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1 Chapter 2 Supply an eman Analysis Solutions to Review uestions 1. Excess eman occurs when price falls below the equilibrium price. In this situation, consumers are emaning a higher quantity than is being mae available by suppliers. This creates pressure for the price to increase. As the price increases, quantity emane will fall as quantity supplie increases returning the market to equilibrium. Excess supply occurs when price is above the equilibrium price. Suppliers have mae available more units than consumers are willing to purchase at the high price. This creates pressure for the price to ecrease. As the price ecreases, the quantity emane will go up while at the same time the quantity supplie will ecrease, returning the market to equilibrium. 2. An increase in the price of a substitute, such as tea, will increase eman for coffee, raising the market equilibrium price an quantity. S Copyright 2008 John Wiley & Sons, Inc. Chapter 2-1

2 a) This stuy will reuce eman for caffeine rinks, lowering the market equilibrium price an quantity. S b) The frost will reuce supply raising the equilibrium price while lowering the equilibrium quantity. S S c) Increasing the price of an input for a cup of coffee will reuce supply, increasing market price an reucing market quantity. This will result in the same figure as that for part c). Copyright 2008 John Wiley & Sons, Inc. Chapter 2-2

3 3. Any factor increasing eman an leaving the remainer of the market unchange will increase both market price an quantity sol. If eman were to increase at the same time as supply change, both market price an quantity sol coul increase if the change in eman is large relative to the change in supply. S S S % 8 4., % The choke price is the price where 0. Using the given eman curve we have $0.50 Copyright 2008 John Wiley & Sons, Inc. Chapter 2-3

4 6. Speeboats coul probably be categorize as a luxury item whereas light bulbs are more likely categorize as a necessity. For the necessity, the change in quantity emane will be relatively small for any percent change in price. The change in quantity emane may be quite large, however, for a luxury item. Since the percent change in quantity emane is likely higher for the luxury item for any given percent change in price, the elasticity of eman woul be less (more negative). 7. Because business travelers receive reimbursement for expenses, they will probably be less sensitive to price changes than the vacation traveler who pays out of her own pocket. This implies the price elasticity for vacationers woul be less (more negative) than for business travelers. 8. If the prices for a particular prouct, such as annon, within a prouct category changes (say it increases) then it is easy for a consumer to switch to another bran, implying a relatively high percent change in quantity emane for the prouct. On the other han, if prices for the entire prouct category change, substitutes are not as easily foun an the percent change in quantity emane for the category will be relatively lower. This implies the elasticity for the entire prouct category will be higher (less negative) than the elasticity for a single prouct. 9. When the cross-price elasticity is positive we have % % A B 0 Either a) both A an B increase or b) they both ecrease. Since they are moving in the same irection, the prouct must be substitutes. Take coffee an tea for example; if the price of tea increases, the quantity of coffee emane will increase. When the cross-price elasticity is negative, A an B are moving in the opposite irection, implying the proucts are complements. Take coffee an cream for example; if the price of cream increases, the quantity of coffee emane will ecrease. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-4

5 10. S These points trace out the market supply curve As the eman curve shifts, the market will reach a new equilibrium. Each new equilibrium occurs at a new price an quantity. These price/quantity combinations trace out the market supply curve. Thus, in orer to ientify the market supply curve one nees to observe shifts in the eman curve. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-5

6 Solutions to roblems 2.1 a) When the price of nuts goes up, quantity emane falls for all levels of price (eman shifts left). Beer an nuts are eman complements. b) When income rises, quantity emane increases for all levels of price (eman shifts rightwar). c) a) The graph is shown below: 10 eman: Slope = b) We know that the value of the price elasticity of eman is given by, b Copyright 2008 John Wiley & Sons, Inc. Chapter 2-6

7 Here, b = 1/2. For eman to be unitary elastic it must be that which implies that = a) 300 S b) lugging 50 back into either the supply or eman equation yiels ε, We can fin elasticities of eman using the following formula, This eman curve is linear. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-7

8 $3 300 Observe that for price $1.50 the elasticity of eman is equal to 1.5, For all prices below $1.50, the eman is inelastic, while for all prices above $1.50, the eman is elastic Using the ata from the problem we can graph the eman curve. The slope of the eman curve is equal to / 1/100 So the equation of the eman curve is = A We can fin the vertical intercept A substituting = 3 an = = A 0.01(300), so A = 6. The vertical intercept (choke price) is = $6. The equation of the eman curve is then = $6 $4 $ Copyright 2008 John Wiley & Sons, Inc. Chapter 2-8

9 Elasticity of eman can be compute using formula E, When the elasticity is -1, = 300 an = $3. Thus eman is unitary elastic at a price = $ The eman for apple pies is = $ $5 $4.50 $ To fin the equation of the eman curve, observe that when she rops the price by $0.50, she sells 3 more pies. So, movement along the eman occurs so that / 3 / The eman curve then has the form = A 6, where A is a constant. We can etermine the value of A using any one of the three ata points on the eman curve. For example, if we use the point = 5 an = 24, we see that 24 = A 6(5), so that A = 54. So the eman curve can be escribe by the equation = To fin elasticity of eman at any point on the eman curve, we use formula E 6, Copyright 2008 John Wiley & Sons, Inc. Chapter 2-9

10 2.7 a) Since the price is being bi up above the official price, quantity emane must excee quantity supplie at the official price. This is a situation of excess eman an the official price must be below the equilibrium price. b) Lowering the official price woul increase the amount of excess eman, but woul have no effect on the eman or supply curves. Thus the equilibrium price woul remain unchange. 2.8 This coul occur as a result of the eman curve shifting to the right, increasing both equilibrium price an quantity. This woul not contraict what was learne regaring ownwar sloping eman curves. 2.9 The law of eman states that, holing other factors fixe, there is an inverse relationship between price an quantity emane, i.e. that an increase in price ecreases quantity an vice versa. If a goo has a positive price elasticity of eman, it must be that an increase in the price of that goo leas to an increase in the quantity emane. Therefore, such a goo violates the law of eman a) S * S * An increase in rainfall will increase supply, lowering the equilibrium price an increasing the equilibrium quantity. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-10

11 b) S * * A ecrease in isposable income will reuce eman, shifting the eman scheule left, reucing both the equilibrium price an quantity a) A perfectly inelastic eman curve will be vertical. b) The renewe interest will shift eman to the right, raising the equilibrium price. Since supply is perfectly inelastic (an therefore vertical) there will be no change in the quantity supplie; the quantity is fixe. S Copyright 2008 John Wiley & Sons, Inc. Chapter 2-11

12 2.12 a) b) The choke price occurs at the point where 0. Setting 0 eman equation above yiels 50. in the inverse c) At 50, the choke price, the elasticity will approach negative infinity Recall that for an elastic goo, a higher price charge by the firm leas to a ecrease in total revenue. Therefore, the firm shoul expect a level of output such that its revenue at a price of $102 is less than $70,000. Only if the output level is 400 or 600 is this possible (102*400 = $40,800) an (102*600 = $61,200). At the other quantities the revenue woul rise Gina s expeniture on ice-cream is *, where is the price an is the number of units of ice cream that she buys. We know that * increases as ecreases which can only mean that increases at a faster rate than the rate at which ecreases. This is equivalent to saying that eman is very sensitive to price changes, or that her eman for ice cream is quite elastic (, < 1). More generally, recall that when price an total revenue (*) move in opposite irections, it is because eman is elastic over that price range a) More elastic in the long run as the theatre owner can increase space or a another screen if the price remains high, but cannot easily ajust the number of seats at short notice. b) More elastic in the short run as people can be relatively flexible about when to unergo an eye exam, but in the long run the nee for eye exams is fixe. c) More elastic in the long run. Cigarettes ten to be aictive an so smokers are less likely to be able to reuce their eman in response to short term fluctuations in price. However if the price remains high for a long time they will consier giving up the habit as it becomes too expensive. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-12

13 2.16 a) Substituting the values of R an T, we get eman : Supply : s In equilibrium, 70 2 = , which implies that = 12. Substituting this value back, = 46. b) Elasticity of eman = 2(12/46), or Elasticity of Supply = 5(12/46) = c) golf, ti tanium 2( ) The negative sign inicates that titanium an golf 46 balls are complements, i.e., when the price of titanium goes up the eman for golf balls ecreases a) When the price of gasoline goes up, it becomes more expensive to rive a private automobile; because private automobiles an taxis are substitutes, the eman for taxi service shoul increase (shift to the right). On the other han, when the average spee of a trip by automobile increases, commuters are more likely to use their cars instea of public transportation; the eman for taxi service shoul shift to the left. On the supply sie, a higher price of gasoline increases to cost of proviing taxi service; the supply curve for taxi service shoul shift to the left. b) Substituting G = 4 an E = 30 into equations for the supply an eman curves we have s , Solving equation = s we have = 2, = 280. Supply an eman curves are graphe below. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-13

14 s $2.70 $ c) In equilibrium = s. When we E 20 G. 125 The equilibrium taxi fare goes up as gasoline price increases an goes own when it private automobiles can travel faster a) Since the two goos are rather close substitutes for each other, you woul expect that the eman for Tylenol woul go up if the price of Avil increases an vice versa. Therefore, the cross price elasticity will be positive. b) Similar to part (a). Although VCRs an V players are not very close substitutes, if the price of VCRs were to go up substantially, potential buyers woul probably ecie to pay a little bit more an get the higher-en V player. Similarly if the latter becomes expensive, some consumers will not be able to affor it an will switch to the VCR instea. The elasticity will be positive. c) Since the two usually go together, a sharp increase in the price of one will lea to a ecline in the eman for the other, an the cross-price elasticity will be negative. a) Assuming re an black umbrellas are substitutes, we woul expect the crossprice elasticity of eman to be positive. b) Coca-cola an epsi are substitutes. We woul expect the cross-price elasticity of eman to be positive. c) Grape jelly an peanut butter are typically complements (people want both on their sanwiches!). We woul expect the cross-price elasticity of eman to be negative. ) Chocolate chip cookies an milk are typically complements (people want to consume them together). We woul expect the cross-price elasticity of eman to be negative. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-14

15 e) Computers an software are complements (consumers want to use them together). We woul expect the cross-price elasticity of eman to be negative a) U U (300) 99(300) 9700 Using U 300 an U 9700 gives, b) Market eman is given by U A. Assuming the airlines charge the same price we have When 300, U A A U. This implies an elasticity equal to, Copyright 2008 John Wiley & Sons, Inc. Chapter 2-15

16 2.21 We know that along a linear eman curve, b Using the given information this implies.05.5 b 10,000, 000 b 100, 000,000 lugging this result into a eman equation using the known price an quantity then implies A b 10,000,000 A 100,000,000(.05) A 15, 000,000 So a eman equation that fits this information is given by 15, 000, ,000,000 Graphically, the eman curve looks like ,000,000 Copyright 2008 John Wiley & Sons, Inc. Chapter 2-16

17 2.22 a) In case of the linear eman = A - b, we know that, b 1 Using the values of an given in the problem we have b b Now we can solve for the secon parameter of the linear eman curve 120 a 15(8) a 240. Hence the linear eman curve is given by equation = E, = b) There exist several linear eman curves for which the eman is equal to 120 at price of $8. Information about elasticity of eman lets us etermine exactly one of those. More formally, we nee secon equation to solve for both parameters of the linear eman curve a) Butter has some reasonably close substitutes such as margarine or cheese, while eggs have no immeiate substitutes. Therefore we woul expect the eman for butter to be more elastic. b) Vacation trips are sensitive to price because leisure travelers can be relatively flexible about when to fly. Your congressman, however, has fixe ates on which to be in Washington an woul be prepare to pay more to ensure that he flies on the ay of his choosing. Therefore, eman for vacation trips is likely to be more elastic (i.e. the price elasticity will be more negative) than the eman for trips by your congressman. c) As iscusse in the chapter, market level elasticities ten to be lower (less negative) than the elasticity of a particular bran. Thus, expect the eman for Tropicana to be more elastic than the eman for generic orange juice. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-17

18 2.24 First, consier each eman curve in its inverse form: long run eman is = , an short run eman is = Thus, the slope of the long run eman is 0.5, which is closer to zero than that of the short run eman, 2. Thus, long run eman is flatter. Secon, consier the graph below: Short run eman Long run eman Again, long run eman is flatter an thus more sensitive to changes in price. Consier, for instance a price of $10. uantity emane is equal in both the long an short runs at = 10. However, consier increasing the price to, say, $15. Although this will reuce quantity emane in the short run by a little, it woul reuce quantity emane all the way to zero in the long run The scare in 1999 woul shift eman to the left, ientifying a secon point on the supply curve. The information implies that price fell $0.50 while quantity fell 1.5 million. This implies.5 b.15 Using a linear supply curve we then have s a a (4) 3 11 a 3 Finally, plugging these values for a an b into the supply equation results in s 3 11 s 11 3 s Copyright 2008 John Wiley & Sons, Inc. Chapter 2-18

19 The floos in 2000 will reuce supply. The shift in supply will ientify a secon point along the eman curve. Because the scare of 1999 is over, assume that eman has returne to its 1998 state. The change in price an quantity in 2000 imply that price increase $3.00 an that quantity fell 0.5 million. erforming the same exercise as above we have 3 b Using the 1998 price an quantity information along with this result yiels a b 5 a 6(4) a 29 Finally, plugging these values for a an b into a linear eman curve results in The equilibrium price in January is equal to = 3 an equilibrium quantity is equal to = 60. We fin equilibrium price by solving s =, which is = When we have equilibrium price we can substitute it to either the eman function or supply function, since they have to give the same quantity at that price, an obtain equilibrium quantity equal to = 60. After the supply ecreases in February, new equilibrium price is per mile is equal to = $3.60, while the emane quantity is equal to = 48. When the eman goes up in March, the quantity in equilibrium is the same as in January but price is even higher an equal to = $4. All those changes are illustrate on the graph below. Copyright 2008 John Wiley & Sons, Inc. Chapter 2-19

20 $6 s $4 $3.60 $ Copyright 2008 John Wiley & Sons, Inc. Chapter 2-20