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Constraints. P4.4 Budget Holding all else equal, indicate how each of the following changes would affect a budget constraint that limits consumption of goods (Y) and services (X). Explain your Register to View Answer Deflation that uniformly drops the price of all goods and services. B. Inflation that consistently increases the price of all goods and services. C. Technical change that reduces the price of goods, but leaves the price of services unchanged. D. Economic growth that boosts the level of disposable income. E. Government-mandated health care coverage for workers that boosts the price of goods by 3% and increases the price of services by 5%. P4.4 SOLUTION A. Deflation that drops the price of all goods and services results in a parallel rightward (outward) shift in the budget constraint. Holding income constant, lower prices make it possible for consumers to buy more goods and services with the same total amount of spending. This beneficial impact on consumption is similar to that following an increase in income. B. Inflation that increases the price of all goods and services results in a parallel leftward (inward) shift in the budget constraint. Holding income constant, higher prices reduce the amount of goods and services that consumers can buy with a fixed amount of spending. This harmful impact on consumption is similar to that following a decrease in income. C. Technical change that reduces the price of goods, but leaves the price of services unchanged results in an outward rotation of the budget constraint along the goods (Y) axis. After such a change, the budget line intersects the Y axis at a higher point, indicating that a greater amount of goods can be purchased with a fixed budget. The amount of services that can be purchased for a fixed amount is unaffected by such a change, and the X intercept (services axis) of the budget constraint is unaffected by such a change. D. Economic growth that boosts the level of disposable income results in a parallel rightward (outward) shift in the budget constraint. Holding prices constant, growing income makes it possible for consumers to buy more goods and services with the same total amount of spending. This beneficial impact on consumption is similar to that following deflation that drops the price of all goods and services. E. Government-mandated health care coverage for workers that boosts the price of goods by 3% and increases the price of services by 5% will have a negative impact on consumption of both goods and services, but the negative impact will be worse in the case of services. Following such a change, the relative price of services will rise relative to the price of goods. The new budget line will move inward 3% along the X axis reflecting the fact that a fixed budget will only be able to buy 97% of the previously affordable goods. The new budget line will move inward 5% along the Y axis reflecting the fact that a fixed budget will only be able to buy 95% of the previously affordable services. The net effect is similar to a decrease in income followed by a unilateral increase in the price of services. P4.5 Elasticity. The demand for personal computers can be characterized by the following point elasticities: price elasticity = - 5, cross-price elasticity with software = - 4, and income elasticity = 2.5. Indicate whether each of the following statements is true or false, and explain your Register to View Answer A price reduction for personal computers will increase both the number of units demanded and the total revenue of sellers. B. The cross-price elasticity indicates that a 5% reduction in the price of personal computers will cause a 20% increase in software demand. C. Demand for personal computers is price elastic and computers are cyclical normal goods. D. Falling software prices will increase revenues received by sellers of both computers and software. E. A 2% price reduction would be necessary to overcome the effects of a 1% decline in income. P4.5 SOLUTION A. True. A price reduction always increases units sold, given a downward sloping demand curve. The negative sign on the price elasticity indicates that this is indeed the case here. The fact that price elasticity equals -5 indicates that demand is elastic with respect to price, and that a price reduction will increase total revenues. B. False. The cross-price elasticity indicates that a 5% decrease in the price of software programs will have the effect of increasing personal computer demand by 20%. C. True. Demand is price elastic (see part A). Since the income elasticity is positive, personal computers are a normal good. Moreover, since the income elasticity is greater than one, personal computer demand is also cyclical. D. False. Negative cross-price elasticity indicates that personal computers and software are compliments. Therefore, falling software prices will increase the demand for computers and resulting revenues for sellers. However, there is no information concerning the price elasticity of demand for software, and therefore, one does not know the effect of falling software prices on software revenues. E. False. A 2% reduction in price will cause a 10% increase in the quantity of personal computers demanded. A 1% decline in income will cause a 2.5% fall in demand. These changes will not be mutually offsetting. P4.6 Optimal Pricing. In an effort to reduce excess end-of-the-model-year inventory, Harrison Ford offered a 1% discount off the average price of 4WD Escape GasElectric Hybrid SUVs sold during the month of August. Customer response was wildly enthusiastic, with unit sales rising by 10% over the previous month's level. A. B. P4.6 Calculate the point price elasticity of demand for Harrison Ford 4WD Escape Gas-Electric Hybrid SUVs sold during the month of August. Calculate the profit-maximizing price per unit if Harrison Ford has an average wholesale (invoice) cost of $23,500 and incurs marginal selling costs of $350 per unit. SOLUTION A. P = Q/Q P/P = 10%/-1% = -10 (Highly elastic) B. The profit-maximizing price can be found using the optimal price formula: P* = MC/(1 + 1/P) = ($23,500 + $350)/[1 + 1/(-10)] = $26,500 P4.7 Cross-Price Elasticity. The South Beach Cafe recently reduced appetizer prices from $12 to $10 for afternoon early bird customers and enjoyed a resulting increase in sales from 90 to 150 orders per day. Beverage sales also increased from 300 to 600 units per day. A. Calculate the arc price elasticity of demand for appetizers. B. Calculate the arc cross-price elasticity of demand between beverage sales and appetizer prices. C. P4.7 Holding all else equal, would you expect an additional appetizer price decrease to $8 to cause both appetizer and beverage revenues to rise? Explain. SOLUTION A. EP = Q P 2 + P1 (150 - 90) ($10 + $12) = = - 2.75 P Q 2 + Q1 ($10 - $12) (150 + 90) E PX = Q P X 2 + P X 1 (600 - 300) ($10 + $12) = = - 3.67 PX ($10 - $12) (600 + 300) Q 2 + Q1 B. C. Yes, the |EP| = 2.75 > 1 calculated in part A implies an elastic demand for appetizers and that additional an price reduction will increase appetizer revenues. E PX = -3.67 < 0 indicates that beverages and appetizers are complements. Therefore, a further decrease in appetizer prices will cause a continued growth in beverage unit sales and revenues. Alternatively, If P = a + bQ, then $12 = a + b(90) and $10 = a + b(150). Solving for the demand curve gives P = $15 - $0.033Q. At P = $12, total revenue is $1,080 (= $12 90). If P = $10, total revenue is $1,500 (= $10 150). At P = $8, total revenue is $1,680 (= $8 210). In any case, to determine the profit effects of appetizer price changes it is necessary to consider revenue and cost implications of both appetizer and beverage sales. P4.8 Income Elasticity. Ironside Industries, Inc., is a leading manufacturer of tufted carpeting under the Ironside brand. Demand for Ironside's products is closely tied to the overall pace of building and remodeling activity and, therefore, is highly sensitive to changes in national income. The carpet manufacturing industry is highly competitive, so Ironside's demand is also very price-sensitive. During the past year, Ironside sold 30 million square yards (units) of carpeting at an average wholesale price of $15.50 per unit. This year, household income is expected to ssurge from $55,500 to $58,500 per year in a booming economic recovery. A. Without any price change, Ironside's marketing director expects current-year sales to soar to 50 million units because of rising income. Calculate the implied income arc elasticity of demand. B. Given the projected rise in income, the marketing director believes that a volume of 30 million units could be maintained despite an increase in price of $1 per unit. On this basis, calculate the implied arc price elasticity of demand. C. Holding all else equal, would a further increase in price result in higher or lower total revenue? P4.8 SOLUTION A. EI = Q I 2 + I1 I Q 2 + Q1 50 - 30 $58,500 + $55,500 $58,500 - $55,500 50 + 30 = 9.5 = B. Without a price increase, sales this year would total 50 million units. Therefore, it is appropriate to estimate the arc price elasticity from a before-price-increase base of 50 million units: EP = = Q P P 2 + P1 Q 2 + Q1 30 - 50 $16.50 - $15.50 = - 8 (Elastic) $16.50 + $15.50 30 + 50 C. Lower. Since carpet demand is in the elastic range, E P = -8, an increase (decrease) in price will result in lower (higher) total revenues. P4.9 Cross-Price Elasticity. B. B. Lean is a catalog retailer of a wide variety of sporting goods and recreational products. Although the market response to the company's spring catalog was generally good, sales of B. B. Lean's $140 deluxe garment bag declined from 10,000 to 4,800 units. During this period, a competitor offered a whopping $52 off their regular $137 price on deluxe garment bags. A. B. A. B. B. Lean's deluxe garment bag sales recovered from 4,800 units to 6,000 units following a price reduction to $130 per unit. Calculate B. B. Lean's arc price elasticity of demand for this product. C. P4.9 Calculate the arc cross-price elasticity of demand for B. B. Lean's deluxe garment bag. Assuming the same arc price elasticity of demand calculated in Part B, determine the further price reduction necessary for B. B. Lean to fully recover lost sales (i.e., regain a volume of 10,000 units). SOLUTION EPX = QY 2-QY1 P X 2-P X1 P X 2+P X1 QY 2+QY1 = 4,800 - 10,000 $85 - $137 $85 + $137 4,800 + 10,000 = 1.5 (Substitutes) B. EP = = Q 2 -Q1 P 2 -P1 P 2+P1 Q 2 + Q1 6,000 - 4,800 $130 - $140 $130 + $140 6,000 + 4,800 = -3 (Elastic) C. EP = Q 2 -Q1 P 2 + P1 P 2 -P1 Q 2 +Q1 -3 = 10,000 - 6,000 + $130 x P2 10,000 + 6,000 P2 - $130 -3 = P 2 + $130 4(P 2 - $130) -12P2 + $1,560 = P2 + $130 13P2 = $1,430 P2 = $110 This implies a further price reduction of $20 because: P = $130 - $110 = $20 P4.10 Advertising Elasticity. Enchantment Cosmetics, Inc., offers a line of cosmetic and perfume products marketed through leading department stores. Product Manager Erica Kane recently raised the suggested retail price on a popular line of mascara products from $9 to $12 following increases in the costs of labor and materials. Unfortunately, sales dropped sharply from 16,200 to 9,000 units per month. In an effort to regain lost sales, Enchantment ran a coupon promotion featuring $5 off the new regular price. Coupon printing and distribution costs totaled $500 per month and represented a substantial increase over the typical advertising budget of $3,250 per month. Despite these added costs, the promotion was judged to be a success, as it proved to be highly popular with consumers. In the period prior to expiration, coupons were used on 40% of all purchases and monthly sales rose to 15,000 units. A. B. Calculate the effective price reduction resulting from the coupon promotion. C. In light of the price reduction associated with the coupon promotion and assuming no change in the price elasticity of demand, calculate Enchantment's arc advertising elasticity. D. P4.10 Calculate the arc price elasticity implied by the initial response to the Enchantment price increase. Why might the true arc advertising elasticity differ from that calculated in part C? SOLUTION A. EP = = Q P 2 + P1 P Q 2 +Q1 9,000 - 16,200 $12 - $9 $12 + $9 9,000 + 16,200 = -2 B. The effective price reduction is $2 since 40% of sales are accompanied by a coupon: P = -$5(0.4) or P2 = $12 - $5(0.4) = -$2 = $10 P = $10 - $12 = -$2 C. To calculate the arc advertising elasticity, the effect of the $2 price cut implicit in the coupon promotion must first be reflected. With just a price cut, the quantity demanded would rise to 13,000, because: EP = -2 = Q* - Q 1 P 2-P1 P 2 + P1 Q* + Q 1 Q* - 9,000 $10 - $12 $10 + $12 Q* + 9,000 -2 = - 11(Q* - 9,000) (Q* + 9,000) -2(Q* + 9,000) = -11(Q* - 9,000) -2Q* - 18,000 = -11Q* + 99,000 9Q* = 117,000 Q* = 13,000 Then, the arc advertising elasticity can be calculated as: EA = = Q 2 - Q* A 2 + A 1 A 2 - A 1 Q 2 + Q* 15,000 - 13,000 $3,750 + $3,250 $3,750 - $3,250 15,000 + 13,000 =1 D. It is important to recognize that a coupon promotion can involve more than just the independent effects of a price cut plus an increase in advertising as is implied in Part C. Synergistic or interactive effects may increase advertising effectiveness when the promotion is accompanied by a price cut. Similarly, price reductions can have a much larger impact when advertised. In addition, a coupon is a price cut for only the most price sensitive (coupon-using) customers, and may spur sales by much more than a dollar equivalent across-the-board price cut. Synergy between advertising and the implicit price reduction that accompanies a coupon promotion can cause the estimate in Part C to overstate the true advertising elasticity. Similarly, this advertising elasticity will be overstated to the extent that targeted price cuts have a bigger influence on the quantity demanded than similar across-the-board price reductions, as seems likely. ... View Full Document

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