Individual and Market Demand

CHAPTER 4 INDIVIDUAL AND MARKET DEMAND EXERCISES 1. The ACME corporation determines that at current prices the demand for its computer chips has a price elasticity of -2 in the short run, while the price elasticity for its disk drives is -1. a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its sales? To its sales revenue? We know the formula for the elasticity of demand is: EP  %Q . %P For computer chips, EP = -2, so a 10 percent increase in price will reduce the quantity sold by 20 percent. For disk drives, EP = -1, so a 10 percent increase in price will reduce sales by 10 percent. Sales revenue is equal to price times quantity sold. Let TR1 = P1Q1 be revenue before the price change and TR2 = P2Q2 be revenue after the price change. For computer chips: TRcc = P2Q2 - P1Q1 TRcc = (1.1P1 )(0.8Q1 ) - P1Q1 = -0.12P1Q1, or a 12 percent decline. 34 Chapter 4: Individual and Market Demand For disk drives: TRdd = P2Q2 - P1Q1 TRdd = (1.1P1 )(0.9Q1 ) - P1Q1 = -0.01P1Q1, or a 1 percent decline. Therefore, sales revenue from computer chips decreases substantially, -12 percent, while the sales revenue from disk drives is almost unchanged, -1 percent. b. Can you tell from the available information which product will generate the most revenue for the firm? If yes, why? If not, what additional information would you need? No. Although we know the responsiveness of demand to changes in price, we need to know both quantities and prices of the products to determine total sales revenue. 2. Refer to Example 4.3 on the aggregate demand for wheat. From 1981 to 1990, domestic demand grew in response to growth in U.S. income levels. As a rough approximation, the domestic demand curve in 1990 was QDD = 1200 - 55P. Export demand, however, remained about the same, due to protectionist policies that limited wheat imports. Calculate and draw the aggregate demand curve for wheat in 1990. Given the domestic demand curve for wheat as QDD = 1,200 - 55P, we find intercepts of 1,200  21.82 on the price axis. The 1,200 on the quantity axis and an intercept of 55 export demand curve for wheat, QDE = 2,550 - 220P, has an intercept of 2,550 on the 2,550  1159 . quantity axis and an intercept of on the price axis. The total demand 220 curve follows the domestic demand curve between the prices of $11.59 and $21.82. At $11.59 and a quantity of 562.6 = 1200 - (55)(11.59), the total demand curve kinks. The total demand curve is the horizontal sum of domestic and export demand, with an intercept of 37,500 = 1,200 + 2,550 on the quantity axis. Price 25 20 15 10 DDE DTotal 5 DDD 5 10 15 20 25 30 35 40 Quantity (in hundreds) Figure 4.2 35 Chapter 4: Individual and Market Demand 3. Vera is shopping for a new videocassette recorder. She hears that the Betamax format is technologically superior to the VHS system. However, she asks her friends and it turns out they all have VHS machines. They agree that the Betamax format provides a better picture, but they add that at the local video store, the Beta format section seems to be getting smaller and smaller. Based on what she observes, Vera buys a VHS machine. Can you explain her decision? Speculate on what would occur if a new 8mm video format is introduced. Vera is consuming under the influence of a positive network externality (not a bandwagon effect). Since her reason for buying a VCR is to watch rented videos, she maximizes her choice of videos by choosing a VHS machine. If her only purpose had been to record and play back television programming, she might have purchased a VCR with the Betamax format. The 8mm video format was introduced with video cameras (handheld camcorders). The primary purpose of camcorders is to document business and personal events. At this time, there is little demand for pre-recorded 8mm cassettes. Therefore, it is unlikely that the type of positive network externality that influenced the consumer in the purchase of a VHS VCR will function here. In the future, however, there may be a bandwagon effect, i.e., the purchase of camcorders with the 8mm standard because almost everyone else has one. With hundreds of thousands of 8mm camcorders in use, manufacturers might introduce 8mm VCRs, prompting videos in the 8mm format. Then the 8mm format section at the local video store might get larger and larger, thus prompting consumers to purchase a VCR with the 8mm format as they replace their VCRs. As more 8mm are purchased, more 8mm videos will become available, eventually crowding out the VHS format. 4. Suppose you are in charge of a toll bridge that is essentially cost free. The demand for bridge crossings Q is given by P = 12 - 2Q. a. Draw the demand curve for bridge crossings. Toll 12 10 8 Consumer Surplus 6 P = 12 - 2Q 4 2 1 2 3 4 5 6 7 Crossings Figure 4.4.a b. How many people would cross the bridge if there were no toll? At a price of zero, the quantity demanded would be 6. 36 Chapter 4: Individual and Market Demand c. What is the loss of consumer surplus associated with the charge of a bridge toll of $6? The consumer surplus with no toll is equal to (0.5)(6)(12) = 36. Consumer surplus with a $6 toll is equal to (0.5)(3)(6) = 9, illustrated in Figure 4.4.a. Therefore, the loss of consumer surplus is $27. 5.a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate price-consumption (for a variable price of orange juice) and income-consumption curves. We know that the indifference curves for perfect substitutes will be straight lines. In this case, the consumer will always purchase the cheaper of the two goods. If the price of orange juice is less than that of apple juice, the consumer will purchase only orange juice and the price consumption curve will be on the “orange juice axis” of the graph. If apple juice is cheaper, the consumer will purchase only apple juice and the price consumption curve will be on the “apple juice axis.” If the two goods have the same price, the consumer will be indifferent between the two; the price consumption curve will coincide with the indifference curve. See Figure 4.5.a.i. Apple Juice P A < PO PA = PO E P A > PO U F Orange Juice Figure 4.5.a.i Assuming that the price of orange juice is less than the price of apple juice, the consumer will maximize her utility by consuming only orange juice. As the level of income varies, only the amount of orange juice varies. Thus, the income consumption curve will be the “orange juice axis” in Figure 4.5.a.ii. 37 Chapter 4: Individual and Market Demand Apple Juice Budget Constraint Income Consumption Curve U1 U2 U3 Orange Juice Figure 4.5.a.ii 5.b. Left shoes and right shoes are perfect complements. price-consumption and income-consumption curves. Draw the appropriate For goods that are perfect complements, such as right shoes and left shoes, we know that the indifference curves are L-shaped. The point of utility maximization occurs when the budget constraints, L1 and L2 touch the kink of U1 and U2. See Figure 4.5.b.i. Right Shoes Price Consumption Curve U2 L1 U1 L2 Left Shoes Figure 4.5.b.i In the case of perfect complements, the income consumption curve is a line through the corners of the L-shaped indifference curves. See Figure 4.5.b.ii. 38 Chapter 4: Individual and Market Demand Right Shoes Income Consumption Curve U2 U1 L1 L2 Left Shoes Figure 4.5.b.ii 6. Heather’s marginal rate of substitution of movie tickets for rental videos is known to be the same no matter how many rental videos she wants. Draw Heather’s income consumption curve and her Engel curve for videos. If we let the price of movie tickets be less than the price of a video rental, the budget constraint, L, will be flatter than the indifference curve for the substitute goods, movie tickets and video rentals. The income consumption curve will be on the “video axis,” since she only consumes videos. See Figure 4.6.a. Movie Tickets Income Consumption Curve L U1 U2 U3 Video Rentals Figure 4.6.a Heather’s Engel curve shows that her consumption of video rentals increases as her income rises, and thus the slope of her Engel curve is equal to the price of a video rental. See Figure 4.6.b. 39 Chapter 4: Individual and Market Demand Movie Tickets Engel Curve + Price of Video +1 Video Rentals Figure 4.6.b 7. You are managing a $300,000 city budget in which monies are spent on schools and public safety only. You are about to receive aid from the federal government to support a special anti-drug law enforcement program. Two programs that are available are (1) a $100,000 grant that must be spent on law enforcement; and (2) a 100 percent matching grant, in which each dollar of local spending on law enforcement is matched by a dollar of federal money. The federal matching program limits its payment to each city to a maximum of $100,000. a. Complete the table below with the amounts available for safety. SCHOOLS SAFETY No Govt. Assistance SAFETY Program (1) $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 40 SAFETY Program (2) Chapter 4: Individual and Market Demand a. See Table 4.7.a. SCHOOLS SAFETY No Govt. Assistance SAFETY Program (1) SAFETY Program (2) $0 $50,000 $300,000 $250,000 $400,000 $350,000 $400,000 $350,000 $100,000 $200,000 $300,000 $300,000 $150,000 $150,000 $250,000 $250,000 $200,000 $100,000 $200,000 $200,000 $250,000 $50,000 $150,000 $100,000 $300,000 $0 $100,000 $0 Table 4.7.a b. Which program would you (the manager) choose if you wish to maximize the satisfaction of the citizens if you allocate $50,000 of the $300,000 to schools? What about $250,000? With $50,000 to schools and $250,000 to law enforcement, both aid programs yield the same amount, $100,000, so you are indifferent between the programs. With $250,000 to schools and $50,000 to law enforcement, program (1) yields $100,000 and program (2) yields $50,000, so you prefer program (1). c. Draw the budget constraints for the three options: no aid, program (1), or program (2). Schools 360 300 A C Budget Constraints: 1. No federal aid, AB 2. Program 1, ACE 3. Program 2, ADE 240 D 180 120 60 B 60 120 180 240 300 Figure 4.7.c 41 E 360 420 Safety Chapter 4: Individual and Market Demand With no aid, the budget constraint is the line segment AB, from $300,000 for schools and nothing for law enforcement to $300,000 for law enforcement and nothing for schools. With program (1), the budget constraint, ACE, has two line segments, one parallel to the horizontal axis, until expenditures on safety equal $100,000, and a second sloping downward until $400,000 is spent on safety. With program (2), the budget constraint, ADE, has two line segments, one from ($0, $300,000) to ($200,000, $200,000) and another from ($200,000, $200,000) to ($400,000, $0). 8. By observing an individual’s behavior in the situations outlined below, determine the relevant income elasticities of demand for each good (i.e., whether the good is normal or inferior). If you cannot determine the income elasticity, what additional information might you need? a. Bill spends all his income on books and coffee. He finds $20 while rummaging through a used paperback bin at the bookstore. He immediately buys a new hardcover book of poetry. Books are a normal good since his consumption of books increases with income. Coffee is a normal or neutral good since consumption of coffee did not fall when income increased. b. Bill loses $10 he was going to use to buy a double espresso. He decides to sell his new book at a discount to his friend and use the money to buy coffee. Coffee is clearly a normal good. c. Being bohemian becomes the latest teen fad. As a result, coffee and book prices rise by 25 percent. Bill lowers his consumption of both goods by the same percentage. Books and coffee are both normal goods since his response to a decline in real income is to decrease consumption of both goods. d. Bill drops out of art school and gets an M.B.A. instead. He stops reading books and drinking coffee. Now he reads The Wall Street Journal and drinks bottled mineral water. His tastes have changed completely, and we do not know why. We could use more information regarding his level of income, his desire for sleep, and maybe even a change in political affiliation. 9. Suppose the income elasticity of demand for food is 0.5, and the price elasticity of demand is -1.0. Suppose also that Felicia spends $10,000 a year on food, and that the price of food is $2 and her income is $25,000. a. If a $2 sales tax on food were to cause the price of food to double, what would happen to her consumption of food? (Hint: Since a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity.) The price of food doubles from $2 to $4, so arc elasticity should be used: EP FP  P Q IG 2 F G J Q Q HP KG G H2 1 2 1 2 42 I J . J J K Chapter 4: Individual and Market Demand We know that EP = -1, P = 2, P = 2, and Q  5,000  10,000 . Thus, if there is no 2 change in income, we may solve for Q: F 24 I J Q IG F 2 1  G J . G J H2 KG 5,000  b 5,000  Q g J G J H K 2 By cross-multiplying and rearranging terms, we find that Q = -2,500. This means that she decreases her consumption of food from 5,000 to 2,500 units. b. Suppose that she is given a tax rebate of $5,000 to ease the effect of the tax. What would her consumption of food be now? A tax rebate of $5,000 implies an income increase of $5,000. To calculate the response of demand to the tax rebate, use the definition of the arc elasticity of income. FI  I Q IG 2 F G J Q Q HI KG G H2 1 EI 1 2 2 I J . J J K We know that EI = 0.5, I = 25,000, I = 5,000, Q = 2,500 (from the answer to 9.a). Assuming no change in price, we solve for Q. F 25,000  30,000 I J FQ IG 2 0.5  G J . G J H5,000 KG 2,500  b 2,500  Q g J G J H K 2 By cross-multiplying and rearranging terms, we find that Q = 238. This means that she increases her consumption of food from 2,500 to 2,738 units. c. Is she better or worse off when given a rebate equal to the sales tax payments? Discuss. We want to know if her original indifference curve lies above or below her final indifference curve after the sales tax and after the tax rebate. On her final indifference curve, she chooses to consume 2,738 units of food (for $10,952) and $19,048 of other goods. Was this combination attainable with her original budget? At the original food price of $2, this combination would have cost her (2,738)($2) + $19,048 = $24,524, thus leaving her an extra $476 to spend on either food or other consumption. Therefore, she would have been better off before the sales tax and tax rebate. She could have purchased more of both food and other goods than she could have after the taxes. 43