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Chapter 17: Problem 8

Suppose a typical automobile tire cost \(\$ 50\) in the base year and had a useful life of 40,000 miles. Ten years later, the typical automobile tire \(\operatorname{cost} \$ 75\) and had a useful life of 75,000 miles. If no adjustment is made for mileage, the CPI would a. underestimate inflation between the two years. b. overestimate inflation between the two years. c. accurately measure inflation between the two years. d. not measure inflation in this case.

Short Answer

Expert verified
In this case, the unadjusted CPI overestimates inflation between the two years because it does not take into account the change in price per mile. The price increased by 50%, but the price per mile decreased by 25%. Therefore, the correct answer is b. overestimate inflation between the two years.

Step by step solution

01

Calculate the price per mile in the base year and ten years later.

In the base year, the tire costs \(50 with a lifespan of 40,000 miles. Ten years later, the tire costs \)75 with a lifespan of 75,000 miles. We need to calculate the price per mile for both years so that we can compare them properly. Base year price per mile: \( \frac{50}{40000} = \frac{1}{800} \) Ten years later price per mile: \( \frac{75}{75000} = \frac{1}{1000} \)
02

Calculate the percentage change in price.

To determine the percentage change in price between the two years, we will use the formula: % change in price = \( \frac{NewPrice - OldPrice}{OldPrice} \times 100 \) % change in price between years = \( \frac{75 - 50}{50} \times 100 \) % change in price between years = \( \frac{25}{50} \times 100 = 50\% \) The increase in price is 50%.
03

Calculate the percentage change in price per mile.

Now, we will calculate the percentage change in price per mile between the two years. % change in price per mile = \( \frac{NewPricePerMile - OldPricePerMile}{OldPricePerMile} \times 100 \) % change in price per mile = \( \frac{\frac{1}{1000} - \frac{1}{800}}{\frac{1}{800}} \times 100 \) % change in price per mile = \( \frac{-\frac{1}{4000}}{\frac{1}{800}} \times 100 = -25\% \) The price per mile has decreased by 25%.
04

Determine the effect of CPI unadjusted for mileage.

In this case, the CPI would be based solely on the price change of 50%. However, we can see that the price per mile (the actual cost of using the tires) has decreased by 25%. This means that the unadjusted CPI overestimates inflation between the two years. Thus, the correct answer is: b. overestimate inflation between the two years.

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Most popular questions from this chapter

When the inflation rate rises, the purchasing power of nominal income a. remains unchanged. b. decreases. c. increases. d. changes by the inflation rate minus one.

Which of the following would overstate the consumer price index? a. Substitution bias b. Improving quality of products c. Neither (a) nor (b) d. Both (a) and (b)

Cost-push inflation is due to a. excess total spending. b. too much money chasing too few goods. c. resource cost increases. d. the economy operating at full employment.

Suppose you place \(\$ 10,000\) in a retirement fund that earns a nominal interest rate of 8 percent. If you expect inflation to be 5 percent or lower, then you are expecting to earn a real interest rate of at least a. 1.6 percent. b. 3 percent. c. 4 percent. d. 5 percent.

Which of the following statements is true? a. Demand-pull inflation is caused by excess total spending. b. cost-push inflation is caused by an increase in resource costs. c. If nominal interest rates remain the same and the inflation rate falls, real interest rates increase. d. If real interest rates are negative, lenders incur losses. e. All of the above are true.
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