CHAPTER 4 WORKING WITH SUPPLY AND DEMAND

Transcription

1 CHAPTER 4 WORKING WITH SUPPLY AND DEMAND ANSWERS TO ONLINE REVIEW QUESTIONS 1. The rate of change along a demand curve measures how much one variable changes for every one-unit change in another variable. In the example in the text, a $1 increase in the price of chocolate bars led to a 1000-unit decrease in demand. Hence, the rate of change is 1/1000. But this tells us little about how sensitive demand is to changes in price, because a 1000-unit decline may be a relatively large or small decline depending on the initial quantity demanded. The same is true of the $1 rise in price. Looking at changes in terms of elasticity neatly avoids this problem by measuring changes in percentage terms. Elasticity tells us the relative change in quantity demanded caused by some relative change in price. ( Q 1 Q0) ( P 1 P0) 2. a. % Δ Q = ;% Δ P =, where Q 1 + Q0 P 1 + P0 2 2 Q 0 is initial quantity demanded Q 1 is new quantity demanded P 0 is the initial price P 1 is the new price b. By taking an average of new and old (i.e., the midpoint between the new and old values), we get the same value for elasticity whether we re moving up or down along any given segment of a demand curve. c. A price elasticity of 0.4 means that, for every 1% change in price, quantity demanded declines by 0.4%. Equivalently, a 10% price increase should lead to a 4% decline in quantity demanded, assuming the elasticity remains at around 0.4 over the entire range being examined. 3. a. Gasoline will have the smaller elasticity, i.e., demand will be more inelastic. The more narrowly an item is defined, the more substitutes it has, and the greater will be its elasticity of demand. Exxon brand gasoline is about as narrowly defined as you can get, and hence its demand curve will be quite elastic even a small price increase, for example, will cause consumers to defect to other brands in droves, making a significant dent in quantity sold. Gasoline, however, has fewer substitutes. b. A strong argument can be made that the demand for plumbers services is likely to be less elastic. Plumbers services probably have fewer close substitutes than beauticians services. Whereas a beautician s expertise can be approximated by home permanents, or by the amateur skills of a friend, even the most ardent do-ityourselfer often finds plumbing chores beyond his or her abilities. c. The demand for photocopies is likely less elastic than the demand for automobiles. Recall that the more of a consumer s total budget that is spent on an item, the higher the price elasticity of demand for that good. An automobile is often the 37

2 second largest purchase that a household makes (behind housing) and, hence, represents a large chunk of the household budget. Photocopies, on the other hand, usually constitute a trivial portion of the consumer budget. d. Demand for business class airfare should be more inelastic than demand for coach. Because of the need to get there fast, business people often have no alternative (no close substitutes) to air travel. Hence, their demand is less elastic than casual travelers or tourists, who are more likely to be able to postpone their trips, or seek alternative modes of transportation. 4. Examples of goods with almost perfectly inelastic demand include such things as insulin to a diabetic (an absolute necessity for a patient with that condition, and a drug for which virtually no substitutes are available). Very broadly defined necessities, like housing or food, would also have near-perfectly inelastic demand over some range of prices. Very narrowly defined products, or goods for which close or exact substitutes exist, are candidates for perfectly elastic demand curves. A particular farmer s wheat, for example, is usually indistinguishable from wheat grown on another farm. Many raw materials share this characteristic. For example, the demand for a particular producer s crude oil (of a particular grade) is likely to be very elastic oil is oil, and one producer s is as good as another s. 5. As summarized in Table 1 in the chapter, if demand is inelastic, a price increase will increase total expenditure. This is because although quantity demanded falls when price rises, it does not fall by as much in percentage terms as price rises in percentage terms. Conversely, if demand is elastic, a price increase decreases total expenditure: Quantity demanded decreases by a greater percentage than price increases. 6. Short-run elasticities are generally smaller (in absolute value) than long-run elasticities because, over a longer time horizon, consumers have greater ability to adjust their behavior and find substitutes for a good. 7. The factors of elasticity are the availability of substitutes, the degree to which the good is a necessity or a luxury, the time horizon, and the importance of the good in the buyer s budget. Goods with close substitutes are likely to have more elastic demand. Even a small price rise induces consumers to switch to a relatively cheaper substitute. The availability of substitutes, however, can depend on how a good is defined: The more narrowly a good is defined, the easier it is to find substitutes and, hence, the greater is its price elasticity of demand. The longer the time horizon, the more elastic demand will be, because it is usually easier to find substitutes for an item in the long run than in the short run. The more significant is a good s share of a household s overall budget, the more elastic its demand is likely to be. Price changes for such a good will have a great impact on how much income is available to spend on other goods. 8. a. Canned spaghetti: inferior good as incomes rise people could afford ingredients for homemade spaghetti. b. Vacuum cleaners: normal good. (Most individual households would have an income elasticity of zero they would buy just one vacuum cleaner once their

3 income reaches a certain level, and then buy no more as income rises. However, classifying goods as normal or inferior depends on market income elasticities. As average income in a market rises, more households will decide to own vacuum cleaners or to replace old ones, so we expect a positive income elasticity.) c. Used books: inferior good as incomes rise people buy new books instead. d. Computer software: normal good as incomes rise people tend to buy more computer software programs. 9. In everyday speech, necessities are goods which are necessary, and luxuries are goods not necessary for human survival, or for a full and active life. Economists, however, rely on a more limited, technical definition. Necessities are goods with income elasticities of demand between zero and 1; luxuries have elasticities greater than 1. In many cases, a good s classification as a necessity or luxury by its income elasticity parallels its classification in ordinary speech. However, this need not be the case in Table 5, cigarettes are shown to have an income elasticity of 0.50; hence, in economic terms, they are a necessity. But few people would call cigarettes a necessity in everyday speech. 10. a. Negative; high. These two goods are clearly complements. A rise in the price of one should lead to a significant decline in quantity demanded of the other. b. Positive; low to moderate. In fact, antibiotics are used to treat infections, while decongestants are used to treat symptoms of viral infections (colds, flu). But much of the public erroneously believes that antibiotics which require a doctor s prescription in the United States can help cure the flu. Therefore, a rise in the price of antibiotics might make people less likely to visit the doctor when they have the flu, and more likely to buy over-the-counter decongestants. c. Negative; low to moderate. The relationship between gasoline and auto repairs is derived from the relation between gas and cars, and cars and auto repairs. An increase in gas prices could be expected to reduce demand for cars (or at least certain kinds of cars), which would, in turn, reduce demand for auto repairs. 11. The short side rule says that when quantity supplied and quantity demanded differ, the short side of the market whichever of the two quantities is smaller will prevail. Therefore, 4000 units would be traded, since 4000 is less than If supply is perfectly elastic and demand is perfectly inelastic, the burden of an excise tax would fall completely on buyers. If the situation were reversed, the burden would fall completely on sellers. 13. a. Dentures may have a negative income elasticity, that is, they may be inferior goods, if, like tooth extractions, mainly those who cannot afford adequate dental care (or more expensive treatments such as root canals) end up needing dentures. b. Lasik surgery is a substitute for prescription eyeglasses, and should increase the price elasticity of demand for prescription eyeglasses. If Lasik surgery was significantly more expensive than prescription eyeglasses, it could conceivably reduce the income elasticity of demand for prescription eyeglasses, as they become

4 an inferior good that only those who could not afford Lasik surgery would buy. However, if Lasik prices continue to fall, this result is less likely to occur. PROBLEM SET 1. a. 40 units will be traded since that is all that buyers are willing and able to buy at the price floor of $50 per ton. b. The government will have to purchase the surplus, limit imports from abroad, or control the production and sale of rice. 2. a. There is excess demand equal to 250 units ( ). b. Only 350 apartments will be rented. c. Since the price ceiling is non-binding, the market will move to equilibrium, where 400 apartments will be rented. There will be neither excess supply nor excess demand. 3. a. This is a straight line demand curve since for every $0.50 increase in price, the quantity of bottles demanded falls by the same amount (100 units). b. Demand is inelastic for this price change E = = = 0.55 c. Demand is elastic for this price change E = = = 3.66 d. As we slide down the demand curve, the price elasticity of demand changes from 3.66 to 0.55, that is, demand becomes less elastic.

5 e. P Q d Total Revenue f. From the table in part e, we can confirm that an increase in price in the inelastic range (from $1 to $1.50) led to an increase in total revenue from $500 to $600, while an increase in price in the elastic range (from $2.50 to $3.00) led to a decrease in total revenue (from $500 to $300). 4. In order for the $60 per unit tax to be divided equally between buyers and sellers, the price paid by buyers would have to be $30 higher than it was originally and the after-tax price received by sellers would have to be $30 lower. That is, the new price paid by consumers would have to be $300 + $30 = $330 and the price received by sellers would have to be $ = $270. From the diagram, however, it s clear that at $330 per ticket, consumers would want to purchase more than 7.5 million tickets per year while at $270 per ticket (after taxes), sellers would want to offer fewer than 7.5 million tickets. Therefore, with an equal split of the tax, the market could not be in equilibrium 5. For the demand curve to be unit elastic, there would have to be no change in revenue as a result of a price change. In the initial situation, 110 units are sold at a price of $9 per unit, so revenue is $9 x 110 = $990. If demand is unit elastic, and the price rises to $11 per unit, a constant revenue implies that the new quantity demanded would have to be $990/$11 = 90 units. Now we know two points on the demand curves. To find other curves, try to come up with price quantity combinations such that p x q = $990. Once you ve found one or two more, plot them and connect them to find that the demand curve must be curved. Price Per Unit ($) $12 $11 $10 $9 $8 D Quantity per year

6 6. When an (effective) price ceiling is imposed, quantity demanded exceeds quantity supplied at that ceiling price. To prevent black-market activity, the government would have to somehow make up for the shortage. It could do this by obtaining the needed units (housing units, in the case of rent control) and selling them at the ceiling price Opinions may vary, but this seems a very inefficient way of enforcing the ceiling. The government would find that the cost of producing the extra units is more than the revenue they would generate. 7. Suppose that the short-run elasticity of demand is Then a 25 percent increase in fares would lead to a 25 x 0.35 = 8.75 percent decrease in revenue. A similar calculation could be used for other short-run elasticities; just multiply 25% by the elasticity to get the percent decrease in revenue. 8. In Chapter 4, we learned that about 25 percent of the world s oil is produced in the Persian Gulf. If half the Gulf s capacity was wiped out, that would amount to a 12.5 percent drop in production. In the long run, with a long-run demand elasticity of 0.4, the price would have to rise by 12.5/0.4 = percent. From an initial price of $60 per barrel, the price would rise by x 60 = $18.75 per barrel to a new price of $78.75/barrel. 9. If the $10,000 subsidy is paid to colleges, the effect would be to shift the supply curve downward by $10,000 per student. That s because part of the cost of providing education would be borne by whoever provides the subsidy (probably, the government). The result, however, would be unchanged. The new tuition would be $21,000 per student and 4.8 million students would be enrolled. Price per Year S 1 $31,000 S After Subsidy 25,000 A 21,000 B D 4 million 4.8 million Number of Students Attending College 10. a. It is not a straight line demand curve since quantity demanded does not fall by the same amounts following repeated price rises by a fixed amount.

7 b. Demand is elastic for this price change E = = = 1.47 c. Demand is elastic for this price change. d. There must be good substitutes available for rosebushes from a particular nursery (either other types of plants or rosebushes from that nursery s competitors), given that over this range of prices, it is unlikely that rosebushes make up a significant share of a household s budget. 11. a. The demand for pork is more elastic than the demand for cigarettes. This is because there are more substitutes for pork (e.g., beef, chicken) than there are for cigarettes. b. If the price of milk rises by 5 percent, then the quantity of milk demanded will fall by 2.7 percent (5 0.54). 12. a. More elastic. b. Quantity demanded will fall by 2,190 bottles. To find this answer, first use the mid-point rule to calculate that the price of Pepsi increased by 10.5%. Then, substitute this value and the value of the price elasticity of demand into the equation for price elasticity of demand, and solve for the change in quantity demanded: 2.08 = x 10.5% x = 21.9% E = = = 2.25 Finally, multiply the initial number of bottles of Pepsi demanded by this price elasticity of demand to find the change in quantity demanded: Change in quantity demanded = 21.9% 10,000 = 2,190

8 c. The price of ground beef will have to increase by 4.9%. Find this by substituting what is known into the equation for price elasticity of demand and solving for x: 1.02 = 5% x x = 4.9% 13. a. They should increase their price to $30/hour. Given that the price elasticity of demand for their service is 0.5, their revenue will increase when they increase their price to $30/hour because the increase in their price will be larger (in percentage terms) than the decrease in their demand. (Also note: They will be doing less moving at a higher price, so their other costs will go down as well, and they will enjoy more leisure.) b. Demand is likely to become more elastic. The availability of substitutes is one of the primary determinants of price elasticity of demand. Increased competition from companies providing essentially the same service will make demand for Three Guys services more sensitive to changes in price, hence, more elastic. MORE CHALLENGING QUESTION 14. Either the supply of PCs in Europe is perfectly inelastic, or the demand for PCs in Europe is perfectly elastic. Neither of these statements is likely to be true, or even close to true.