Answers to Review Questions 1. Price changes affect quantity demanded for two reasons: They attractiveness of substitute goods and they alter the real value of the consumers purchasing power. The second effect grows larger as the share of the consumers bud get spent on the good increases 2. Elasticity of demand at any point is the price-quantity ratio at that point times the reciprocal of the slope of the demand curve. The slope, and hence its reciprocal, is constant along a straight-line demand curve, but the price quantity ratioand hence price elasticity of demand--declines as we move down the curve 3. If the demand for a good is inelastic with respect to its price, an increase in price will lead to a reduction in total expend iture 4. Because the algebra ic sign of the elasticity of demand for a good with respect to its own price is always negative, knowing that sign conveys no useful information. In contrast, the elasticity of demand for a good with respect to the price of another good can be either positive or negative, so it is important to keep track of the sign 5. To increase the quantity of output supplied when price rises, firms need to increase the amount of inputs they buy, a time-consuming process for certain kinds of input The process can be speeded up, but only if the firm is willing to incur add itional costs Answers to problems 1. For the demand curve shown, the slope is 1 so(1/slope) is also 1. The absolute value of the price elasticity of demand at any point on this demand curve is thus the ratio(P/Q)at that point infinity B D
Answers to Review Questions 1. Price changes affect quantity demanded for two reasons: They alter the attractiveness of substitute goods and they alter the real value of the consumer’s purchasing power. The second effect grows larger as the share of the consumer’s budget spent on the good increases. 2. Elasticity of demand at any point is the price-quantity ratio at that point times the reciprocal of the slope of the demand curve. The slope, and hence its reciprocal, is constant along a straight-line demand curve, but the price quantity ratio—and hence price elasticity of demand—declines as we move down the curve. 3. If the demand for a good is inelastic with respect to its price, an increase in price will lead to a reduction in total expenditure. 4. Because the algebraic sign of the elasticity of demand for a good with respect to its own price is always negative, knowing that sign conveys no useful information. In contrast, the elasticity of demand for a good with respect to the price of another good can be either positive or negative, so it is important to keep track of the sign. 5. To increase the quantity of output supplied when price rises, firms need to increase the amount of inputs they buy, a time-consuming process for certain kinds of inputs. The process can be speeded up, but only if the firm is willing to incur additional costs. Answers to Problems 1. For the demand curve shown, the slope is 1 so (1/slope) is also 1. The absolute value of the price elasticity of demand at any point on this demand curve is thus the ratio (P/Q) at that point. A infinity B 3 C 1 D 1/3 E 0
B Q P (S/pack 18(1000s of packs/day b. Use the formula: elasticity =(P/Q)(1/slope). When P=3, Q=9 and 1/slope is 3 So elasticity =3(3/9)=1.0 c If the price increases from $3 to $4, revenue will fall from $27,000 to $24,000 d Using the same formula as in b, elasticity=(2/12)X(3)=0.5 e If the price increases from $2 to $3, revenue will rise from $24,000 to $27,000 3. To maximize revenue from the sale of tickets price should be set at the midpoint of he demand curve, p=$6/visit
P Q 100 75 50 25 25 50 75 100 A B C D E 2. a. P ($/pack) Q (1000s of packs/day 6 9 18 3 b. Use the formula: elasticity = (P/Q) (1/slope). When P = 3, Q = 9 and 1/slope is 3. So elasticity = 3(3/9) = 1.0. c. If the price increases from $3 to $4, revenue will fall from $27,000 to $24,000. d. Using the same formula as in b, elasticity = (2/12)x(3) = 0.5. e. If the price increases from $2 to $3, revenue will rise from $24,000 to $27,000. 3. To maximize revenue from the sale of tickets price should be set at the midpoint of the demand curve, p = $6/visit
P (S/visit) elastic Inelastic region Q(visitors per day) 4. The price elasticity of a good generally increases with the number of substitutes it has. It is easier to substitute a Ford or Toyota for a Chevrolet than it is to substitute a motorcycle or a skateboard for a car. Thus the market demand curve for cars is likely to be less elastic with respect to price than the market demand curve for Chevrolets 5. The more income a person has, the smaller a given expend iture will be as a proportion of her overall budget, and hence the less likely she will be to respond dramatically to a price change. Thus senior executives, the most highly paid of the three groups, should have the least price-elastic demand curves. Students, the least well paid, should have the most price-elastic demand curves 6. The cross-price elasticity is(percent change in Qsyrup/percent change in Pmilk)=-4/2 -2. Since this cross elasticity is negative, the two are complements 7. The expression for supply elasticity is(P/Q)x(1/slope). Since the slope of this supply curve is AP/AQ= 2/3, the elasticity of supply at A is(4/9)x(3/2 F2/3. The elasticity at B is(6/12)x (3/2)3/4 △P 912 8. The inputs required to produce each slice of pizza cost a total of $1.20, and this marginal cost is constant. The supply curve of pizza is thus a horizontal line at P
P ($/visit) Q (visitors per day) 6 12 3 6 elastic region inelastic region 4. The price elasticity of a good generally increases with the number of substitutes it has. It is easier to substitute a Ford or Toyota for a Chevrolet than it is to substitute a motorcycle or a skateboard for a car. Thus the market demand curve for cars is likely to be less elastic with respect to price than the market demand curve for Chevrolets. 5. The more income a person has, the smaller a given expenditure will be as a proportion of her overall budget, and hence the less likely she will be to respond dramatically to a price change. Thus senior executives, the most highly paid of the three groups, should have the least price-elastic demand curves. Students, the least well paid, should have the most price-elastic demand curves. 6. The cross-price elasticity is (percent change in Qsyrup/percent change in Pmilk) = -4/2 = -2. Since this cross elasticity is negative, the two are complements. 7. The expression for supply elasticity is (P/Q)x(1/slope). Since the slope of this supply curve is P/Q = 2/3, the elasticity of supply at A is (4/9)x(3/2)=2/3. The elasticity at B is (6/12)x(3/2)=3/4. Price 6 A Quantity 9 12 4 B Q P S 8. The inputs required to produce each slice of pizza cost a total of $1.20, and this marginal cost is constant. The supply curve of pizza is thus a horizontal line at P =
$1.20 P (S/slice (slices per day) 9. The absolute value of the slope of this demand curve is 1/3, so plugging in the P and Q values at point A into the formula elasticity =(1/slope )P/Q, we have elasticit at a=3(4/6)=2. A one percent price increase will thus translate into a two percent decrease in the quantity demanded. Total expenditure, which was PQ, will thus now be(1.01P)x(98Q), which is approximately equal to 99Q. So total expend iture will decline by about one percent 10. What government officials failed to take into account was that people dont demand electricity for its own sake, but rather as a means to accomplish other ends such as producing cooler air for their homes. By requiring people to buy more efficient air conditioners, the government effectively reduced the price of buying cooler air. If the demand for cool air is sufficiently elastic with respect to its price people may buy enough more of it than before that they end up using more electricit
$1.20. S Q (slices per day) P ($/slice) 9. The absolute value of the slope of this demand curve is 1/3, so plugging in the P and Q values at point A into the formula elasticity = (1/slope)P/Q, we have elasticity at A = 3(4/6) = 2. A one percent price increase will thus translate into a two percent decrease in the quantity demanded. Total expenditure, which was PQ, will thus now be (1.01P)x(.98Q), which is approximately equal to .99Q. So total expenditure will decline by about one percent. 10. What government officials failed to take into account was that people don’t demand electricity for its own sake, but rather as a means to accomplish other ends, such as producing cooler air for their homes. By requiring people to buy more efficient air conditioners, the government effectively reduced the price of buying cooler air. If the demand for cool air is sufficiently elastic with respect to its price, people may buy enough more of it than before that they end up using more electricity