Tag: Solved problem

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.)

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.

Solved Problem: How Do You Calculate GDP?

Supports: Macroeconomics, Chapter 8, Economics, Chapter 18, and Essentials of Economics, Chapter 12.

In a report, a consulting firm claimed that wealth is a better measure of the financial health of an economy than is GDP. They made the following argument:

“GDP counts items multiple times. For instance, if someone is paid USD 100 for a product/service and they then pay someone else that same USD 100 for another product/service, that adds USD 200 to a country’s GDP, despite the fact that only USD 100 was produced at the start.”

Briefly explain whether you agree with the consulting firm’s argument.

Solving the Problem

Step 1:  Review the chapter material. This problem is about how GDP is calculated, so you may want to review Macroeconomics, Chapter 8, Section 8.1, “Gross Domestic Product Measures Total Production” (Economics, Chapter 18, Section 8.1 and Essentials of Economics, Chapter 12, Section 12.1)

Step 2: Answer the question by explaining whether the consulting firm has correctly explained how the Bureau of Economic Analysis calculates GDP. The consulting firm has given an incorrect explanation of how GDP is calculated, so you should disagree with the firm’s argument. The definition of GDP in the chapter is: “The market value of all final goods and services produced in a country during a period of time.” The quoted excerpt is incorrect in claiming that GDP counts items multiple times. In terms of the example, if you pay $100 for a (very nice!) haircut at a hair salon and the owner of the hair salon uses that $100 to buy groceries, both transactions should be included in GDP because they represent $200 worth of production—a $100 haircut and $100 worth of groceries. Only buying and selling of used goods or of intermediate goods is excluded from GDP. In other words, contrary to the firm’s claim, when the Bureau of Economic Analysis calculates GDP, it doesn’t “count items multiple times.”

H/T Wojtek Kopczuk on X.

The Effect on a Firm’s Costs of Using a Generative AI Program

Supports: Microeconomics, Chapter 11, Section 11.5; Economics, Chapter 11, Section 11.5; and Essentials of Economics, Chapter 8, Section 8.5

Photo from the Wall Street Journal.

Imani owns a firm that sells payroll services to companies in the Atlanta area. Her largest cost is for labor. She employs workers who use software to prepare payroll reports and to handle texts and calls from client firms. She decides to begin using a generative AI program, like ChatGPT, which is capable of quickly composing thorough answers to many questions and write computer code. She will use the program to write the additional computer code needed to adapt the payroll software to individual client’s needs and to respond to clients seeking advice on payroll questions. Once the AI program is in place, she will need only half as many workers. The number of additional workers she needs to hire for every 20 additional firms that buy her service will fall from 5 to 1. She will have to pay a flat monthly licensing fee for the AI program; the fee will not change with the number of firms she sells her services to. Imani determines that making these changes will reduce her total cost of providing services to her current 2,000 clients from $2,000,000 per month to $1,600,000 per month

In answering the following questions, assume that, apart from the number of workers, none of the other inputs—such as the size of her firm’s office, the number of computers, or other software—change as a result of her leasing the AI program.

a. Briefly explain whether each of the following statements about the cost situation at Imani’s firm after she begins using the AI program is correct or incorrect.

  1. Her firm’s average total cost, average variable cost, and average fixed cost curves will shift down, while her firm’s marginal cost curve will shift up.
  2. Her firm’s average total cost, average variable cost, average fixed cost and marginal cost curves will all shift up.
  3. Her firm’s average total cost, average variable cost, and marginal cost curves will shift down, while her average fixed cost curve will shift up.
  4. Her firm’s average total cost, average variable cost, average fixed cost, and marginal cost curves will all shift down.
  5. Her firm’s average fixed cost curve will shift up, but her other cost curves will be unchanged.

b. Draw a graph illustrating your answer to part a. Be sure to show the original average total cost, average variable cost, average fixed cost, and marginal cost curves. Also show the shifts—if any—in the curves after Imani begins using the AI program.

Solving the Problem

Step 1:  Review the chapter material. This problem requires you to understand definitions of costs, so you may want to review the sections “The Difference between Fixed Costs and Variable Costs,” “Marginal Costs,” and “Graphing Cost Curves”

Step 2:  Answer part (a) by explaining whether each of the five listed statements is correct or incorrect. The cost of the AI program is fixed because it doesn’t change with the quantity of her services that Imani sells. Her firm will have greater fixed costs after licensing the AI program but she will have lower variable costs because she is able to produce the same level of output with fewer workers. Her marginal cost will also decline because she needs to hire fewer workers as the quantity of services she sells increases. We know that the average total cost per month of providing her service to 2,000 clients has decreased because we are given the information that it changed from ($2,000,000/2,000) = $1,000 to ($1,600,000/2,000) = $800.

  1. This statement is incorrect because her average fixed cost curve will shift up as a result of her total fixed cost having increased by the amount of the AI program license and because her marginal cost curve will shift down, not up.
  2. This statement is incorrect because all of her cost curves, except for average fixed cost, will shift down, not up.
  3. This statement is correct because it describes the actual shifts in her cost curves. 
  4. This statement is incorrect because her average fixed cost curve will shift up, not down.
  5. This statement is incorrect because her rather than being unaffected, her average total cost, average variable cost, and marginal cost curves will shift down.

Step 3:  Answer part (b) by drawing the cost curves for Imani’s firm before and after she begins using the AI program. Your graph should look like the following, where the curves representing the firm’s costs before Imani begins leasing the AI program are in blue and the costs after leasing the program are in red.