Another Middling Inflation Report

A meeting of the Federal Open Market Committee (Photo from federalreserve.gov)

On Friday, May 31, the Bureau of Eeconomic Analysis (BEA) released its “Personal Income and Outlays” report for April, which includes monthly data on the personal consumption expenditures (PCE) price index. Inflation as measured by changes in the consumer price index (CPI) receives the most attention in the media, but the Federal Reserve looks instead to inflation as measured by changes in the PCE price index to evaluate whether it’s meeting its 2 percent annual inflation target. 

The following figure shows PCE inflation (blue line) and core PCE inflation (red line)—which excludes energy and food prices—for the period since January 2015 with inflation measured as the change in the PCE from the same month in the previous year. Measured this way, PCE inflation in April was 2.7 percent, which was unchanged since March. Core PCE inflation was also unchanged in April at 2.8 percent. (Note that carried to two digits past the decimal place, both measures decreased slightly in April.)

The following figure shows PCE inflation and core PCE inflation calculated by compounding the current month’s rate over an entire year. (The figure above shows what is sometimes called 12-month inflation, while this figure shows 1-month inflation.) Measured this way, PCE inflation declined from 4.1 percent in March to 3.1 percent in April. Core PCE inflation declined from 4.1 percent in March to 3.0 percent in April.  This decline may indicate that inflation is slowing, but data for a single month should be interpreted with caution and, even with this decline, inflation is still above the Fed’s 2 percent target.

The following figure shows another way of gauging inflation by including the 12-month inflation rate in the PCE (the same as shown in the figure above—although note that PCE inflation is now the red line rather than the blue line), inflation as measured using only the prices of the services included in the PCE (the green line), and the trimmed mean rate of PCE inflation (the blue line). Fed Chair Jerome Powell has said that he is particularly concerned by elevated rates of inflation in services. The trimmed mean measure is compiled by economists at the Federal Reserve Bank of Dallas by dropping from the PCE the goods and services that have the highest and lowest rates of inflation. It can be thought of as another way of looking at core inflation by excluding the prices of goods and services that had particularly high or particularly low rates of inflation during the month.

Inflation using the trimmed mean measure was 2.9 percent in April, down from 3.0 percent in March. Inflation in services remained high, although it declined slightly from 4.0 percent in March to 3.9 percent in April.

It seems unlikely that this month’s PCE data will have much effect on when the members of the Fed’s policy-making Federal Open Market Committee (FOMC) will decide to lower the target for the federal funds rate. The next meeting of the FOMC is June 11-12. That meeting is one of the four during the year at which the committee publishes a Summary of Economic Projections (SEP). The SEP should provide greater insight into what committee members expect will happen with inflation during the remained of the year and whether it’s likely that the committee will lower its target for the federal funds rate this year.

Solved Problem: Elasticity and the Incidence of the Gasoline Tax

Supports: Microeconomics and Economics, Chapter 6.

Photo from the New York Times.

Blogger Matthew Yglesias made the following observation in a recent post: “If you look at gasoline prices, it’s obvious that if fuel gets way more expensive next week, most people are just going to have to pay up. But if you compare the US versus Europe, it’s also obvious that the structurally higher price of gasoline over there makes a massive difference: They have lower rates of car ownership, drive smaller cars, and have a higher rate of EV adoption.” (The blog post can be found here, but may require a subscription.)

  1. What does Yglesias mean by Europe having a “structurally higher price” of gasoline?
  2. Assuming Yglesias’s observations are correct, what can we conclude about the price elasticity of the demand for gasoline in the short run and in the long run?
  3. Currently, the federal government imposes a tax of 18.4 cents per gallon of gasoline. Suppose that Congress increases the gasoline tax to 28.4 cents per gallon. Again assuming that Yglesias’s observations are correct, would you expect that the incidence of the tax would be different in the long run than in the short run? Briefly explain.
  4. Would you expect the federal government to collect more revenue as a result of the 10 cent increase in the gasoline tax in the short run or in the long run? Briefly explain. 

Solving the Problem

Step 1: Review the chapter material. This problem is about the determinants of the price elasticity of demand and the effect of the value of the price elasticity of demand on the incidence of a tax, so you may want to review Chapter 6, Section 6.2 and Solved Problem 6.5. (Note that a fuller discussion of the effect of the price elasticity of demand on tax incidence appears in Chapter 17, Section 17.3.)

Step 2: Answer part a. by explaining what Yglesias means when he writes that Europe has a “structurally higher” price of gasoline. Judging from the context, Yglesias is saying that European gasoline prices are not just temporarily higher than U.S. gasoline prices but have been higher over the long run.

Step 3: Answer part b. by expalining what we can conclude from Yglesias’s observations about the price elasticity of demand for gasoline in the short run and in the long run. When Yeglesias is referring to gasoline prices rising “next week,” he is referring to the short run. In that situation he says “most people are going to have to pay up.” In other words, the increase in price will lead to only a small decrease in the quantity demanded, which means that in the short run, the demand for gasoline is price inelastic—the percentage change in the quantity demanded will be smaller than the percentage change in the price.

Because he refers to high gasoline prices in Europe being structural, or high for a long period, he is referring to the long run. He notes that in Europe people have responded to high gasoline prices by owning fewer cars, owning smaller cars, and owning more EVs (electric vehicles) than is true in the United States. Each of these choices by European consumers results in their buying much less gasoline as a result of the increase in gasoline prices. As a result, in the long run the demand for gasoline is price elastic—the percentage change in the quantity demanded will be greater than the percentage change in the price.

Note that these results are consistent with the discussion in Chapter 6 that the more time that passes, the more price elastic the demand for a product becomes.

Step 4: Answer part c. by explaining how the incidence of the gasoline tax will be different in the long run than in the short run. Recall that tax incidence refers to the actual division of the burden of a tax between buyers and sellers in a market. As the figure in Solved Problem 6.5 illustrates, a tax will result in a larger increase in the price that consumers pay for a product in the situation when demand is price inelastic than when demand is price elastic. The larger the increase in the price that consumers pay, the larger the share of the burden of the tax that consumers bear. So, we can conclude that the tax incidence of the gasoline tax will be different in the short run than in the long run: In the short run, more of the burden of the tax is borne by consumers (and less of the burden is borne by suppliers); in the long run, less of the burden of the tax is borne by consumers (and more of the burden is borne by suppliers).

Step 5: Answer part d. by explaining whether you would expect the federal government to collect more revenue as a result of the 10 cent increase in the gasoline tax in the short run or in the long run. The revenue the federal government collects is equal to the 10 cent tax multiplied by the quantity of gallons sold. As the figure in Solved Problem 6.5 illustrates, a tax will result in a smaller decrease in the quantity demanded when demand is price inelastic than when demand is price elastic. Therefore, we would expect that the federal government will collect more revenue from the tax in the short run than in the long run.

Solved Problem: How Much Did Using a Ticket to a Taylor Swift Concert Cost You?

Supports: Microeconomics, Macroeconomics, Economics, and Essentials of Economics, Chapter 1.

Photo of Taylor Swift from the Wall Street Journal.

Suppose that as a “verified fan” of Taylor Swift, you are able to buy a ticket to one of her concerts for $215. The price of the ticket isn’t refundable. (We discuss how Taylor Swift handles the sale of tickets to her concerts in the Apply the Concept “Taylor Swift Tries to Please Fans and Make Money” in Microeconomics and in Economics, Chapter 10, and in Essentials of Economics, Chapter 7.) You had been hoping to work a few hours of overtime at your job to earn some extra money. The day of the concert, your boss tells you that the only overtime available for the next month is that night from 6 pm to 10 pm—the same time as the concert. Working those hours of overtime will earn you $100 (after taxes). You check StubHub and find that you can resell your ticket for $1,000 (afer paying StubHub’s fee).

Given that information, briefly explain which of the following statements is correct:

  1. If you attend the concert, the cost of using your ticket is $215—the price that you paid for it.
  2. If you attend the concert, the cost of using your ticket is $1,000—the amount you can resell your ticket for.
  3. If you attend the concert, the cost of using your ticket is $1,000 + $100 = $1,100—the amount you can resell your ticket for plus the amount you would have earned from working overtime rather than attending the concert.
  4. If you attend the concert, the cost of using your ticket is $1,000 + $100 – $215 = $885—the amount you can resell your ticket for plus the amount you would have earned from working overtime rather than attending the concert minus the price you paid to buy the ticket. 

Solving the Problem

Step 1: Review the chapter material. This problem is about the concept of opportunity cost, so you may want to review Chapter 1, Section 1.2.

Step 2: Solve the problem by using the concept of opportunity cost to determine which of the four statements is correct. Economists measure the cost of engaging in an activity as an opportunity cost—the value of what you have to give up to engage in the activity. Using this definition, only statement c. is correct; if you decide to use your ticket to attend the concert you will give up the $1,000 you could have received from selling the ticket plus the $100 you fail to earn as a result of attending the concert rather than working overtime. Note that the price you paid for the ticket isn’t relevant to your decision whether to attend the concert because the price of the ticket is nonrefundable. (The amount you paid for the ticket is a sunk cost because it can’t recovered. We discuss the role of sunk costs in decision making in Microeconomics and Economics, Chapter 10, Section 10.4, and in Essentials of Economics, Chapter 7, Section 7.4.)

More Data on the Progressivity of the U.S. Income Tax

Photo from the Associated Press via the Wall Street Journal.

A tax is progressive if people with lower incomes pay a lower percentage of their income in tax than do people with higher incomes. (We discuss the U.S. tax system in Microeconomics and Economics, Chapter 17, Section 17.2.) Recently, the Joint Committee on Taxation (JCT) of the U.S. Congress released a report, “Overview of the Federal Tax System as in Effect for 2024,” that provides data on the progressivity of the U.S. tax system. (An overview of the role of the JCT can be found here.)

The progressivity of the federal individual income tax is shown in the following figure from the JCT report. The column on the right shows that for each category of taxpayers shown—single people, heads of households (who are unmarried people who financially support at least one other person), and married people—the marginal income tax rate increases with a taxpayer’s income. The marginal tax rate is the rate that someone pays on additional income that they earn. So, for instance, the table shows that an individual who has taxable income of $80,000 faces a marginal tax rate of 22 percent because that is the rate the person pays on the income they earn between $47,150 and $80,000. An individual who has a taxable income of $700,000 faces a marginal tax rate of 37 percent because that is the rate the person pays on the income they earn between $609,350 and $700,000.

In Chapter 17, we use data from the Tax Policy Center to show the average income tax rate paid by different income groups. The average tax rate is computed as the total tax paid divided by taxable income. The marginal tax rate is a better indicator than the average tax rate of how a change in a tax will affect a person’s willingness to work, save, and invest. For instance, if you are considering working more hours in your job or taking on a second job, such driving part time for Uber or Lyft, you want to know what your tax rate is on the additional income you will earn. For that purpose, you should ignore your average tax rate and instead focus on your marginal tax rate.

The following table from the JCT report is similar to the table in Chapter 17, which was based on data from the Tax Policy Center. The JCT report has the advantage of direct access to government tax data, which, as a private group, the Tax Policy Center doesn’t have. In addition, the JCT reports on an income group—the top 0.1 percent of income earners—compiled from government data not available to the Tax Policy Center. (Much political discussion has focused on the income earned and taxes paid by the top 1 percent of earners, which is a much larger group than the top 0.1 percent. We discuss the top 1 percent in the Apply the Concept, “Who Are the 1 Percent, and How Do They Earn Their Incomes,” in Microeconomics and Economics, Chaper 17, Section 17.4.)

The table shows data for the first four quntiles (or groups of 20 percent of taxpayers), with the highest quintile divided further. The table shows that the federal individual income tax is highly progressive, with the two lowest income quintiles having negative average tax rates because they receive more in tax credits than they pay in taxes. Employment taxes—primarily the payroll tax used to fund the Social Security and Medicare Systems—are regressive, with the lowest deciles paying a larger percentage of their income in these taxes than do the higher deciles. The regressivity of employment taxes is the result of both payroll taxes being levied on the first dollar of wages and salaries individuals earn and the part of the payroll tax used to fund the Social Security system dropping to zero for incomes above a certain level—$168,600 in 2024. Because income taxes are much larger in total than employment taxes or excise taxes—such as the federal taxes on gasoline, airline tickets, and alcoholic beverages—the total of these three types of federal taxes is progressive, as shown by the fact that the average tax rate rises with income. (Although note that the top 0.1 percent pay taxes at a slightly lower rate than do the other taxpayers included in the top 1 percent.)

Would Caleb Williams Be Better Off Playing for the Jacksonville Jaguars Instead of the Chicago Bears?

USC quarterback Caleb Williams is shown with NFL Commissioner Roger Goodell at the NFL college draft in Detroit. (Photo from Reuters via the Wall Street Journal)

In late April, the National Football League (NFL) held its annual draft of eligible college players. NFL teams choose players through seven rounds in reverse order of how the teams finished in the previous year: The team with the worst record picks first and the winner of the Super Bowl picks last. Teams are allowed to trade picks with each other. This year, although the Carolina Panthers finished with the worst record during the 2023 season, they had traded their first round pick to the Chicago Bears, who picked first.

The Bears choose University of Southern California (USC) quarterback Caleb Williams with the first pick in the draft. Drafted players usually have no choice but to sign contracts with the team that chose them. A player can refuse to sign with the team that drafted him and not play that year, hoping that the next year a team they like better will draft them. Very few players have chosen that option.

When football fans and sportswriters discuss whether a team is a good match for a player they usually focus on factors such as whether a player’s skills are well suited to the team’s style of play and on how many other good players are on the team. One other factor that is seldom discussed is whether a player will benefit more financially by playing for the team that drafted him rather than for another team. Players chosen in the college draft are paid an amount fixed as a result of bargaining between the NFL and the National Football League Players Association (NFLPA), which is the labor union that represents NFL players.

As the first pick in the draft, Caleb Williams’s contract will pay him $39.4 million in total over the next four seasons. A sizeable fraction of that amount—probably $25.5 million—will be in the form of a lump-sum bonus that the Bears will pay Williams in full when he signs his contract. The dollar amount Williams is paid as the first pick in the draft would be the same whichever of the 32 NFL teams had drafted him. However, football players—like everyone else—are interested in their after-tax income and state and local income tax rates vary widely. Football players pay state and local income taxes based on where their teams’ games are played. In the 17-game NFL schedule, teams play either 8 or 9 games in their home city and the rest (road games) in the home cities of their opponents.

Jared Walczak of the Tax Foundation has compiled a table showing the tax rate each NFL team’s players will pay in 2024 based on the state and local taxes levied in their home city and the state and local taxes levied by the cities where the team’s road games will be played. To keep the numbers simple, let’s look at how the much in taxes Williams will owe on a $20 million bonus, which the Bears will pay him as soon as he signs his contract. (Note that, as indicated earlier, Williams’s bonus is likely to be greater than $20 million and he will also receive a salary during his first season of about $3.75 million.)

Given the income tax rate levied by the state of Illinois (the city of Chicago doesn’t levy a tax on income) and the state and local taxes levied by the cities and states in which the Bears will play their road games this year, Williams will owe a tax of $1,079,075 on his bonus. (Note that we are ignoring the substantial federal income tax that Williams will owe on the bonus because the federal tax won’t change no matter which city he plays in.) The lowest tax that Williams would pay on the bonus is $120,421, which would be his tax if he played for the Jacksonville Jaguars. Neither the city of Jacksonville nor the state of Florida levies a personal income tax, so Williams would only owe state and local income taxes on what he earns playing in cities where the Jaguars play their road games. The largest tax Williams would pay is $1,301,028, which would be his tax if he had been drafted by any of the three teams that play in California: the Los Angeles Rams, the Los Angeles Chargers, or the San Francisco ’49ers.

Although college players who are drafted are obliged to play for the team that drafted them, after players have completed their contracts they have the option of signing with a different team. At that stage of their careers, players—and their agents—can take into account state and local income taxes when deciding which team to sign a new contract with.

Solved Problem: When to Close a Sandwich Shop

Supports: Microeconomics and Economics, Chapter 12, and Essentials of Economics, Chapter 9.

Photo from the Wall Street Journal.

A recent article in the Los Angeles Times discussed the problems faced by the owners of a sandwich shop in the Chinatown neighborhood of Los Angeles.  The owners had closed the shop and then decided to reopen it. The article quoted one of the owners as saying: “After closing [the shop] we realized we still have our lease, we still have our loans from the [federal government’s Small Business Association], from COVID, the bills are still coming in. We can’t even afford to close. We can’t afford to be open, we can’t afford to be closed.”

a. What does the owner of the sandwich shop mean by saying they can’t afford to be open but they also can’t afford to be closed? Answer by explaining what the likely relationship is between the revenue the owners were earning from the shop and the shop’s fixed, variable, and total costs . 

b. Are the owners likely to keep the sandwich shop open in the long run? Briefly explain.

Solving the Problem

Step 1: Review the chapter material. This problem is about when a firm should decide to shut down in the short run, so you may want to review the section “Deciding Whether to Produce or to Shut Down in the Shortrun” in Microeconomics (and Economics), Chapter 12, Section 12.4, (Essentials of Economics, Chapter 9, Section 9.4).

Step 2: Answer part a. by explaining what the sandwich shop’s owner meant by her statement, using the likely relationship between the shop’s revenue and its fixed, variable, and total cost in your explanation. That the owner states that “we can’t afford to be open” indicates that the firm is incurring a loss, so the revenue from the shop is less than the toal cost of operating it. But after closing the shop, the owners reopened it because “we can’t afford to be closed.” That statement indicates that the owners will incur a smaller loss by operating the shop than by keeping it closed. If the shop is closed, the owners still have to pay the shop’s fixed costs, such as the rent on the shop and the payments the owners must make on loans. We can infer that the loss from remaining open is less than the loss from being closed. In that situation, the shop’s revenue must be enough to cover the variable cost of operating it, although not enough to cover the total cost.

Step 3: Answer part b. by explaining whether the owners are likely to keep the sandwich shop open in the long run. By definition, in the long run, the owners will no longer have any fixed costs because the period of its lease will have ended and it will have paid off its loans—or possibly defaulted on them. If the revenue from operating the shop remains less than the total cost of operating it in the long run, the owners will permanenly close the shop.

Inflation Cools Slightly in Latest CPI Report

Inflation was running higher than expected during the first three months of 2024, indicating that the trend in late 2023 of declining inflation had been interrupted. At the beginning of the year, many economists and analysts had expected that the Federal Reserve’s policy-making Federal Open Market Committee (FOMC) would begin cutting its target for the federal funds rate sometime in the middle of the year. But with inflation persisting above the Fed’s 2 percent inflation target, it has become likely that the FOMC will wait until later in the year to start cutting its target and might decide to leave the target unchanged through the remainder of 2024.

Accordingly, economists and policymakers were intently awaiting the report from the Bureau of Labor Statistics (BLS) on the consumer price index (CPI) for April. The report released this morning showed a slight decrease in inflation, although the inflation rate remains well above the Fed’s 2 percent target. (Note that, as we discuss in Macroeconomics, Chapter 15, Section 15.5 (Economics, Chapter 25, Section 25.5), the Fed uses the personal consumption expenditures (PCE) price index, rather than the CPI in evaluating whether it is hitting its 2 percent inflation target.)

The inflation rate for April measured by the percentage change in the CPI from the same month in the previous month—headline inflation—was 3.4 percent—about the same as economists had expected—down from 3.5 percent in March. As the following figure shows, core inflation—which excludes the prices of food and energy—was 3.6 percent in April, down from 3.8 percent in March.

If we look at the 1-month inflation rate for headline and core inflation—that is the annual inflation rate calculated by compounding the current month’s rate over an entire year—the declines in the inflation rate are larger. Headline inflation declined from 4.6 percent in March to 3.8 percent in April. Core inflation declined from 4.4 percent in March to 3.6 percent in April. Note that the value for core inflation is the same whether we measure over 12 months or over 1 month. Overall, we can say that inflation seems to have cooled in April, but it still remains well above the Fed’s 2 percent target.

As has been true in recent months, the path of inflation in the prices of services has been concerning. As we’ve noted in earlier posts, Federal Reserve Chair Jerome Powell has emphasized that as supply chain problems have gradually been resolved, inflation in the prices of goods has been rapidly declining. But inflaion in services hasn’t declined nearly as much. Powell has been particularly concernd about how slowly the price of housing has been declining, a point he made again in the press conference that followed the most recent FOMC meeting.

The following figure shows the 1-month inflation rate in service prices and in service prices not included including housing rent. The figure shows that inflation in all service prices has been above 4 percent in every month since July 2023, but inflation in service prices slowed markedly from 6.6 percent in March to 4.4 percent in April. Inflation in service prices not including housing rent declined more than 50 percent, from 8.9 percent in March to 3.4 percent in April. But, again, even though inflation in service prices declined in April, as the figure shows, the 1-month inflation in services is volatile and even these smaller increases aren’t yet consistent with the Fed meeting its 2 percent inflation target.

Finally, in order to get a better estimate of the underlying trend in inflation, some economists look at median inflation, which is calculated by economists at the Federal Reserve Bank of Cleveland and Ohio State University. If we listed the inflation rate in each individual good or service in the CPI, median inflation is the inflation rate of the good or service that is in the middle of the list—that is, the inflation rate in the price of the good or service that has an equal number of higher and lower inflation rates. As the following figure shows, at 4.3 percent, median inflation in April was unchanged from its value in March.

Today’s report was good news for the Fed in its attempts to reduce the inflation rate to its 2 percent target without pushing the U.S. economy into a recession. But Fed Chair Jerome Powell and other members of the FOMC have made clear that they are unlikely to begin cutting the target for the federal funds rate until they receive several months worth of data indicating that inflation has clearly resumed the downward path it was on during the last months of 2023. The unexpectedly high inflation data for the first three months of 2024 has clearly had a significant effect on Fed policy. Powell was quoted yesterday as noting that: “We did not expect this to be a smooth road, but these [inflation readings] were higher than I think anybody expected,”

How Has Inflation Affected People at Different Income Levels?

Photo courtesy of Lena Buonanno

In the new 9th edition of Macroeconomics, in Chapter 9, Section 9.7 (Economics, Chapter 19, Section 19.7 and Essentials of Economics, Chapter 13, Section 13.7), we have an Apply the Concept feature that looks at research conducted by economists at the U.S. Bureau of Labor Statistics into the effects of inflation on households at different income levels. That research involved looking at the differences between the mix of goods that households at different income levels consume and at differences in increases in the wages they earn. The following figure, reproduced from this feature shows that as a percentage of their total consumption expenditures households with low incomes spend more on housing and food, and less on transportation and recreation than do households with high incomes.

During the three-year period from March 2020 to April 2023, wages increased faster than did prices for households with low incomes, while wages increased at a slower than did prices for households with high incomes. We concluded from this research that: “during this period, workers with lower incomes were hurt less by the effects of inflation than were workers with higher incomes.”

The Congressional Budget Office (CBO) has just released a new study that uses different data to arrive at a similar conclusion. The CBO divided households into five equal groups, or quintiles, from the 20 percent with the lowest incomes to the 20 percent with the highest incomes. The following table shows how income quintiles divide their consumption across different broad categories of goods and services. For example, compared with households in the highest income quintile, households in the lowest income quintile spend a much larger fraction of their budget on rent and a significantly larger fraction on food eaten at home. Households in the lowest quintile spent significantly less on “other services,” which include spending on hotels and on car maintenance and repair.

The CBO study measures the effect of inflation over the past four years on different income quintiles by comparing the change in the fraction of their incomes households needed to buy the same bundle of goods and services in 2024 that they bought in 2019. The first figure below shows the result when household income includes only market income—primarily wages and salaries. The second figure shows that result when transfer payments—such as Social Security benefits received by retired workers and unemployment benefits received by unemployed workers—are added to market income. (The values along the vertical axis are percentage points.)

The fact that, in both figures, the fraction of each quintiles’ income required to buy the same bundle of goods and services is negative means that between 2019 and 2023 income increased faster than prices for all income quintiles. Looking at the bottom figure, households in the highest income quintile could spend 6.3 percentage points less of their income in 2024 to buy the same bundle of goods and services they had bought in 2019. Households in the lowest income quintile could spend 2.0 percentage points less. Households in the middle income quintile had the smallest reduction—0.3 percentage point—of their income to buy the same bundle of goods and services.

It’s worth keeping mind that the CBO data represent averages within each quintile. There were certainly many households, particularly in the lower income quintiles, that needed to spend a larger precentage of their income in 2024 to buy the same bundle of goods and services that they had bought in 2019, even though, as a group, the quintile they were in needed a smaller percentage.

 

Solved Problem: The Price Elasticity of Demand for iPhones in China

Supports: Microeconomics and Economics, Chapter 6, and Essentials of Economics, Chapter 7.

Photo from from Reuters via the Wall Street Journal.

An article on bloomberg.com noted that in China after Apple cut by 10 percent the price of its iPhone 15 Pro Max—the most expensive iPhone model—sales of this model increased by 12 percent.

a. Based on this information, is the demand in China for this model iPhone price elastic or price inelastic? Briefly explain.

b. Do you have enough information to be confident in your answer to part a.? Briefly explain.

c. Assuming that the price elasticity you calculated in part a. is accurate, should managers at Apple be confident that if they cut the price of this iPhone model by an additional 10 percent they would sell 12 percent more? Briefly explain.

Solving the Problem

Step 1: Review the chapter material. This problem is about the price elasticity of demand, so you may want to review Microeconomics (and Economics), Chapter 6, Sections 6.1, 6.2 and 6.3 (Essentials of Economics, Chapter 7, Sections 7.5, 7.6, and 7.7)

Step 2: Answer part a. by using the information provided to determine whether the demand for this iPhone model in China is price elastic or price inelastic. In Section 6.1, we define the price elasticity of demand as being equal to (Percentage change in quantity demanded)/(Percentage change in price). From the information given, the price elasticity of demand for this iPhone model in China equals 12%/–10% = –1.2. Because this value is greater than 1 in absolute value, we can conclude that demand for this iPhone model in China is price elastic.

Step 3: Answer part b. by discussing whether you have enough information to be confident in your answer to part a. If we have values for the change in price and the change in the quantity demanded, we can calculate the price elasticity of demand provided that nothing that would affect the willingness of consumers to buy the good—other than the price of the good—has changed. In this case, if other factors that are relevant to consumers in making their decision about buying that iPhone model have changed, then the demand curve will have shifted and the 12 percent increase in iPhones sold will be a mixture of the effect of the price having decreased and the effects of other factors having changed. For example, if the prices of smartphones sold by Vivo and Huawei—two Chinese firms whose smartphones compete with the iPhone—had increased, then the demand curve for the iPhone 15 Pro Max will have shifted to the right and our calculation in part a. will not give us an accurate value for the price elasticity of demand for the iPhone 15 Pro Max.

Step 4: Answer part c. by explaining whether, assuming that the price elasiticity you calculated in part a. is accurate, Apple’s managers can be confident that if they if they cut the price of this iPhone model by an additional 10 percent they would sell 12 percent more of this model. The first price cut for this iPhone model caused a movement down the demand curve. For Apple’s managers to be confident that that the same percentage price cut would result in the same percentage increase in the quantity sold, the price elasticity would have to be constant along the demand curve for this model. As we show explicitly for a linear demand curve in Section 6.3, the price elasticity of demand is unlikely to be constant along the demand curve (although in an unusual case it would be). In general, we expect that in moving further down the demand curve the price elasticity of demand will decline in absolute value. If that result holds in this case, then an additional 10 percent cut in price is likely to result in less than a 12 percent increase in the quantity demanded.

Is Sugar All You Need?

Dylan’s Candy Bar in New York City (Photo from the New York Times)

Can prices of one type of good track inflation accurately? As we’ve discussed in a number of blog posts (for instance, here, here, and here), there is a debate among economists about which of the data series on the price level does the best job of tracking the underlying rate of inflation.

The most familiar data series on the price level is the consumer price index (CPI). Core CPI excludes the—typically volatile—food and energy prices. In gauging whether it is achieving its goal of 2 percent annual inflation, the Federal Reserve uses the personal consumption expenditures (PCE) price index. The PCE price index includes the prices of all the goods and services included in the consumption category of GDP, which makes it a broader measure of inflation than the CPI. To understand the underlying rate of inflation, the Fed often focuses on movements in core PCE.

With the increase in inflation that started in the spring of 2021, some economists noted that the prices of particular goods and services—such as new and used cars and housing—were increasing much more rapidly than other prices. So some economists concentrated on calculating inflation rates that excluded these or other prices from either the CPI or the PCE.

For example, the following figure shows the inflation rate measured by the percentage change from the same month in the previous year using the median CPI and using the trimmed mean PCE. If we list the inflation rate in each individual good or service in the CPI, median inflation is the inflation rate of the good or service that is in the middle of the list—that is, the inflation rate in the price of the good or service that has an equal number of higher and lower inflation rates. The trimmed mean measure of PCE inflation is compiled by economists at the Federal Reserve Bank of Dallas by dropping from the PCE the goods and services that have the highest and lowest rates of inflation. During the period when the inflation rate was increasing rapidly during 2021 and 2022, CPI inflation increased more and was more volatile than PCE inflation. That difference between movements in the two price level series is heightened when comparing median inflation in the CPI with trimmed mean inflation in the PCE. In particular, using trimmed mean PCE, the inflation of late 2021 and 2022 seems significantly milder than it does using median CPI.

The United States last experienced high inflation rates in the 1970s, when few people used personal computers and easily downloading macroeconomic data from the internet wasn’t yet possible. Today, it’s comparatively easy to download data on the CPI and PCE and manipulate them to investigate how the inflation rate would be affected by dropping the prices of various goods and services. It’s not clear, though, that this approach is always helpful in determining the underlying inflation rate. In a market system, the prices of many goods and services will be affected in a given month by shifts in demand and supply that aren’t related to general macroeconomic conditions.

In a recent blog post, economists B. Ravikumar and Amy Smaldone of the Federal Reserve Bank of St. Louis note that there is a strong correlation between movements in the prices of the “Sugar and Sweets” component of the CPI and movements in the overall CPI. Their post includes the following two figures. The first shows the price level since 1947 calculated using the prices of all the goods and services in the CPI (blue line) and the price level calculated just using the prices of goods included in the “Sugar and Sweets” category (red line). The data are adjusted to an index where the value for each series in January 1990 equals 100. The second figure shows the percentage change from the previous month for both series for the months since January 2000.

The two figures show an interesting—and perhaps surprising—correlation between sugar and sweets prices and all prices included in the CPI. The St. Louis Fed economists note that although the CPI is only published once per month, prices on sugar and sweets are available weekly. Does that mean that we could use prices on sugar and sweets to predict the CPI? That seems unlikely. First, consider that the sugar and sweets category of the CPI consists of three sub-categories:

  1. White, brown, and raw sugar and natural and artificial sweetners
  2. Chocolate and other types of candy, fruit flavored rolls, chewing gum and breath mints
  3. Other sweets, including jelly and jams, honey, pancake syrup, marshmallows, and chocolate syrup

Taken together these products are less than 3 percent of the products included in the CPI. In addition, the prices of the goods in this category can be heavily dependent on movements in sugar and cocoa prices, which are determined in world wide markets. For instance, the following figure shows the world price of raw cocoa, which soared in 2024 due to bad weather in West Africa, where most cocoa is grown. There’s no particular reason to think that factors affecting the markets for sugar and cocoa will also affect the markets in the United States for automobiles, gasoline, furniture, or most other products.

In fact, as the first figure below shows, if we look at the inflation rate calculated as the percentage change from the same month in the previous year, movements in sugar and sweets prices don’t track very closely movements in the overall CPI. Beginning in the summer of 2022—an important period when the inflation that began in the spring of 2021 peaked—inflation in sugar and sweets was much higher than overall CPI inflation. Anyone using prices of sugar and sweets to forecast what was happening to overal CPI inflation would have made very poor predictions. We get the same conclusion from comparing inflation calculated by compounding the current month’s rate over an entire year: Inflation in sugar and sweets prices is much more volatile than is overall CPI inflation. That conclusion is unsurprising given that food prices are generally more volatile than are the prices of most other goods.

It can be interesting to experiment with excluding various prices from the CPI or the PCE or with focusing on subcategories of these series. But it’s not clear at this point whether any of these adjustments to the CPI and the PCE, apart from excluding all food and energy prices, gives an improved estimate of the underlying rate of inflation.