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Chapter 6: Problem 11

Taiwan is a major world supplier of semiconductor chips. A recent earthquake severely damaged the production facilities of Taiwanese chip-producing companies, sharply reducing the amount of chips they could produce. a. Assume that the total revenue of a typical nonTaiwanese chip manufacturer rises due to these events. In terms of an elasticity, what must be true for this to happen? Illustrate the change in total revenue with a diagram, indicating the price effect and the quantity effect of the Taiwan earthquake on this company's total revenue. b. Now assume that the total revenue of a typical nonTaiwanese chip manufacturer falls due to these events. In terms of an elasticity, what must be true for this to happen? Illustrate the change in total revenue with a diagram, indicating the price effect and the quantity effect of the Taiwan earthquake on this company's total revenue.

Short Answer

Expert verified
Answer: The total revenue of a non-Taiwanese chip manufacturer can either increase or decrease due to the Taiwan earthquake, depending on the price elasticity of demand for semiconductor chips. If the demand is inelastic (E < 1), the increase in price outweighs the decrease in quantity demanded, leading to an increase in total revenue. If the demand is elastic (E > 1), the decrease in quantity demanded is greater than the increase in price, resulting in a decrease in total revenue.

Step by step solution

01

1. Define price elasticity of demand

Price elasticity of demand is a measure of how sensitive the quantity demanded of a good is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This can be represented as: E = (\text{percentage change in quantity demanded})/(\text{percentage change in price})
02

2. Analyze the case where total revenue increases

If the total revenue of a non-Taiwanese chip manufacturer increases after the earthquake, it means that the increase in price outweighs the potential decrease in quantity demanded. For this to happen, the price elasticity of demand must be inelastic (E < 1). This is because, when demand is inelastic, consumers are less sensitive to price changes, and an increase in price will lead to a decrease in quantity demanded that is proportionally smaller than the price increase. Thus, total revenue will increase in this case.
03

3. Illustrate the change in total revenue with a diagram

To show this change in total revenue, we can draw a demand curve (D) that represents an inelastic demand for semiconductor chips. When the Taiwan earthquake occurs, the supply of chips decreases, leading to an increase in price (P1 to P2) and a decrease in quantity demanded (Q1 to Q2). Since the demand is inelastic, the decrease in quantity demanded will be smaller than the increase in price, leading to a higher total revenue (P2 * Q2 > P1 * Q1). [Insert a graph of inelastic demand with the changes in price and quantity] #b. Total revenue decreases#
04

1. Analyze the case where total revenue decreases

If the total revenue of a non-Taiwanese chip manufacturer decreases after the earthquake, it means that the increase in price doesn't outweigh the decrease in quantity demanded. For this to happen, the price elasticity of demand must be elastic (E > 1). This is because, when demand is elastic, consumers are more sensitive to price changes, and an increase in price will lead to a decrease in quantity demanded that is proportionally greater than the price increase. Thus, total revenue will decrease in this case.
05

2. Illustrate the change in total revenue with a diagram

To show this change in total revenue, we can draw a demand curve (D) that represents an elastic demand for semiconductor chips. When the Taiwan earthquake occurs, the supply of chips decreases, leading to an increase in price (P1 to P2) and a decrease in quantity demanded (Q1 to Q2). Since the demand is elastic, the decrease in quantity demanded will be larger than the increase in price, leading to a lower total revenue (P2 * Q2 < P1 * Q1). [Insert a graph of elastic demand with the changes in price and quantity]

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Most popular questions from this chapter

The U.S. government is considering reducing the amount of carbon dioxide that firms are allowed to produce by issuing a limited number of tradable allowances for carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) emissions. In an April 25 , 2007, report, the U.S. Congressional Budget Office (CBO) argues that "most of the cost of meeting a cap on \(\mathrm{CO}_{2}\) emissions would be borne by consumers, who would face persistently higher prices for products such as electricity and gasoline \(\ldots\) poorer households would bear a larger burden relative to their income than wealthier households would." What assumption about one of the elasticities you learned about in this chapter has to be true for poorer households to be disproportionately affected?

A recent report by the U.S. Centers for Disease Control and Prevention (CDC), published in the CDC's Morbidity and Mortality Weekly Report, studied the effect of an increase in the price of beer on the incidence of new cases of sexually transmitted disease in young adults. In particular, the researchers analyzed the responsiveness of gonorrhea cases to a tax-induced increase in the price of beer. The report concluded that "the.... analysis suggested that a beer tax increase of \(\$ 0.20\) per six-pack could reduce overall gonorrhea rates by \(8.9 \% . "\) Assume that a sixpack costs \(\$ 5.90\) before the price increase. Use the midpoint method to determine the percent increase in the price of a six-pack, and then calculate the cross-price elasticity of demand between beer and incidence of gonorrhea. According to your estimate of this cross-price elasticity of demand, are beer and gonorrhea complements or substitutes?

What can you conclude about the price elasticity of demand in each of the following statements? a. "The pizza delivery business in this town is very competitive. I'd lose half my customers if I raised the price by as little as \(10 \%\)." b. "I owned both of the two Jerry Garcia autographed lithographs in existence. I sold one on eBay for a high price. But when I sold the second one, the price dropped by \(80 \%\)." c. "My economics professor has chosen to use the Krugman/Wells textbook for this class. I have no choice but to buy this book." d. "I always spend a total of exactly \(\$ 10\) per week on coffee."

The accompanying table gives part of the supply schedule for personal computers in the United States. $$ \begin{array}{c|c} \text { Price of computer } & \text { Quantity of computers supplied } \\\ \$ 1,100 & 12,000 \\\ 900 & 8,000 \end{array} $$ a. Calculate the price elasticity of supply when the price increases from $\$ 900\( to \)\$ 1,100$ using the midpoint method. Is it elastic, inelastic or unit-elastic? b. Suppose firms produce 1,000 more computers at any given price due to improved technology. As price increases from \(\$ 900\) to \(\$ 1,100\), is the price elasticity of supply now greater than, less than, or the same as it was in part a? c. Suppose a longer time period under consideration means that the quantity supplied at any given price is \(20 \%\) higher than the figures given in the table. As price increases from \(\$ 900\) to \(\$ 1,100,\) is the price elasticity of supply now greater than, less than, or the same as it was in part a?

The accompanying table shows the price and yearly quantity sold of souvenir T-shirts in the town of Crystal Lake according to the average income of the tourists visiting. $$ \begin{array}{c|c|c} & \begin{array}{c} \text { Quantity of T-shirts } \\\ \text { demanded when } \\\ \text { average tourist } \end{array} & \begin{array}{c} \text { Quantity of T-shirts } \\\ \text { demanded when } \end{array} \\\ \text { Price of } & \text { average tourist } \\\ \text { T-shirt } & \text { income is } \$ 20,000 & \text { income is } \$ 30,000 \\ \hline \$ 4 & 3,000 & 5,000 \\\ 5 & 2,400 & 4,200 \\\ 6 & 1,600 & 3,000 \\\ 7 & 800 & 1,800 \end{array} $$ a. Using the midpoint method, calculate the price elasticity of demand when the price of a T-shirt rises from \(\$ 5\) to \(\$ 6\) and the average tourist income is \(\$ 20,000 .\) Also calculate it when the average tourist income is \(\$ 30,000\). b. Using the midpoint method, calculate the income elasticity of demand when the price of a T-shirt is \(\$ 4\) and the average tourist income increases from \(\$ 20,000\) to \(\$ 30,000 .\) Also calculate it when the price is \(\$ 7\)
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