# Macro Solved Problems on Treasury Bonds and Defining Inflation￼

With the owners of the Major Labor Baseball teams and the Major League Players Association having finally settled on a new collective bargaining agreement, the baseball season will soon begin. Ernie Banks, the late Hall of Fame shortstop for the Chicago Cubs, was known for his upbeat personality. However bad the weather might be at Chicago’s Wrigley Field, Banks would run on the field and say, “What a great day for baseball! Let’s play two.”

In honor of Ernie Banks, today let’s do two Solved Problems in macro. They both involve errors that students in principles courses often make. So, in that sense they would also work as Don’t Let This Happen to You features.

Solved Problem 1.: Bond Yields and Bond Prices

An article in the Financial Times had the following headline:  “U.S. Government Bond Prices Drop Ahead of Federal Reserve Meeting.” The first sentence of the article reads: “U.S. government bond yields rose to multiyear highs on Monday ahead of this week’s Federal Reserve meeting ….”

a. When a media article mentions “U.S. government bonds,” what type of bonds are they referring to?

b. Is there a contradiction between the headline and the first sentence of the article? Is the article telling us that U.S. government bonds went up or down? Briefly explain.

Solving the Problem

Step 1:  Review the chapter material. This problem is about the inverse relationship between bond yields and bond prices, so you may want to review Macroeconomics, Chapter 6, Appendix, “Using Present Value” (Economics, Chapter 8, Appendix, “Using Present Value”). You may also want to review the discussion of U.S. Treasury bonds in Macroeconomics, Chapter 16, Section 16.6, “Deficits, Surpluses, and Federal Government Debt” (Economics, Chapter 26, Section 26.6, “Deficits, Surpluses, and Federal Government Debt”).

Step 2: Answer part a. by explaining what media articles are referring to when they use the phrase “U.S. government bonds.” As discussed in Chapter 16, Section 16.6, most of the bonds issued by the federal government of the United States are U.S. Treasury bonds. The Treasury sells these bonds to investors when the federal government doesn’t collect enough in tax revenues to pay for all of its spending. So, when the media refers to U.S. government bonds, without further explanation, the reference is always to U.S. Treasury bonds.

Step 3: Answer part b. by explaining that there is no contradiction between the headline and the first sentence of the article. An important fact about bond markets is that when the price of a bond falls, the yield—or interest rate—on the bond rises. The reverse is also true: When the price of a bond rises, the yield on the bond falls.  The reason why this relationship holds is explained in the Appendix to Chapter 6: The price of a bond (or other financial asset) should be equal to the present value of the payments an investor receives from owning that asset. If you buy a U.S. Treasury bond, the price will equal the present value of the coupon payments the Treasury sends you during the life of the bond and the final payment to you by the Treasury of the principal, or face value of the bond. Remember that present value is the value in today’s dollars of funds to be received in the future. The higher the interest rate, the lower the present value of a payment to be received in the future. So a higher yield, or interest rate, on a bond results in a lower price of the bond because the higher yield reduces the present value of the payments to be received from the bond.

Therefore, whenever the yield on a bond rises, the price of the bond must fall (and whenever the yield on a bond falls, the price of the bond must rise. So, we can conclude that the headline of the Financial Times article and the first sentence of the article are consistent, not contradictory:  Because the prices of Treasury bonds fell, the yields on the bonds must have risen.

Source: Nicholas Megaw, Naomi Rovnick, George Steer, and Hudson Lockett, “U.S. Government Bond Prices Drop Ahead of Federal Reserve Meeting,” ft.com, March 14, 2022.

Solved Problem 2: Being Careful about the Definition of Inflation

An article in the New York Times contrasted inflation during the 1970s with inflation today:

“Price increases had run high for more than a decade by the time Mr. Volcker became chair [of the Federal Reserve Board of Governors] in 1979 …. Shopper expected prices to go up, businesses knew that, and both acted accordingly. This time, inflation has been anemic for years (until recently), and most consumers and investors expect costs to return to lower levels before long, survey and market data show.”

a. What does the article mean by “inflation has been anemic for years”?

b. In the last sentence what “costs” is the article referring to?

c. Is the article correctly using the definition of inflation in the last sentence? Briefly explain.

Solving the Problem

Step 1:  Review the chapter material. This problem is about the definition of inflation, so you may want to review Macroeconomics, Chapter 9, Section 9.4, “Measuring Inflation” (Economics, Chapter 20, Section 20.4, “Measuring Inflation”).

Step 2: Answer part a. by explaining what the phrase “inflation has been anemic for years” means. Anemia is a medical disorder that usually has the symptom of fatigue. So, the word “anemic” is often used to mean weak. The article is arguing that until recently, the inflation rate had been weak, or slow.

Step 3: Answer part b. by explaining what the article is referring to by “costs.” Economists typically use the word costs for the amount that firm pays to produce a good—labor costs, raw material costs, and so on. Here, though, the article is using “costs” to mean “prices.”  Costs is often used this way in everyday conversation: “I didn’t buy a new car because they cost too much.” Or: “Has the cost of a movie ticket increased?”

Step 4: Answer part c. by explaining whether the article is correctly using the definition of inflation. In writing “consumers and investors expect costs to return to lower levels” the article is making a common mistake. The article seems to mean that consumers and investors expect that the rate of inflation will be lower in the future. But even if the rate of inflation declines from nearly 8 percent in early 2022 to, say, 3 percent in 2023, prices will still be increasing. So, prices (“costs” in the sentence) will still be higher next year even if the rate of inflation is lower. In other words, even if the rate of increase in prices—inflation—declines, the price level will still be higher.

It’s a common mistake to think that a decline in the inflation rate means that prices will be lower, when actually prices will still be increasing, just more slowly.

Source: Jeanna Smialek, “Powell Admires Volcker. He May Have to Act Like Him,” New York Times, March 14, 2022.