Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual Chapter 2 Supply and Demand Analysis Solutions to Problems 2.1 Explain why a situation of excess demand will result in an increase in the marke t price. Why will a situation of excess supply result in a decrease in the market price? Excess demand occurs when price falls below the equilibrium price. In this situa tion, consumers are demanding a higher quantity than is being made available by suppli ers. This creates pressure for the price to increase ± sellers can ask for higher price s and still find buyers, and buyers offer higher prices to secure the units they want. As th e price increases, quantity demanded will fall as quantity supplied increases returning the market to equilibrium. Excess supply occurs when price is above the equilibrium price. Suppliers have m ade available more units than consumers are willing to purchase at the high price. T his creates pressure for the price to decrease ± buyers can get away with paying less because sellers are happy to find a buyer at all, and sellers are willing to sell for le ss wanting to make sure they find a buyer. As the price decreases, the quantity demanded will go up while at the same time the quantity supplied will decrease, returning the market to equilibrium. 2.2 Suppose we observe that the price of soybeans goes up, while the quantity of soybeans sold goes up as well. Use supply and demand curves to illustrate two possible explanations for this pattern of price and quantity changes. Any factor increasing demand and leaving the remainder of the market unchanged w ill increase both market price and quantity sold. If demand were to increase at the same time as supply changed, both market price and quantity sold could increase if the change in dem and is large relative to the change in supply (in either direction). FOR MORE OF THIS COURSE AND ANY OTHER COURSES, TEST BANKS, FINAL EXAMS, AND SOLUTION MANUALS CONTACT US AT
[email protected] Copyright © 2015 John Wiley & Sons, Inc. Chapter 2 - 1
Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version 2.3. Solutions Manual Explain why the price elasticity of demand for an entire product category (such as yogurt) is likely to be less negative than the price elasticity of demand for a typical brand (such as Dannon) within that product category. If the prices for a particular product, such as Dannon, within a product categor y changes (say it increases) then it is easy for a consumer to switch to another brand, implying a relatively high percent change in quantity demanded for the product. On the other hand, if price s for the entire product category change, substitutes are not as easily found and the percent cha nge in quantity Copyright © 2015 John Wiley & Sons, Inc. Chapter 2 - 2
Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual demanded for the category will be relatively lower. This implies the elasticity for the entire product category will be higher (less negative) than the elasticity for a single product. 2.4. The demand for beer in Japan is given by the following equation: Qd = 700 - 2
P PN + 0.1I, where P is the price of beer, PN is the price of nuts, and I is avera ge consumer income. a) What happens to the demand for beer when the price of nuts goes up? Are beer and nuts demand substitutes or demand complements? b) What happens to the demand for beer when average consumer income rises? c) Graph the demand curve for beer when PN = 100 and I = 10, 000. a) When the price of nuts goes up, the beer quantity demanded falls for all levels of price (demand shifts left). Beer and nuts are demand complements. b) When income rises, quantity demanded increases for all levels of price (demand s hifts rightward). c) Now: Qd = 700 - 2P - 100 + 0.1*10,000 = 1,600 ± 2P P = 800 ± 0.5 Qd P 800 1600 Q 2.5. The demand and supply curves for coffee are given by Qd = 500 - 4P and Qs = 100 + 2P, where P is the price of cranberries expressed in euros per barrel and quanti ty is in thousands of barrels per year. a) Plot the supply and demand curves on a graph and show where the equilibrium o ccurs. b) Using algebra, determine the market equilibrium price and quantity of cranber ries. a) Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual d) 500 4 P 100 2 P 600 6 P 100 P Plugging P 100 back into either the supply or demand equation yields Q 100 . 2.6. Suppose that demand for bagels in the local store is given by equation Qd = 300 100P. In this equation, P denotes the price of one bagel in dollars. a) Fill in the following table: P 0.10 0.45 0.50 0.55 2.50 d Q eQ,P b) At what pric is d mand in lastic? c) At what pric is d mand lastic? P 0.10 0.45 0.50 0.55 2.50 d Q 290 255 250 245 50 eQ,P ±0.035 ±0.176 ±0.2 ±0.225 ±5 W can find lasticiti s of d mand using th following formula Q,P Q d P
P P . 100
d P Q 300 100 P P 3 This d mand curv is lin ar. Th inv rs d mand function is P = 3 ± 1/100 Qd P $3 300 Q d Obs rv that for pric $1.50 th
lasticity of d mand is
Copyright © 2015 John Wil y & Sons, Inc. Chapt r 2 - 4
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Solutions Manual 1.5 1 . 1.5 3 For all pric s b low $1.50, th d mand is in lastic, whil for all pric s abov $1.50, th d mand is lastic. 2.7. You hav d cid d to study th mark t for fr sh pick d ch rri s. You l arn t hat ov r th last 10 y ars, ch rry pric s hav ris n, whil th quantity of ch rri s purc has d has also ris n. This s ms puzzling b caus you l arn d in micro conomics that an incr as in pric usually d cr as s th quantity d mand d. What might xplain this s mingly stran g patt rn of pric s and consumption l v ls? This could occur as a r sult of th d mand curv shifting to th right, incr asi ng both quilibrium pric and quantity. This would not contradict what was l arn d r garding downwar d sloping d mand curv s. 2.8. Suppos that, ov r a p riod of six months, th pric of corn incr as d. Y t , th quantity of corn sold by produc rs d cr as d. Do s this contradict th law of su pply? If not, why not? This do s not contradict th law of supply. For xampl , farm rs may hav xp ri nc d som thing that shift d th supply curv for corn l ftward (such as a flooding or a drought). This would hav th ff ct of incr asing th quilibrium pric of corn, whil d cr as ing th quantity of corn sold by produc rs. This is shown in th figur b low. Anoth r possibilit y is that, alt rnativ ly, th supply curv for corn could hav shift d l ftward, and th d mand curv s for could hav also shift d, but in such a way that th ov rall ff ct is to incr as th quilibrium pric and d cr as th quilibrium quantity. Th s cas s ar also shown in th f igur b low. Copyright © 2015 John Wil y & Sons, Inc. Chapt r 2 - 5
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Pric (dollars p r bush l) Solutions Manual S2 S1 D2 D1 Quantity (bush ls p r y ar) Supply curv shifts l ftward, d mand curv also shifts l ftward Pric (dollars p r bush l) S2 S1 D2 D1 Supply curv shifts l ftward, d mand curv shifts rightward Quantity (bush ls p r y ar) 2.9. Explain why a good with a positiv pric lasticity of d mand must violat th law of d mand. Th law of d mand stat s that, holding oth r factors fix d, th r is an inv rs r lationship b tw n pric and quantity d mand d, i. . that an incr as in pric d cr as s qu antity and vic v rsa. If a good has a positiv pric lasticity of d mand, it must b that an i ncr as in th pric Copyright © 2015 John Wil y & Sons, Inc. Chapt r 2 - 6
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Solutions Manual of that good l ads to an incr as in th quantity d mand d. Th r for , such a go od violat s th law of d mand. 2.10. Suppos that th d mand for aluminium in th Unit d Stat s is giv n by th quation Qd = 500 - 50P + 10I, wh r P is th pric of aluminium xpr ss d in do llars p r kilogram and I is th av rag incom p r p rson in th Unit d Stat s (in thousan ds of dollars p r y ar). Av rag incom is an important d t rminant of th d mand for automobil s and oth r products that us aluminium, and h nc is a d t rminant of th d mand for aluminium its lf. Furth r, suppos that th U.S. supply of aluminium (wh n P ³ 8) is giv n by th quation Qs = -400 + 50P. In both th d mand and supply funct ions, quantity is m asur d in millions of kilograms p r y ar. a) Sk tch a graph of d mand and supply curv s that shows th ff ct of an incr a s in rainfall on th quilibrium pric and quantity of aluminum. b) Calculat and illustrat th mark t quilibrium pric of aluminum wh n I = 10 . If I falls to 5, calculat and illustrat th ff ct on th quilibrium in th aluminum mar k t. a) An incr as in incom will incr as d mand, raising th cr asing th quilibrium quantity. b) Copyright © 2015 John Wil y & Sons, Inc. Chapt r 2 - 7
quilibrium pric and in
B sanko & Bra utigam ± Micro conomics, 5th
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Solutions Manual Wh n I = 10 w hav QD = 500 - 50P + 100 = Qs = -400 + 50P at quilibrium, or 10 00 _ 100P or P* = 10. At this pric , using ith r th supply or d mand quation w hav Q* = 100. Wh n incom falls to 5 w hav QD = 500 - 50P + 50 = Qs = -400 + 50P or 950 = 100P or P* = 9.5. At this pric , using ith r th supply or d mand quation, w hav Q* = 75. As inco m drops, d mand shifts to th l ft, r ducing both th quilibrium pric and quantity. Thi s supports th alg braic solution. 2.11. Suppos that th quantity of st l d mand d in Franc is giv n by Q s = 10 0 ± 2Ps + 0.5Y + 0.2PA, wh r Qs is th quantity of st l d mand d p r y ar, Ps is th mar k t pric of st l, Y is r al GDP in Franc , and PA is th mark t pric of aluminum. In 2011, Ps = 10, Y = 40, and PA = 100. How much st l will b d mand d in 2011? What is th pric lasticity of d mand, giv n mark t conditions in 2011? W ar giv n that Y = 40, and PA = 100, and so substituting th s valu s into th quation that d t rmin s th quantity d mand d giv s us QS = 100 ± 2PS + 0.5(40) + 0.2(100) or QS = 140 ± 2PS. This is th quation for th d mand curv for st l in Franc . Wh n th pric of st l is 10, th quantity of st l d mand d is thus 120. From quation (2.4) in th t xt, th pric lasticity of d mand for st l wh n t h pric is 10 is giv n by 2.12. Gina usually pays a pric b tw n $5 and $7 p r gallon of ic cr am. Ov r that rang of pric s, h r monthly total xp nditur on ic cr am incr as s as th pri c d cr as s. What do s this imply about h r pric lasticity of d mand for ic cr am? Gina's xp nditur on ic -cr am is P*Q, wh r P is th pric and Q is th numb r o f units of ic cr am that sh buys. W know that P*Q incr as s as P d cr as s which can only m an that Q incr as s at a fast r rat than th rat at which P d cr as s. This is quival n t to saying that d mand is v ry s nsitiv to pric chang s, or that h r d mand for ic cr am is q uit lastic (Q,P < ±1) . Mor g n rally, r call that wh n pric and total r v nu (P*Q) mov in opp osit dir ctions, it is b caus d mand is lastic ov r that pric rang . Copyright © 2015 John Wil y & Sons, Inc. Chapt r 2 - 8
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Solutions Manual 2.13. Consid r th following d mand and supply r lationships in th mark t for g olf balls: Qd = 90 - 2P - 2T and Qs = -9 + 5P - 2.5R, where T is the price of titanium, a me tal used to make golf clubs, and R is the price of rubber. a) If R = 2 and T = 10, calculate the equilibrium price and quantity of golf bal ls. b) At the equilibrium values, calculate the price elasticity of demand and the p rice elasticity of supply. c) At the equilibrium values, calculate the cross price elasticity of demand for golf balls with respect to the price of titanium. What does the sign of this elasticity tel l you about whether golf balls and titanium are substitutes or complements? a) Substituting the values of R and T, we get Demand : Q d 70 2 P Supply : Q s 14 5P In equilibrium, 70 ± 2P = ±14 + 5P, which implies that P = 12. Substituting this val ue back, Q = 46. b) Elasticity of Demand = ±2(12/46), or ±0.52. Elasticity of Supply = 5(12/46) = 1.30. c) golf ,titanium 2(
10 ) 0.43, . The negative sign indicates that titanium and golf balls are 46 complements, i.e., when the price of titanium goes up the demand for golf balls decreases. 2.14. In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway between the airport and downtown. The market for taxi cab service is competitive. There is a special lane for taxicabs, so taxis are always able to t ravel at 55 miles per hour. The demand for trips by taxi cabs depends on the taxi fare P, th e average speed of a trip by private automobile on the highway E, and the price of petrol G. The number of trips supplied by taxi cabs will depend on the taxi fare and the price of gasoline. a) How would you expect an increase in the price of petrol to shift the demand f or transportation by taxi cabs? How would you expect an increase in the average spe ed of a trip by private automobile to shift the demand for transportation by taxi cabs? How would you expect an increase price of petrol to shift the demand for transportation by taxi cabs?
b) Suppose the demand for trips by taxi is given by the equation Qd = 1000 + 50G 4E 400P. The supply of trips by taxi is given by the equation Qs = 200 30G + 100P. On a graph draw the supply and demand curves for trips by taxi when G = 4 and E =30. Find equilibrium taxi fare. c) Solve for equilibrium taxi fare in a general case; that is, when you do not k now G and E. Show how the equilibrium taxi fare changes as G and E change. a) When the price of petrol goes up, it becomes more expensive to drive a private automobile; because private automobiles and taxis are substitutes, the demand fo r taxi service should increase (shift to the right). On the other hand, when the average speed of a trip by Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual automobile increases, commuters are more likely to use their cars instead of pub lic transportation; the demand for taxi service should shift to the left. On the sup ply side, a higher price of petrol increases to cost of providing taxi service; the supply curve fo r taxi service should shift to the left. b) Substituting G = 4 and E = 30 into equations for the supply and demand curves we have Q d 1080 400 P, Q s 80 100 P. Solving equation Qd = Qs we have P = 2, Q = 280. Supply and demand curves are gr aphed below. P Qs $2.70 $2 Qd 80 280 1080 Q In equilibrium Qd = Qs. When we 1 P 200 E 20 G . 125 The equilibrium taxi fare goes up as petrol price increases and goes down when i t private automobiles can travel faster. c) 2.15. For the following pairs of goods, would you expect the cross price elastic ity of demand to be positive, negative, or zero? Briefly explain your answer. a) Red umbrellas and black umbrellas b) Coca Cola and Pepsi c) Strawberries and cream d) Chocolate chip cookies and milk e) Computers and software a) Assuming red and black umbrellas are substitutes, we would expect the cross pric e elasticity of demand to be positive.
b) Coca cola and Pepsi are substitutes. We would expect the cross price elasticity of demand to be positive. c) Strawberries and cream are typically complements (people want to consume them together). We would expect the cross price elasticity of demand to be negative. d) Chocolate chip cookies and milk are typically complements (people want to consum e them together). We would expect the cross price elasticity of demand to be negat ive. Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual e) Computers and software are complements (consumers want to use them together). We would expect the cross price elasticity of demand to be negative. 2.16. Suppose that the market for air travel between London and Corfu is served by just two airlines, Easyjet and Aegean. An economist has studied this market and has e stimated that the demand curves for round trip tickets for each airline are as follows: Q dE = 10,000 100PE + 99PA (Easyjet's demand) QdA = 10,000 - 100PA + 99PE (Aegean's demand) where PE is the price charged by Easyjet, and PA is the price charged by Aegean. a) Suppose that both Aegean and Easyjet charge a price of £300 each for a round tr ip ticket between London and Corfu. What is the price elasticity of demand for Easy jet flights between London and Corfu? b) What is the market level price elasticity of demand for air travel between Lo ndon and Corfu when both airlines charge a price of £300? (Hint: Because Easyjet and Aegean are the only two airlines serving the London±Corfu market, what is the equation for th e total demand for air travel between London and Corfu, assuming that the airlines charg e the same price?) a) QEd 10000 100(300) 99(300) QEd 9700 Using PE 300 and QEd 9700 gives 300 3.09 9700 Q, P 100
b) Market demand is given by Qd QUd QAd . Assuming the airlines charge the same pri ce we have Q d 10000 100 PE 99 PA 10000 100 PA 99 PE Q d 20000 100 P 99 P 100 P 99 P Q d 20000 2 P When P 300 , Qd 19400 . This implies an elasticity equal to 300 .0309 19400 Q, P 2
2.17. For each of the following, discuss whether you expect the elasticity (of d emand or of supply, as specified) to be greater in the long run or the short run. a) The supply of seats in the local movie theater. b) The demand for eye examinations at the only optometrist in town. c) The demand for cigarettes. Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual a) More elastic in the long run as the theatre owner can increase space or add anot her screen if the price remains high, but cannot easily adjust the number of seats at short notice. b) More elastic in the short run as people can be relatively flexible about when to undergo an eye exam, but in the long run the need for eye exams is fixed. c) More elastic in the long run. Cigarettes tend to be addictive and so smokers are less likely to be able to reduce their demand in response to short term fluctuations in pric e. However if the price remains high for a long time they will consider giving up the habit as it becomes too expensive. 2.18. In February 2013, there is an unexpected temporary surge in the demand for notebook hard drives, increasing the monthly demand for hard drives by 25 percen t at any possible price. As a result of this, the price of notebook hard drives increased by $5 per megabyte by the end of February. This surge in demand ended in March 2013, and t he price of notebook hard drives fell back to its level just before the temporary d emand surge occurred. Later that year, in August 2013, a permanent increase in the demand for notebook computers occurs, increasing the monthly demand for hard drives by 25 percent pe r month at any possible price. Nine months later, the price of notebook hard drives had increased, by £1 per unit. In both circumstances, the market experienced a shift in demand of exactly the s ame magnitude. Yet, the change in the equilibrium price appears to have been differe nt. Why? When demand surges temporarily, putting upward pressure on price, the quantity s upplied expands along the short run supply curve SS, as shown in the figure below. If de mand increases by the identical rate, but the increase is permanent, the industry would expand along the long run supply curve LS. The long run supply curve is likely to be more price elastic th an the short run supply curve. If the demand increase and the resulting upward pressure on price is temporary, producers may be able to do very little to increase supply except to utilize the ir existing production facilities more intensively (perhaps by hiring some temporary labor). If the demand increase is permanent, industry supply can increase in response to upward pressu re on price in a number of ways: existing firms can produce more output in their existing facilit ies; existing firms
can expand their plants; and new firms can enter the industry and produce. Thus, over a longer horizon, the industry's supply response when prices begin to rise is more flexible than it is over a shorter horizon. Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual 25 percent increase in quantity demanded at any price Price (dollars per megabyte) SS Increase in price due to temporary demand surge Increase in price due to permanent demand surge LS D1 D2 Quantity (megabytes worth of hard drives per month) Supply curve shifts leftward, demand curve shifts rightward 2.19. The demand for dinners in the only restaurant in town has a unitary price elasticity of demand when the current average price of a dinner is $8. At that price 120 pe ople eat dinners at the restaurant every evening. a) Find a linear demand curve that fits this information and draw it on a clearl y labeled graph. b) Do you need the information on the price elasticity of demand to find the cur ve? Why? a) In case of the linear demand Q = A
bP, we know that Q ,P b
P 1
Q Using the values of P and Q given in the problem we have 8
120 1 b b 15 . 120 8 Now we can solve for the second parameter of the linear demand curve 120 a 15(8) a 240 . Hence the linear demand curve is given by equation Qd = 240 ± 15P. Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual P 16 EQ,P = 8 Q 120
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240 b) There exist several linear demand curves for which the demand is equal to 120 at price of $8. Information about elasticity of demand lets us determine exactly one of thos e. More formally, we need second equation to solve for both parameters of the linear dem and curve. 2.20. The price for a trip from Newtown to Bitcity on the local commuter rail ha s been 10 pounds for a number of years. Suppose that the market for trips is characterized by the following demand curves: in the long run: Q = 30 - 2P; in the short run: Q = 15 - P/ 2. Verify that the long run demand curve is ªflatterº than the short run curve. What do es this tell you about the sensitivity of demand to price for this good? Discuss wh y this is the case. First, consider each demand curve in its ªinverseº form: long run demand is P = 15 ± 0 .5Q, and short run demand is P = 30 ± 2Q. Thus, the slope of the long run demand is ±0.5, whi ch is closer to zero than that of the short run demand, ±2. Thus, long run demand is fla tter. Second, consider the graph below: P 30 Short run demand 15 10 Long run demand 15 Q 30 Again, long run demand is flatter and thus more sensitive to changes in price. C onsider, for instance a price of £10. Quantity demanded is equal in both the long and short run s at P = 10.
However, consider increasing the price to, say, £15. Although this will reduce qua ntity demanded in the short run by a little, it would reduce quantity demanded all the way to zero in the long run. Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual 2.21. Consider the demand curve for pomegranates in two countries. In one countr y, pomegranates are a critical part of the diet and are central to the preparation of many popular food recipes. For most of these dishes, there is no feasible substitute for pomegranates. In the second country, households will purchase pomegranates if th e price is right, but they are not considered by consumers to be particularly special or un ique, and few popular dishes rely on pomegranates in their recipes. Suppose pomegranates are native to both countries. Suppose, further, that due to inherent limitations of shipping options, there is no inter country trade in pomegranates . Each country's market for pomegranates is independent of the other countries. Finally, suppose that in both countries, droughts and other weather related shocks periodically c ause unexpected changes in supply conditions. The graph below shows the time paths of pomegranate prices over a 10 year period in each country (the blue (solid) line is the time path in one country; the red (dashed) line is the time path in the other country.) Based on the information provided, which is the time path for each country? Price of Pomegranates Time The price path for Country A is the one in which there is substantial price vari ation over time, while the price path for Country B is the one on in which there is more modest p rice variation over time. Here is why. Based on the information given, we can infer that the demand for pomegranates is probably less sensitive to price in Country A (where pomegranates have few good substitutes) t han it is in Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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Besanko & Braeutigam ± Microeconomics, 5th edition, International Student Version Solutions Manual country B. For a given shift in the supply curve in each country, the change in the equilibrium price in country A will be larger than the change in the equilibrium price in co untry B. FOR MORE OF THIS COURSE AND ANY OTHER COURSES, TEST BANKS, FINAL EXAMS, AND SOLUTION MANUALS CONTACT US AT
[email protected] Copyright © 2015 John Wiley & Sons, Inc. Chapter 2
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