管理经济学第七版英文教辅ch04_keat7e.pdf

Copyright 2014 Pearson Education,Inc.CHAPTER 4 DEMAND ELASTICITY QUESTIONS 1.Elasticity refers to the percentage change in one variable relative to a percentage change in another variable.It is a relative measure of how responsive the change in one variables value will be to the change in the values of some other variables.Price elasticity of demand is defined as the percentage change in quantity demanded resulting from a one percent change in price.2.Point elasticity(in connection with the price elasticity of demand)refers to the elasticity at a given point on a demand curve.It measures the percentage change in quantity caused by a very small(actually infinitesimally small)percentage change in price,assuming these values can change continuously.Arc elasticity measures the elasticity over a certain discrete segment of the demand curve.If arc elasticity were defined as change in quantity/quantity change in price/price then the elasticity coefficient would differ if we moved up on a demand curve as against moving down on it.To make an upward movement have the same elasticity coefficient as a movement down,average quantity and average price are used in the formula.In practical business situations,arc elasticity would probably be the more useful concept,because a businessperson would most likely be interested in the effect on quantity of a change in price of some discrete magnitude rather than an infinitesimally small change in price.3.This result follows from an application of the notion of elasticity of derived demand.The demand for skilled crafts people is probably more inelastic than the demand for industrial workers,since the degree of input substitutability is less for the former than the latter.Thus a substantial increase in the wage of skilled crafts people would cause a smaller decrease in employment than a similar percentage increase in the wages of less skilled workers.4.a.Probably fairly inelastic since mayonnaise is a staple and accounts for a small portion of a persons or a familys total budget.b.Probably fairly elastic,since there are many good substitutes for a specific brand of mayonnaise.c.Probably relatively elastic since there are numerous substitutes.Also,it represents a relatively large portion of a persons budget.d.As a“luxury,”the demand elasticity for a Jaguar could be considered to be relatively elastic.But since such automobiles are purchased by people in a high income category,the demand elasticity could also be quite low.The answer probably depends on whether other high-priced cars(Mercedes,BMW,Infinity,etc.)are considered to be close substitutes.Demand Elasticity 19 Copyright 2014 Pearson Education,Inc.e.Probably rather elastic.It represents a significant expenditure.Further,a repair may significantly prolong its life.f.Probably rather elastic since other vacation arrangements(driving,bus,train)could be substituted.Also,it represents a significant portion of total vacation cost.g.Quite inelastic,since it is considered a staple,and usually represents a small part of a persons budget.h.Probably quite elastic since they represent a large expenditure.If given as a gift,there are probably many good substitutes.5.The income elasticity for restaurant food is probably quite high.Thus,during declines in economic activity(and thus,possibly declines in incomes),spending on restaurant food would most likely decline more than spending at home.Actually,since the two are substitutes,spending on food at home may actually go up during economic declines.6.a.Negative they are complements.b.Positivethey are substitutes.c.Positivethey are substitutes.d.They appear to be unrelated products(thus,cross-elasticity of demand is not significantly different than zero).While there is no relationship between these two products,both of these may compete for budget dollars.From a total budget viewpoint,they could be considered to be substitutes.But usually,the relationship between the two would be very tenuous.7.When the demand curve is inelastic,marginal revenue is negative.Thus,selling on the inelastic portion of the demand curve would result in a decrease in total revenue for every additional unit sold.8.Most likely automobiles,since they represent a larger expenditure and are more likely to be purchased by borrowing on a longer term basis.9.Yes.Elasticity of demand is expected to be higher in the long run.Thus,a larger decrease in gasoline consumption would have been expected.In fact,gasoline prices decreased to pre-crisis levels rather quickly.10.A five-cent increase probably did not affect consumption of gasoline significantly since it was a relatively small change.The demand for gasoline is probably relatively inelastic in such a small range.This is quite different from the doubling of prices,which had occurred during the oil embargo in 1973,for instance.11.Since the demand curve for cigarettes and alcohol is generally thought to be rather inelastic,imposing a tax on these products would not be expected to decrease consumption a great deal.The tax revenue from such products would be considerably larger than from products whose demand curve was rather elastic and whose consumption would decrease greatly upon the imposition of an additional tax.12.No.Since the percentage changes between quantity and price are different at each point of the demand curve.13.This firm is faced by considerable competition.Theoretically,if it raises its price by any small amount,it would lose all of its business,because there are many other firms in the industry that are offering this same product at the lower price.20 Demand Elasticity Copyright 2014 Pearson Education,Inc.14.False.If a companys demand curve is elastic,a price decrease will increase its revenue.But if,as it sells more,its costs should rise more than its revenue,the price action would decrease the companys profit.So,if the company wants to maximize its profits,it will not lower its price in this case.15.a.Less than 1.Elasticity may actually be negative if consumers switch to more expensive butter as their incomes increase.b.Most likely greater than 1.This is a luxury item and increased income may bring about a larger than proportional increase in consumption.c.Probably close to 1.But,as incomes increase,consumers may switch to more expensive furniture.Thus elasticity could be greater than 1.d.Probably greater than 1.Since lobsters are generally an expensive food,people with increasing incomes may increase their expenditure on lobster more than proportionally.16.A one percent increase in income will bring about a.25%increase in spending on tomatoes.17.Elasticity would indicate a movement along the demand curve.However,the drop in used car prices may have resulted from movements in both the demand curve and the supply curve.18.The decision-makers at the U.S.Postal Service are assuming that the demand for mail services is inelastic,and that the price increase will bring about a smaller than proportional percentage decrease in quantity demanded,thus resulting in an increase in revenue.This may very well be true in the short run.However,it may not be a good policy for the long run.Given time,more postal customers may adjust their consumption patterns,and switch to alternative services.As was discussed in the text,in the long run,demand curves become more elastic.Also,the increase in substitute services available over time would increase the price elasticity of demand for mail service,thereby making future postage rate increases more likely to reduce total revenues.19.Providing the U.S.Olympic Team with free clothing items would qualify as an advertising expense.The management of Roots expected sales quantities to experience a high percentage increase relative to their increase in advertising expenses.They apparently turned out to be right.Demand Elasticity 21 Copyright 2014 Pearson Education,Inc.PROBLEMS 1.%change Q .2 =-2%change P-.1 2.a.Q=20-2P;slope Q/P=-2 At P=5 Q=20-2 x 5=10 At P=9 Q=20-2 x 9=2 When Q=10 and P=5 p=-2 x 5/10=-1 Unitary elastic When Q=2 and P=9 p=-2 x 9/2 =-9 Elastic b.At P=5,Q=10 At P=6,Q=8 c.Price Quantity Total Revenue 4 12 48 5 10 50 6 8 48 7 6 42 At a price of$5,revenue reaches its peak.This is also where point price elasticity is 1,as shown in part a.of this problem.3.a.Q=2000 100(6)Q=2000 600=1400 b.1800=2000 100P 100P=2000 1800 100P=200 P=2 c.Q=2000 100(0)Q=2000 d.0=2000 100P 100P=2000 0 P=20 e.Slope=Q/P=100 P=100 x 6/1400 P=100 x 0.0043 P=0.43 4.a.When price changes by 1,quantity will change by 10 in the opposite direction.When income changes by 1,quantity will change by.5 in the same direction.b.Point elasticity:22 Demand Elasticity Copyright 2014 Pearson Education,Inc.Q =100-(10)(7)+(.5)(50)=100-70+25 =55 Slope=-10 p=(-10)x(7/55)=-1.27 Arc elasticity,between P=7 and P=6:at P=6,Q=100-(10)(6)+(.5)(50)=65 E p=(65-55)/(65+55)/(6-7)/(6+7)=-1.08 c.Point elasticity Slope=0.5 y=(.5)x(50/55)=0.45 Arc elasticity,between Y=50 and Y=60 at Y=60,Q=100-(10)(7)+(.5)(60)=60 Ey=(60-55)/(60+55)/(60-50)/(60+50)=0.48 d.Point elasticity Q=100-(10)(8)+(.5)(70)=55 p=(-10)x(8/55)=-1.45 Arc elasticity,between P=8 and P=7 Q=100-(10)(7)+(.5)(70)=65 Ep=(65-55)/(65+55)/(7-8)/(7+8)=-1.25 5.a.At P=7,Q=30-(2)(7)=16 Slope=-2 p=(-2)x(7/16)=-0.88 b.At P=5,Q=30-(2)(5)=20 P=6,Q=30-(2)(6)=18 Ep=(18-20)/(18+20)/(6-5)/(6+5)=-0.58 c.Elasticity will be the same.Equation is now Q=3000-200P At P=7,Q=3000-(200)(7)=1600 Demand Elasticity 23 Copyright 2014 Pearson Education,Inc.Slope=-200 p=-200 x(7/1600)=-0.88 6.a.(x-4000)(63-70)-2.5=/(x+4000)(63+70)x=5212 At P=70,TR=4000 x 70=280,000 P=63,TR=5212 x 63=328,356 Revenue will increase,because demand curve is elastic.(x-3000)(22-25)7.a.-3=/(x+3000)(22+25)x=4421 (x-3000)(24-28)b.3=/(x+3000)(24+28)x=2865 8.If price elasticity is-4,and the Redbirds wish to increase attendance from 50,000 to 80,000,the price(x)must be:(80000-50000)(x-30)-4=/(80000+50000)(x+30)x=26.73 If price is lowered from$30 to 27,and attendance rises from 50,000 to 60,000,price elasticity is:(60000-50000)(27-30)Ep=/(60000+50000)(27+30)=-1.727 9.Arc price elasticity for spreadsheet program:(120-100)(350-400)Ep=,(120+100)(350+400)24 Demand Elasticity Copyright 2014 Pearson Education,Inc.=-1.36 Arc cross elasticity for graphics program:(56-50)(350-400)Ex=,(56+50)(350+400)=-0.85 The quantity demanded for spreadsheets increased due to the price change.The price elasticity is greater than(absolute)1,and therefore revenue will rise from$40,000 to$42,000.The graphics program is a complementary commodity to the spreadsheet program,and its quantity sold benefited from the price decrease in the spreadsheet program.The cross-elasticity is-0.85(the negative sign shows complementarity),and is quite strong.10.Demand Elasticity Total Marginal Price Quantity Arc Point Revenue Revenue 7.00 100 700 6.50 200 -9.00-6.50 1300 6.00 6.00 300 -5.00-4.00 1800 5.00 5.50 400 -3.29-2.75 2200 4.00 5.00 500 -2.33-2.00 2500 3.00 4.50 600 -1.73-1.50 2700 2.00 4.00 700-1.31-1.14 2800 1.00 3.50 800-1.00-0.88 2800 0.00 3.00 900-0.76-0.67 2700 -1.00 2.50 1000-0.58-0.50 2500 -2.00 2.00 1100-0.43-0.36 2200 -3.00 1.50 1200-0.30-0.25 1800 -4.00 11.a.Negative:television sets and DVRs are complements.b.Positive:rye bread and whole-wheat bread are substitutes.c.Negative:construction of residential housing and furniture purchases are complements.d.Probably zero:breakfast cereal and mens shirts are unrelated products.However,they may be thought of as substitutes in the competition for a consumers budget dollars.12.a.130 70 2.50 3.50 Ep=/130+70 2.50+3.50 EP=1.8 b.90-40 2.50 3.50 Demand Elasticity 25 Copyright 2014 Pearson Education,Inc.Ex=/90+40 2.50+3.50 Ex=2.3 13.a.The price elasticity for shoes in the U.S.is 0.7.However,the elasticity for Brown Shoe Companys shoes may be higher,since a particular make of shoes has more substitutes than shoes in general.The exact demand elasticity for Browns product is not known,but it could easily be greater than 1(or less than negative one),and thus a price decrease could lead to an increase in revenue.b.The quantity of shoes sold in the U.S.would rise by 9%.14.1.5=-30%/-20%.UBS would lose 30%of its sales.15.a.There is a 14.3%decrease in price.With a 20%increase in quantity,this implies an elasticity coefficient of-1.4.b.Syrup is a complementary good in relation to ice cream.Cross elasticity would measure this effect.+0.1/-0.143=-0.7 The coefficient of cross elasticity is-0.7,confirming complementarity of syrup to ice cream.The coefficient is quite high,and thus one could conclude that the two products are fairly close complements.c.Yes,revenues for both ice cream and syrup rise.Unless costs rise more quickly(a very dubious conclusion),this action should increase the supermarkets profit.16.In computing the elasticities,remember that an elasticity measure can be calculated only if all other things remain constant.Price elasticities Months 3-4-1.00 20/(220+240)/2 -10/(120+110)/2 Months 4-5-0.96-10/(240+230)/2 5/(110+115)/2 Months 7-8-0.49 10/(220+230)/2 -10/(115+105)/2 Cross elasticities Months 1-2 0.45 10/(200+210)/2 15/(130+145)/2 Months 5-6 0.46-15/(230+215)/2 -20/(145+125)/2 Month 9-10 0.79-15/(235+220)/2 26 Demand Elasticity Copyright 2014 Pearson Education,Inc.-10/(125+115)/2 Income elasticities Months 2-3 0.95 10/(210+220)/2 200/(4000+4200)/2 Months 6-7 0.49 5/(215+220)/2 200/(4200+4400)/2 Months 8-9 0.48 5/(230+235)/2 200/(4400+4600)/2 17.a.1800 2000-200 b.$0 2000=2000-20P$100 0=2000-20P$25 1500=2000-20P c.Q=2000-20P 20P=2000-Q P=100-.05Q TR=PQ=100Q-.05Q2 MR=100-.1Q d.Q=2000-20(70)=600 TR=600 x 70=42000 or TR=100Q-.05Q2 =60000-.05(600)2 =60000-18000 =42000 MR=100-.1(600)=100-60=40 e.=dQ/dP x P/Q =20 x 70/600 =1400/600=2.33 f.Q=2000-20(60)=800 TR=800 x 60=48000 MR=100-.1(800)=20 Demand Elasticity 27 Copyright 2014 Pearson Education,Inc.=20 x 60/800 =1200/800=1.5 g.At =1 MR=0 0=100-.1Q .1Q=100 Q=1000 Proof:1000=2000-20P 20P=1000 P=50 =20 x 50/1000=1000/1000=1 18.a.672,000 x$1$672,000 623,000 x$1.15 716,450 Revenue increase$44,450 b.Ep=(672000-623000)/(672000+623000)/(1-1.15)/(1+1.15)=.037838/-.069767 =-.542 c.Increases in gasoline prices and automobile insurance during the year may have mitigated the bus fare increases,thus causing fewer commuters to switch away from using buses.Increases in personal income may also have been instrumental.These changes would have affected the demand curves for commuting,rather than be an example of price elasticity.19.Ep =(355000-518000)/(355000+518000)/(45-30)/(45+30)=-.18671/.2 =-.934 Revenue before price decrease 355000 x.45 159750 Revenue after price decrease 518000 x.30 155400 Decrease in revenue 4350 20.EA=1050 900 x 10000+15000 15000 10000 900+1050 =150 x 25000 5000 1950 =0.03 x 12.82=0.38 The elasticity of 0.38 means that for every 1%increase in advertising expense,sales will increase by 0.38%.Whether this move was wise depends on the production cost of the 28 Demand Elasticity Copyright 2014 Pearson Education,Inc.yoga apparel.To make thi