Suppose that people consume only three goods, as shown in this table: $$\begin{array}{lccc} & \begin{array}{c}\text { Tennis } \\\\\text { Balls }\end{array} & \text { Golf Balls } & \begin{array}{c}\text { Bottles of } \\\\\text { Gatorade }\end{array} \\\\\hline 2020 \text { price } & \$ 2 & \$ 4 & \$ 1 \\\2020 \text { quantity } & 100 & 100 & 200 \\\2021 \text { price } & \$ 2 & \$ 6 & \$ 2 \\\2021 \text { quantity } & 100 & 100 & 200 \\\\\hline\end{array}$$ a. What is the percentage change in the price of each of the three goods? b. Using a method similar to the CPI, compute the percentage change in the overall price level. c. If you were to learn that a bottle of Gatorade increased in size from 2020 to 2021 , should that information affect your calculation of the inflation rate? If so, how? d. If you were to learn that Gatorade introduced new flavors in 2021 , should that information affect your calculation of the inflation rate? If so, how?

The Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It's calculated by taking price changes for each item in the predetermined basket of goods and averaging them. These prices are collected periodically from different types of retail stores, service establishments, rental units, and doctors' offices across the country.

To understand the CPI, picture a shopping cart filled with different goods and services that might be purchased by a household. To measure CPI, we track the price changes of these goods and services over time. For instance, if the total cost of the goods in the cart was \(100 in the base year and \)110 the next year, we say that the CPI has increased from 100 to 110, indicating inflation.

In our exercise, we can see how the price and quantity of different items change. To compute the CPI, we would calculate the cost of the same basket of goods in different years and compare them. In simple terms, CPI helps us understand how much more or less expensive it is to live compared to a previous time.

The percentage change in price is a simple yet insightful measure showing how much a price has increased or decreased over a certain period, usually a year. It’s calculated using the formula:
\[ \text{{Percentage Change}} = \left(\frac{{\text{{New Price}} - \text{{Old Price}}}}{{\text{{Old Price}}}}\right) \times 100 \]
If the result is positive, it means prices have gone up, indicating inflation. If it's negative, prices have declined, which indicates deflation. This metric is useful for tracking the cost of specific goods or services over time.

In the context of our textbook exercise, we would calculate the percentage change in price for each item—tennis balls, golf balls, and bottles of Gatorade—between 2020 and 2021. Notice that understanding this concept is crucial for analyzing individual item price trends as well as for the overall inflation rate calculation.

Quality adjustment is a concept used in measuring inflation where changes to the quality or quantity of a product are taken into account in its pricing. When a product improves in quality or quantity without a corresponding price increase, consumers are getting more value for the same price. This change should be reflected in the calculation of the inflation rate.

For example, if a bottle of Gatorade increased in size from one year to the next, the larger bottle would cost more if all else were equal. To account for this, an adjustment would be made to reflect that some of the price increase is due to the increased size (better quality) rather than just inflation. This prevents an overstatement of inflation. In our exercise, if the quantity of Gatorade increased in 2021 without a price hike, the actual inflation rate would be lower once we quality adjust the price to account for the bigger bottle.

A price index is a measurement that shows how the price of a set of goods changes over time. It is represented as a simple number or percentage. Think of it as a tag on the goods that tells you how much more or less the entire set costs compared to a base period. The CPI is one type of price index where the base period is given an index value of 100.

In our textbook example, to calculate a price index, we first find the total cost of the goods in the basket for each year. Then we use the following formula to determine the price index for 2021, taking 2020 as our base year:
\[ \text{{Price Index for 2021}} = \left(\frac{{\text{{Total cost in 2021}}}}{{\text{{Total cost in 2020}}}}\right) \times 100 \]
Should the price index of a subsequent year be higher than 100, it suggests prices have gone up, reflecting inflation. If it is lower, it indicates deflation. This index can help consumers, businesses, and policymakers understand and make decisions about purchasing power and economic policy.