Chapter 9: Business Cycles, Unemployment, and Inflation

Practice Problems

Warm-Up: Quick Concept and Calculation Checks

  1. In a small town, 142 people are employed and 8 are actively looking for work but do not have a job. What is the size of the labor force?
  2. Using the town from part (a), what is the unemployment rate?
  3. For each person, say whether they are counted as unemployed, employed, or not in the labor force: (i) a retiree who is not looking for work, (ii) a college student working 10 hours a week at a campus job, (iii) a laid-off worker who has stopped looking for a job entirely.
  4. For each situation, name the type of unemployment (frictional, structural, cyclical, or seasonal): (i) a ski instructor is out of work every summer, (ii) a recession sharply reduces orders at a factory and workers are laid off, (iii) a recent graduate spends three weeks interviewing before accepting a job offer, (iv) a coal miner’s skills no longer match the jobs available after coal plants close in the region.
  5. The Consumer Price Index rises from 210.0 to 218.5 over one year. What is the inflation rate?
  6. The nominal interest rate on a loan is 6 percent, and inflation is 3.5 percent. What is the approximate real interest rate?
  7. True or False: full employment means the unemployment rate is zero percent.
Show Answer
  1. \(142 + 8 = 150\) people.
  2. \(8 / 150 \approx 5.3\) percent.
    1. Not in the labor force (not looking for work). (ii) Employed (has a job, even part-time). (iii) Not in the labor force (a discouraged worker who stopped looking is no longer counted as unemployed).
    1. Seasonal. (ii) Cyclical. (iii) Frictional. (iv) Structural.
  5. \((218.5 - 210.0)/210.0 \approx 4.0\) percent.
  6. \(6 - 3.5 = 2.5\) percent.
  7. False. Full employment means cyclical unemployment is zero, but frictional and structural unemployment (the natural rate) are still present even in a healthy economy.

Problem 1: The Labor Force and the Unemployment Rate

A regional economy has a working-age population of 500,000 people. Of these, 60,000 are retired, full-time students, or otherwise not looking for work. Of the people who remain, 405,000 currently have jobs.

  1. How many people are in the labor force?
  2. How many people are unemployed?
  3. What is the unemployment rate?
  4. What is the labor force participation rate (labor force divided by the working-age population)?
  5. Suppose 5,000 unemployed workers become discouraged and stop looking for work altogether, with no other changes. What happens to the labor force, the unemployment rate, and the labor force participation rate?
Show Answer
  1. Labor force \(= 500{,}000 - 60{,}000 = 440{,}000\).
  2. Unemployed \(= 440{,}000 - 405{,}000 = 35{,}000\).
  3. Unemployment rate \(= 35{,}000 / 440{,}000 \approx 8.0\) percent.
  4. Participation rate \(= 440{,}000 / 500{,}000 = 88.0\) percent.
  5. The labor force shrinks to \(435{,}000\) (those 5,000 people are no longer counted as looking for work). Unemployed falls to \(30{,}000\), so the unemployment rate becomes \(30{,}000/435{,}000 \approx 6.9\) percent, it falls, even though nobody found a job. The participation rate falls to \(435{,}000/500{,}000 = 87.0\) percent. This is a classic case where a falling unemployment rate does not necessarily mean the job market improved.

Problem 2: Tracking Inflation with the CPI

The table below shows a country’s Consumer Price Index over three years (base period CPI \(=100\)).

Year CPI
1 204.0
2 211.0
3 219.0
  1. What was the inflation rate from Year 1 to Year 2?
  2. What was the inflation rate from Year 2 to Year 3?
  3. A worker’s nominal wage was $22.00 per hour in Year 1 and rose to $22.75 in Year 2. Did the worker’s real wage rise or fall from Year 1 to Year 2? (Compare the wage’s percent growth to the inflation rate you found in part (a).)
  4. If the CPI had instead fallen from 204.0 to 200.0 over a year, what would we call that situation, and what would it mean for the purchasing power of a dollar?
Show Answer
  1. \((211.0 - 204.0)/204.0 \approx 3.4\) percent.
  2. \((219.0 - 211.0)/211.0 \approx 3.8\) percent.
  3. The wage grew \((22.75 - 22.00)/22.00 \approx 3.4\) percent, almost exactly matching the 3.4 percent inflation rate from part (a). The worker’s real wage stayed roughly flat, the raise kept pace with inflation but did not get the worker ahead.
  4. That would be deflation, a general decline in the price level. A dollar would buy more than before, its purchasing power would rise.

Problem 3: Who Wins and Who Loses from Inflation?

Inflation over one year turns out to be 6 percent, higher than almost anyone expected.

  1. A retiree lives on a pension fixed at $2,400 per month in nominal dollars. What happens to the real value of that pension over the year?
  2. A homeowner has a 30-year mortgage with a fixed interest rate of 4 percent, borrowed before the inflation surprise. Are they better off or worse off because of the unexpectedly high inflation? Why?
  3. A worker’s employer raises her nominal salary from $58,000 to $60,500 for the year. Is her real income rising or falling? By approximately how much?
  4. Based on (a) through (c), state in one sentence who tends to gain and who tends to lose from unanticipated inflation.
Show Answer
  1. The pension stays fixed in nominal dollars, but prices rose 6 percent, so its real purchasing power falls by roughly 6 percent.
  2. Better off. They are repaying a fixed 4 percent rate with dollars that are now worth less than expected, unanticipated inflation transfers real value from lenders to borrowers with fixed-rate debt.
  3. Nominal salary grew \((60{,}500-58{,}000)/58{,}000 \approx 4.3\) percent, which is less than the 6 percent inflation rate, so her real income falls by roughly \(4.3 - 6 = -1.7\) percent.
  4. Losers tend to be people with fixed nominal incomes and savers or lenders holding fixed-rate debt; winners tend to be borrowers repaying fixed-rate debt with money that is now worth less.

Problem 4: Business Cycle Phases and the Cost of Inflation

  1. Put these four phases of the business cycle in order, starting from a business cycle peak: trough, expansion, peak, recession.
  2. During a recession, which industry would you expect to see a larger drop in sales: a grocery store, or a company that manufactures new cars? Explain using the idea of postponable spending.
  3. A country’s inflation rate accelerates from a modest 3 percent to over 200 percent per year (hyperinflation). What are some ways this could damage the economy’s total output, beyond simply making goods more expensive?
  4. Explain briefly why even a low, stable, fully anticipated inflation rate (say, 2 percent) still imposes some real cost on an economy, rather than being completely harmless.
Show Answer
  1. Peak, recession, trough, expansion, and then back toward a new peak.
  2. The car manufacturer. Cars are a durable good, and durable-good purchases can be postponed, a household can keep driving its current car for another year or two if money is tight. Grocery spending on food is much harder to postpone, so it holds up better in a downturn.
  3. Many possible answers: people rush to spend money immediately before it loses more value, which disrupts normal saving and planning; businesses struggle to set prices and sign contracts when prices change by the day or hour; normal exchange breaks down as money stops functioning as a reliable store of value, all of which can cause total output to fall sharply.
  4. Even fully anticipated inflation imposes menu costs (the real resources businesses spend updating posted prices, menus, and contracts) and shoe-leather costs (the time and effort people spend trying to avoid holding cash that is losing value, such as more frequent trips to the bank). These are real resources used up simply coping with inflation rather than producing goods and services.