123Frank and Bernanke Chapter Problems Note from Professor Salemi: I have included the key to all end-of-chapter problems. Some of these problems concern material I have not emphasized and that is not testable. Chapter 4: Elasticity 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 2.a. PQ1007550251005025 75ABCDE124P($/pack)Q(1000s of packs/day61893 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 = $6/visit. P($/visit)Q (visitors per day)61236elastic regioninelastic 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-125elastic 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. Price6AQuantity9124B Q PS 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 = $1.20. SQ(slices per day)P($/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.12610. 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. Chapter 7: Efficiency and Exchange Answers to Problems 1a. Consumer surplus is the triangular area between the demand curve and the price line. Its area is equal to 0.5bh, where b is the base of the triangle and h is the height. The base is 6 units and the height is 1.5 units, measured in dollars. Therefore, consumer surplus is 0.5($1.50/unit)(6 units/wk), or $4.50 per week. b. Producer surplus is the triangular area between the supply curve and the price line. Using the base-height formula, it is (0.5)($4.50/unit)(6 units/wk), or $13.50 per week. c. The maximum weekly amount that consumers and producers together would be willing to pay to trade in used DVDs is the sum of gains from trading in used DVDs—namely, the total economic surplus generated per week, which is $18 per week. 2a. At a price of $7.50, the quantity supplied per week = 2. The quantity demanded at this price is 18 per week, which implies a weekly shortage of 16 used DVDs. b. The weekly economic surplus lost as a result of the price ceiling is the area of the dark-shaded triangle in the diagram, or the sum of the areas of the two triangles ABC and ACD. Using the information given in the graph, this amount is calculated as (0.5)(4)(1) + (0.5)(4)(3) = $8/wk. 124866QuantityPriceP=6+0.75QP=12-0.25Q1623ABCD4 3a. When there is no charge for the tour, the surplus enjoyed by someone who takes it equals his or her reservation price for the tour. If the warden operates the tour on a first-come-first127served basis, Faith, Penny, and Fran will be turned away. The combined consumer surplus when the four who arrive first take the tour is $20 + $14 + $30 + $15=$79. b. An offer of $15 compensation generates 3 volunteers to return another day: Fran, Jack and Jon. The four who go on the tour receive a total consumer surplus of $40 + $30 + $20 + $17=$107. The warden pays $45 in compensation payments to the three volunteers, which causes him a loss in economic surplus of $45 that is exactly offset by the gain in economic surplus to the three volunteers. Total economic surplus from the tour operation is now $107—$28 higher than before. c. The compensation policy is more efficient than the first-come-first-served policy because it establishes a market for a scarce resource that would otherwise be allocated by non-market means. People who choose not to miss the tour that day are paying an opportunity cost of $15 not to miss it. Therefore, only those people to whom the tour is worth more than $15 will actually take it. d. Suppose the Warden auctions off the right to take the tour by steadily increasing the tour price by $1 increments until only 4 people are willing to pay. The auction will stop when the price reaches $16, and Faith, Penny, Herman, and Kate will be the four remaining. The warden will collect $64 from the auction. He can then give refunds to Herman and Kate, who would have gotten to go for free under the first-come-first-served scheme, so they will be just as well off as before. He can give $16 to Jack, which is $1 more than enough