Demand Analysis. Chapter 3. Solutions to Exercises

Transcription

1 Chapter 3 Demand Analysis Solutions to Exercises 1. With more rural households, Canadian demand for gasoline maybe less price sensitive than U.S. demand where urbanities are offered more mass transit alternatives. 2. %ΔQ = 20 E Y = 1.5 %ΔP = +5 E X = 0.3 %ΔY = 2 %ΔP gas = +20 a. %ΔQ = 1.5( 2%) = 3% b. %ΔQ = 0.3(20%) = 6% c. 20% = 1.5( 2%) + ( 0.3)(20%) + ( )(5%) = a. = [( )/( )]/[( )/( )] = 1.46 b. E Y = [( )/( )]/[( )/( )] E = 3.53 Y c. E Y = 3.53 = [( 400)/( +400)]/[( )/( )] = 505 airplanes d. %ΔQ P = (%ΔP) = 1.46 [( )/( )/2](100) = -8.85% %ΔQ Y = E Y (%ΔY) = 3.53 [( )/( )/2](100) =

2 Chapter 3/Demand Analysis Net effect = %ΔQ P + %ΔQ Y = 8.85% % = 14.3% 17 Using the average quantity [( + Q 1 )/2] as the base in computing the percentage change yields: %ΔQ = 14.3% = [(Q 400)/(Q + 400)/2](100) 2 2 = airplanes Using the initial quantity (Q 1 = 400) as the base in computing the percentage change yields: = Q 1 (1 + net effect) = 400( ) = airplanes Note that these two alternative solutions differ by less than 1 percent. 4. New demand = 100% +.04( 1.5)(100%) +.11(.6)(100) = 100.6% Total revenue will increase since both price and quantity are increased. The effect on profits is indeterminate, since we don't know the amount of advertising or the shape of the firm's cost function. 5. a. It assumed that demand was highly inelastic that is, the increase in the price of the plates would not be offset by an equally large decrease in the quantity of plates sold. b. = [( )/( )]/[(75 25)/(75+25)] =.93 c. It realized that a greater increase in revenues could be obtained from a smaller increase in price. 6. a. These goods are extremely close substitutes. A 1 percent increase (decrease) in the price of one good results in a 1.2 percent increase (decrease) in the quantity demanded for the other. b. 1.2 = %ΔQ / +5% A %ΔQ A = 6% (Note: A cross price elasticity this high would be extremely unusual. If such a number had been derived from empirical analysis, it would be wise to reexamine all of the assumptions of the model.) 7. Ridership for 2006: Cross elasticity =.2 = [(Q 5000)/(Q+5000)]/[( )/( )] Q = 5526 Ridership for 2007: Price elasticity = 1.2 = [(Q 5526)/(Q+5526)]/[( )/( )] Q = 4238

3 18 Chapter 3/Demand Analysis 8. a. Q = Y 5.5P P = 150 guilders; Y = 15(000) guilders Q = (15) 5.5(150) = 1400 = 5.5(150/1400) = 0.59 b. E y = 15(15/1400) = If the price of DVD players declines by 20% and the total revenue rises, this indicates that the demand for DVD players is price elastic. We cannot determine the impact of this price reduction on the firm's profits without also knowing the cost function facing the firm. 10. MR = P(1 + 1/ ) 15 = P(1 + 1/ 1.2) P = $ a. P = $10 Q = (10) = 4500 P = $20 Q = (20) = 4000 P = $30 Q = (30) = 3500 b. between $10 and $20: = [( )/( )]/[(20 10)/(20+10)] = between $20 and $30: = [( )/( )]/[(30 20)/(30+20)] = c. = 50(10/4500) = = 50(20/4000) = = 50(30/3500) = d. Q D = 4250 = P P = $15

4 Chapter 3/Demand Analysis 12. Year 1-2: Price elasticity = [( )/( )]/[( )/( )] = Year 2-3: Income elasticity E Y = [( )/( )]/[( )/( )] E Y = 1.22 Year 3-4: Cross price elasticity E X = [( )/( )]/[(.90.65)/( )] =.16 Year 4-5: Price elasticity = [( )/( )]/[( )/( )] = 3.65 Year 5-6: Price elasticity = [( )/( )]/[( )/( )] =.74 Year 6-7: Income elasticity E Y = [( )/( )]/[( )/( )] = 0.90 Year 7-8: Cross price elasticity E X = [( )/( )]/[(.65.90)/( )] = a. Price Quantity Arc Elasticity Total Revenue Marginal Revenue b. MR has a slope 2X as steep as the demand function. MR = 0 when TR is maximized at 560.

5 20 Chapter 3/Demand Analysis 14. Forecasted demand = 11 million[1 + income elasticity %Δ in DPI + price elasticity %Δ in price] Chow estimate: 11M[ (.04) 1.2(.06)] = M Alkinson: 11M[ (.04) 1.4(.06)] = M Roos: 11M[ (.04) 1.5(.06)] = M Suits: 11M[ (.04) 1.2(.06)] = M 15. a. E X = [( )/( )]/[(30 35)/(30+35)] E X = 1.34 (The products are very close substitutes.) b. = 1.5 = [( )/( )]/[(P 2 25)/P 2 +25)] P 2 = $21.77 c. Before: TR 1 = P 1 Q 1 = 25(6500) = $162,500 After: TR 2 = P 2 = $21.77(8000) = $174,160 d. The increase in total revenue is not necessarily desirable. One would also have to look at the change in costs and the resulting effect on profits before determining whether the price cut was desirable. 16. a. = 30%/+100% = 0.3 b. Ridership probably would not return to the original level because some people may have invested in alternatives (cars, etc.) or found other transit options that they are reluctant to give up. 17. a. Future income levels = (1 +.04) 5 = 1.22 or a 22% increase in income over five years. Rental market impact:.8(22%) = +17.6% to 1.0(22%) = +22% Owner-occupant market impact:.7(22%) = +15.4% to 1.15(22%) = 25.3% b. The price increase should tend to partially offset this effect, ceteris paribus, unless consumers expect even greater price increases in the future. 18. = [( )/( )]/[( )/( )] = 0.727

6 Chapter 3/Demand Analysis 19. a. E X = [( )/( )]/[(8 10)/(8+10)] = b. If the cross elasticity remains constant at 2.25 when the price of B-8 is increased, sales of A-6 should increase as follows: 2.25 = [(Q A2 500)/(Q A2 +500)]/[(12 10)/(12+10)] Q A2 = 757 c. The evidence indicates that these products are very close substitutes. The cross price elasticity coefficient is so high as to suggest that it may not have been estimated properly, i.e., the ceteris paribus assumptions may have been violated. 20. = %ΔQ/ 20% = 2.2 %ΔQ = +44% 21. a. i. Q = 16, (P) Q = 16, (100) Q = 3,278 = (100/3278) = 4.01 ii. Q = 16, (80) Q = 5,905 = (80/5905) = 1.78 b. = [( )/( )]/[(40 50)/50+40)] = a. E X = [( )/( )]/[( )/( )] E X = 1.00 b. Yes, a 1% decrease in price by Spring City leads to a 1% decrease in sales by Potomac. Other factors influencing the observed relationship could be (a) a seasonal decline in demand for new ovens, perhaps related to seasonal changes in housing starts; (b) publicity by governmental agencies about radiation or other dangers in ultrasonic ovens; (c) an economic recession during the period of the observation. c. 3.0 = [( )/( )]/[(P 2 500)/(P )] P 2 = $454.54

7 22 Chapter 3/Demand Analysis Solution to Case Exercise: Polo Golf Shirt Pricing 7 $38.31 $268 $28 $28 8 $36.50 $292 $24 $28 9 $34.50 $311 $19 $28 10 $32.70 $327 $16 $28 11 $30.91 $340 $13 $28 12 $29.17 $350 $10 $28 13 $27.46 $357 $7 $28 14 $25.79 $361 $4 $28 15 $24.07 $361 $0 $28 16 $22.50 $360 ($1) $28 17 $20.94 $356 ($4) $28 18 $19.39 $349 ($7) $28 Sales revenue is maximized at $361 at a price of $ In contrast, operating profit is maximized at a price of $38.31, where marginal revenue covers the marginal cost of another shirt. Sales personnel working on commission (a given percentage of sales revenue) would prefer the $24.07 price. Profitsharing plans can be used to align employee and owner interests.