Question

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

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

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: \( \frac{75}{75000} = \frac{1}{1000} \)

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%.

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%.

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.

Key concepts

Inflation Measurement

Inflation measures how the price level of goods and services in an economy changes over time. It's important because it affects your purchasing power. When the prices of goods and services increase, the value of money decreases.
Consequently, understanding inflation helps gauge the economic well-being of a nation.

One of the major ways we measure inflation is through the Consumer Price Index (CPI). CPI calculates the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Simply put, it is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically.

In the context of our exercise, the CPI can reflect inflation either correctly or incorrectly depending on how it is adjusted.
If no adjustment is made for differences in quality or product features (such as lifespan), CPI may not accurately represent inflation in the true sense.
It may either overestimate or underestimate the increase in the cost of living.

Price Calculation

Proper price calculation is crucial to understanding actual economic conditions. In our exercise, we learn to calculate the cost of using a product by its price per unit of usage—in this case, price per mile for a tire.

To determine the price per mile, you divide the total cost of a tire by the number of miles it lasts. For instance:

• In our base year, a tire costs \(\\(50\) and runs for 40,000 miles, so its price per mile is \(\frac{50}{40000} = \frac{1}{800}\).
• Ten years later, a tire costs \(\\)75\) with a lifespan of 75,000 miles, resulting in a price per mile of \(\frac{75}{75000} = \frac{1}{1000}\).

These calculations are key to understand the true cost of a product over its useful life rather than relying only on its upfront price. They allow us to accurately assess how costs and efficiencies have changed over time.

Cost Comparison

A thorough cost comparison can reveal insights into pricing efficiency and economic value over time. By comparing costs on a per mile basis, you appreciate how the value of a product evolves.

In our example, we calculate both the percentage change in actual price and the percentage change in price per mile:

• The total price increased by 50%: \(\frac{75-50}{50} \times 100\).
• However, when we calculate by price per mile, the cost has decreased by 25%: \(\frac{\frac{1}{1000} - \frac{1}{800}}{\frac{1}{800}} \times 100\).

The decrease in price per mile indicates a gain in efficiency; even though the price has increased, users are getting more out of each tire. This highlights how failing to adjust comparisons for quality or resilience improvements can skew inflation perceptions. It emphasizes understanding both the raw price and the functionally adjusted price to appreciate true cost behavior.