Chapter 8: Economic Growth

Practice Problems

Warm-Up: Quick Concept and Calculation Checks

  1. A country’s real GDP per capita grows at 2.5 percent per year. Using the Rule of 70, approximately how many years will it take to double?
  2. A country’s real GDP per capita grows at 5 percent per year instead. Approximately how many years will it take to double?
  3. For each, say whether it is a supply factor, the demand factor, or the efficiency factor in economic growth: (i) a country discovers a large new oil field, (ii) total spending in the economy is too low to buy up all the goods the economy is capable of producing, (iii) a factory switches from an outdated, high-cost production method to a modern, lower-cost one.
  4. In a given year, hours worked in an economy grow 0.8 percent and labor productivity (output per hour) grows 2.1 percent. Approximately what is the growth rate of real GDP?
  5. Rank these contributors to U.S. productivity growth from most to least quantitatively important, according to growth accounting studies: education and training, technological advance, capital per worker (capital deepening), economies of scale and improved resource allocation.
  6. True or False: a positive relationship between a nation’s productivity growth rate and its average real hourly wage growth rate exists because competitive labor markets tend to pay workers according to what they produce.
Show Answer
  1. \(70 / 2.5 = 28\) years.
  2. \(70 / 5 = 14\) years.
    1. Supply factor (more natural resources). (ii) Demand factor (total spending must be enough to purchase the expanding potential output). (iii) Efficiency factor (using resources at their lowest-cost combination, productive efficiency).
  4. Approximately \(0.8 + 2.1 = 2.9\) percent (labor input growth plus productivity growth).
  5. Largest to smallest: technological advance, capital per worker, education and training, economies of scale and improved resource allocation.
  6. True.

Problem 1: Small Growth Differences, Compounded

Country A and Country B both start with real GDP per capita of $8,000. Country A grows at 2 percent per year. Country B grows at 4 percent per year.

  1. Using the Rule of 70, how many years does it take each country to double its GDP per capita?
  2. Estimate each country’s real GDP per capita after 35 years by compounding the growth rate year by year.
  3. How many times larger is Country B’s GDP per capita than Country A’s after 35 years?
  4. Both countries started at the same GDP per capita and neither growth rate sounds dramatic in a single year. What does this problem illustrate about long-run growth?
Show Answer
  1. Country A: \(70/2 = 35\) years. Country B: \(70/4 = 17.5\) years.
  2. Country A: \(8{,}000 \times 1.02^{35} \approx \$16{,}000\). Country B: \(8{,}000 \times 1.04^{35} \approx \$31{,}600\).
  3. \(31{,}600 / 16{,}000 \approx 2.0\), Country B’s GDP per capita is about twice Country A’s after 35 years, even though B’s doubling time is only half of A’s.
  4. A growth rate that looks small year to year, a gap of just 2 percentage points here, compounds into an enormous difference in living standards over a working lifetime. This is exactly why economists care so much about small, sustained differences in growth rates rather than dismissing them as trivial.

Problem 2: Where Does Growth Come From?

An economy’s real GDP grew by approximately 3.2 percent over one year. Economists estimate that total hours worked in the economy grew by 0.9 percent over the same year.

  1. Approximately what was the growth rate of labor productivity (output per hour) that year?
  2. If, instead, hours worked had fallen by 0.4 percent while real GDP still grew 3.2 percent, approximately what would labor productivity growth have been?
  3. In part (b), the economy produced more total output with fewer hours worked. What does that imply about labor productivity, and why might that be a healthier long-run growth pattern than growth driven mainly by more hours worked?
Show Answer
  1. Real GDP growth is approximately labor input growth plus productivity growth, so \(3.2 - 0.9 = 2.3\) percent productivity growth.
  2. \(3.2 - (-0.4) = 3.6\) percent productivity growth.
  3. It implies productivity grew faster than total output, each hour worked produced substantially more. Growth driven by rising productivity can continue indefinitely as workers and firms find better technology, tools, and methods, while growth driven mainly by working more hours runs into a hard limit, there are only so many hours in a day and so many working-age people. Sustained increases in living standards ultimately depend on productivity growth, not on people simply working more.

Problem 3: Is Faster Growth Always Better?

A country is debating a policy that would raise its long-run real GDP growth rate from 2.0 percent to 3.0 percent per year, mainly by encouraging more saving, investment in new capital, and faster adoption of new technology.

  1. Using the Rule of 70, how much sooner would the country’s GDP per capita double under the faster growth rate?
  2. Name one real resource cost this faster growth might require today, connecting back to the Chapter 6 saving and investment tradeoff.
  3. Suppose the policy succeeds in raising average GDP per capita, but nearly all of the additional growth goes to the top of the income distribution. Connecting back to Chapter 6, why might the typical household not feel much better off, even though the national statistics look better?
  4. Name one non-income cost that faster growth might impose that GDP per capita does not capture at all.
Show Answer
  1. Doubling time at 2 percent: \(70/2 = 35\) years. At 3 percent: \(70/3 \approx 23.3\) years. The faster growth rate would cut the doubling time by roughly 12 years.
  2. More investment in new capital means less current consumption, resources devoted to building factories, machines, and infrastructure today are resources not used to produce consumer goods today. That is the same saving-versus-consumption tradeoff from Chapter 6.
  3. GDP per capita is a mean. If growth is concentrated among a small share of households, the mean can rise substantially while the median household’s income barely changes, the same mean-versus-median gap discussed in Chapter 6.
  4. Any reasonable answer describing an externality or nonmarket cost is acceptable, for example: environmental damage from more production, resource depletion, or less leisure time if the faster growth comes from working more rather than working smarter.