Suppose that people consume only three goods, as shown in...

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?

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?

Key Concepts

Percentage Change Calculation

This concept involves computing the relative change in the price of a good between two periods by taking the difference of the two prices, dividing by the initial price, and then converting the result into a percentage. It is a fundamental technique used in various economic measures, including inflation, as it quantitatively expresses how much the price of a good has increased or decreased over time.

Consumer Price Index (CPI) Construction

The CPI is a statistical measure that tracks changes in the overall price level of a fixed basket of goods and services over time. In constructing the CPI, the quantities (or weights) of each good in the consumption basket are used to aggregate individual price changes into a single measure that reflects the cost of living for a typical consumer. This index is a primary tool for measuring inflation and evaluating economic well?being.

Inflation Measurement

Inflation measurement involves determining the rate at which the general price level of goods and services is rising over time, often using the percentage change in the CPI. It reflects the average change in prices across an economy and is crucial for monetary policy, cost-of-living adjustments, and economic planning.

Quality Adjustment and Product Differentiation

When measuring price changes and inflation, it is important to account for changes in the quality or characteristics of products. If a product is improved, such as an increase in size or the introduction of new features like different flavors, these quality changes may affect its value to consumers. Properly adjusting for changes in quality ensures that the measured price change is not misleadingly attributed solely to inflation rather than to an enhancement in the product itself.

Transcript

00:01 In this question, we're given a country that only consumes three goods, tennis balls, golf balls, and bottles of gatorade.

00:07 And we're given the prices and quantities of two years, 2020 and 2021, and asked to find the percentage change in price of each of the three goods, the inflation, things like that.

00:18 So first, let's start with percentage change in each of these three goods.

00:21 So how would you calculate percentage change? so what you do for any type of inflation or percentage change from one year to the next is you're going to have fraction that looks like this.

00:34 So we're going to do, so if we're just doing change in price, right? so we're going to do the 2021 price, the new price minus the old price.

00:43 So minus 2020 price.

00:45 And we're going to divide that.

00:47 Let me drop that in for us.

00:49 We're going to divide that by our last year's price, right? because we want to see how much it changed relative to the year before, how much it increased from the year before.

01:02 Right, so what we would do, let me make this a bit simpler for us.

01:09 All right, so how would this work then? so this is going to be, our central math for this is going to be, so we had a price of two, the second year, and a price of two the first year.

01:22 And we can already tell that our percentage change will be zero because it didn't change at all.

01:27 But just to go through the math, right, so you would have the price of 2021, which is 2, minus 2, divided by 2, and you're going to get 0 % change for tennis balls.

01:38 So if we do that same thing for golf balls, we're going to find that it has a 50 % increase.

01:44 And we could just see that from $4 to $6, right, because it's increasing half of four.

01:49 And then finally we have gatorade, which went from 1 to 2, which is 100 % increase.

01:56 All right.

01:57 Now we're trying to find a change in the overall price level.

02:01 So how do we do that? same thing.

02:02 We want to take 2021 and subtract 20 -20 from it.

02:07 So what are we calculating here? so we want the 2021 basket, right, the all of the goods in our prices, minus the 2020 basket, all divided by.

02:18 So here i'll just use parentheses, all divided by the 2020 basket.

02:26 Right, so how do we compute a basket? so basically for 2021, 2021 basket is going to be equal to 2021 quantities, but you're going to multiply that by, or sorry, 2021 prices, but we're multiplying that by 2020 quantities.

02:44 Right, so we're always using our original quantities because we want to see how much the price of the basket that we had in 2020 is inflating.

02:53 We want to see the effect of price, not necessarily the change in quantities, right? so this is our 2021 basket, the 2020 basket is then going to be equal to 2020 prices times 2020 quantities.

03:10 All right, so let's go through this, right? so, for example, our 2021 basket is going to be going to, be equal to, so our 20, the sum of each of these, right? so for tennis balls, for example, we're going to have our 2021 price to be $2, and our 2020 quantity was 100.

03:34 So we're doing two times 100, and then we're going to add the next one.

03:40 So next we have golf balls, which our 2021 price was six times our 2020 quantity of 100.

03:52 And then finally we have our theta -aid, which was a 2021 price of 2 and a 2020 quantity of 200.

04:02 Right.

04:02 So our 2021 basket overall going to be equal to 200 plus 600 plus 400, right? so we're going to be equal to 1200.

04:18 All right.

04:19 So now that we have that, next are 2020 basket going to be equal to.

04:26 So we still have all the same quantities.

04:28 We just need to see how the price change, right? so for this one, it's actually not going to change, right? because we had no price or quantity change...

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