?
Show Answer
- NI \(= 560 + 20 + 30 + 70 + 110 + 65 = \$855\) billion.
- GDP \(=\) NI \(+\) depreciation \(= 855 + 90 = \$945\) billion. NDP \(=\) GDP \(-\) depreciation \(= \$855\) billion (equal to NI here because the statistical discrepancy and net foreign factor income are zero).
- PI \(= 855 - 65 - 55 - 35 - 40 + 85 = \$745\) billion. Taxes on production and imports, Social Security contributions, corporate income taxes, and undistributed profits are earned but never reach households, so they are subtracted. Transfer payments reach households without being earned by producing anything, so they are added.
- DI \(= 745 - 60 = \$685\) billion. Disposable income is what households actually have available to spend or save.
- \(560 / 855 \approx 65.5\) percent. Wages, salaries, and benefits are by far the largest slice of national income.
Problem 3: Nominal vs. Real GDP with Multiple Goods
A small economy produces only two goods, coffee and phone chargers. Prices and quantities in Year 1 (the base year) and Year 2 are:
| Year 1 Price | Year 1 Quantity | Year 2 Price | Year 2 Quantity | |
|---|---|---|---|---|
| Coffee | $2 | 100 | $3 | 120 |
| Phone chargers | $5 | 40 | $6 | 45 |
- Compute nominal GDP in Year 1 and in Year 2.
- Compute real GDP in Year 2, using Year 1 as the base year (that is, value Year 2 quantities at Year 1 prices).
- What is the nominal GDP growth rate from Year 1 to Year 2? What is the real GDP growth rate?
- These two growth rates are quite different. What does that difference tell you about what actually happened in this economy?
Show Answer
- Nominal GDP, Year 1: \((2 \times 100) + (5 \times 40) = 200 + 200 = \$400\). Nominal GDP, Year 2: \((3 \times 120) + (6 \times 45) = 360 + 270 = \$630\).
- Real GDP, Year 2 (in Year 1 prices): \((2 \times 120) + (5 \times 45) = 240 + 225 = \$465\).
- Nominal GDP growth: \((630 - 400)/400 = 57.5\) percent. Real GDP growth: \((465 - 400)/400 = 16.25\) percent.
- Nominal GDP growth (57.5 percent) reflects both more output and higher prices for both goods. Real GDP growth (16.25 percent) strips out the price increases by valuing both years’ output at the same, Year 1, prices, so it isolates how much more stuff the economy actually produced. The large gap between the two growth rates tells us that a substantial part of this economy’s nominal growth was simply inflation, not a real increase in output, which is exactly why economists track real GDP rather than nominal GDP when asking whether an economy is actually producing more.
Problem 4: Deflating Nominal GDP with a Price Index
An economy reports nominal GDP and a GDP price index (with 2020 as the base year, so the index equals 100 in 2020):
| Year | Nominal GDP (billions) | GDP Price Index |
|---|---|---|
| 2020 | $1,800 | 100 |
| 2022 | $2,160 | 108 |
| 2024 | $2,600 | 125 |
- Calculate real GDP for each year (in 2020 dollars).
- Calculate the growth rate of nominal GDP and of real GDP from 2022 to 2024.
- For 2022 and 2024, are you inflating or deflating nominal GDP to get real GDP? Why?
- By how much did the overall price level rise from 2022 to 2024? How does that compare with the gap between the two growth rates in part (b)?
Show Answer
- Real GDP \(=\) nominal GDP \(/ (\text{index}/100)\). 2020: \(1{,}800 / 1.00 = \$1{,}800\) billion. 2022: \(2{,}160 / 1.08 = \$2{,}000\) billion. 2024: \(2{,}600 / 1.25 = \$2{,}080\) billion.
- Nominal growth, 2022 to 2024: \((2{,}600 - 2{,}160)/2{,}160 \approx 20.4\) percent. Real growth: \((2{,}080 - 2{,}000)/2{,}000 = 4.0\) percent.
- Deflating. In both years the price index is above 100 (prices are higher than in the base year), so nominal GDP overstates output and has to be scaled down to get real GDP.
- The price level rose \((125 - 108)/108 \approx 15.7\) percent. That inflation accounts for most of the gap between 20.4 percent nominal growth and 4.0 percent real growth. Only the 4.0 percent is actual growth in output.
Problem 5: Is Higher GDP Per Capita Always Better?
Two countries have these (hypothetical) figures per person per year:
| Country A | Country B | |
|---|---|---|
| Measured GDP per capita | $50,000 | $46,000 |
| Estimated value of unpaid household work (cooking, childcare, home repair) | $8,000 | $14,000 |
| Average work week | 46 hours | 36 hours |
| Paid vacation | 10 days | 30 days |
- Which country has the higher measured GDP per capita?
- Add the value of unpaid household work to each country’s GDP per capita. Which country is ahead now?
- Name two other things in the table, or beyond it, that GDP fails to capture and that might change your view of which country’s residents are better off.
- Despite these shortcomings, why do economists still rely on GDP so heavily?
Show Answer
- Country A: $50,000 versus $46,000 for Country B.
- Country A: $50,000 \(+\) $8,000 \(=\) $58,000. Country B: $46,000 \(+\) $14,000 \(=\) $60,000. Once unpaid work is counted, Country B comes out ahead, the ranking flips.
- Leisure: Country B residents work ten fewer hours each week and get twice as much vacation, and GDP assigns that free time no value at all. Other examples: environmental damage and pollution (production is counted, damage is not subtracted), the underground economy (real output that goes unrecorded), and how evenly the income is distributed (a mean says nothing about the typical household, as in Chapter 6).
- GDP is measured consistently across countries and over time, follows clear rules, and is strongly correlated with many things people care about, like life expectancy and education. It is an imperfect but useful measure of a country’s production, not a complete measure of its well-being.