Exercises: Price Indices, the CPI, and the Costs of Inflation

Define the consumer price index (CPI) and the market basket it uses. Name the US government agency that calculates the CPI.

A fixed market basket costs $\$200$ in the base year and $\$230$ in the current year. Compute the CPI for the current year. Show the formula you use.

The CPI was 250 last year and is 260 this year. Compute the inflation rate between the two years. State whether the economy experienced inflation, deflation, or disinflation if last year's inflation rate had been 6%.

A college student's market basket contains 10 burgers and 5 movie tickets. In the base year, a burger costs $\$4$ and a ticket costs $\$10$. In the current year, a burger costs $\$5$ and a ticket costs $\$12$. Compute the cost of the basket in each year and the CPI for the current year. Then explain in words what that CPI value means.

When inflation reaches 12% per year, a restaurant chain must reprint its menus every month, and many households make extra trips to the bank so they hold less cash that loses value. Identify which cost of inflation each of these two situations illustrates (shoe-leather costs or menu costs), and explain each one. Then explain why these costs are larger when inflation is high.

Mateo borrows from a bank at a fixed nominal interest rate of 4%. At the time, both he and the bank expected inflation of 2% over the loan period. Actual inflation turns out to be 5%. Compute the expected real interest rate and the actual real interest rate. Who gains and who loses from the unexpected inflation, and why?

The CPI is 200 in year 1, 210 in year 2, and 220.5 in year 3. Sophia's annual salary is $\$50{,}000$ in year 1, $\$52{,}000$ in year 2, and $\$53{,}000$ in year 3. (a) Compute the inflation rate in years 2 and 3. (b) Compute Sophia's salary in each year expressed in year 1 dollars. (c) Evaluate whether her purchasing power rose or fell over the period, and explain what this tells you about comparing nominal incomes across time.

A CPI-style basket in the base year contains 10 pounds of beef at $\$5$ per pound and 10 pounds of chicken at $\$3$ per pound. In the current year, beef costs $\$8$ per pound and chicken costs $\$3.30$ per pound. (a) Compute the CPI for the current year using the fixed basket. (b) Consumers respond by buying only 5 pounds of beef and 15 pounds of chicken. Compute the cost of this new bundle at base-year prices and at current prices, and the price index implied by those two costs. (c) Explain what these results show about substitution bias in the CPI, and name one other reason the CPI can overstate the true change in the cost of living.