Chapter 2: Answers Answers to Questions and Problems 1. a. Since X is is a normal normal good, good, a decrease decrease in income will lead lead to a decrease decrease in the demand for X (the demand curve for X will shift to the left). b. Since Y is is an inferior good, an increase in income will lead to a decrease in the demand for good Y (the demand curve for Y will shift to the left). c. Since goods goods X and Y are substitu substitutes, tes, an increas increasee in the price price of good Y will lead lead to an increase in the demand for good X (the demand d emand curve for X will shift to the right). d. Not necessaril necessarily. y. he term !inferi !inferior or good" does not mean mean !inferior !inferior #uality #uality," ," it simply means that income and consumption con sumption are inversely related. $. a. he supply supply of good good X will increase increase (shift (shift to the the right). right). b. he supply of good X will decrease. %ore specifically, the supply curve will shift vertically up by e&actly ' at each level of output. c. he supply supply of good X will will decrease. decrease. %ore %ore specifical specifically, ly, the supply supply curve will will rotate countercloc*wise. d. he supply supply curve curve for good good X will will increase increase (shift (shift to to the right). right). . a. Q x =−30 + 2 ( 600 ) −4 ( 60 )=930 units. s b. Notice that although Q x =−30 + 2 ( 80 ) −4 ( 60 )=−110 , negative output is impossible. hus, #uantity supplied is +ero. c. o find find the the supply supply func functio tion, n, inser insertt P z - into the supply e#uation to obtain s Q x =−30 + 2 P x −4 ( 60 )=−270 + 2 P x . hus, the supply e#uation is s simply solve this Q x =−270 + 2 P x . o obtain the inverse supply e#uation, simply s e#uation for P x to obtain P x =135 + 0.5 Q x . he inverse supply function is graphed in /igure $1. s
$500 $400 $300
Price of X $200 $100 $0 0
100
200
300
400
500
Quantity of X
Figure 2-1 Managerial Economics and Business Strategy, 8e
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0. a. ood Y is a complement for X, while good 2 is a substitute for X. b. X is a normal good. d
1
1
2
10
Q x =6,000 − ( $ 5,230 )− $ 6,500 + 9 ( $ 100 ) +
c.
( $ 70,000 )= 4,785
d. /or the given income and prices of other goods, the demand function for good X is
d
1
1
2
10
Q x =6,000 − P x −$ 6,500 + 9 ( $ 100 )+
( $ 70,000 ) which simplifies to
1
d
Q x =7,400 − P x . o find the inverse demand e#uation, solve for price to 2
d
obtain P x =14,800 −2 Q x . he demand function is graphed in /igure $$. $16,000 $14,000 $12,000 $10,000
Price of X
$8,000 $6,000 $4,000 $2,000 $0 0
1000 2000 3000 4000 5000 6000 7000
Quantity of X
Figure 2-2
3. a. Solve the demand function for P x to obtain the following inverse demand function4
1
d
P x =150 − Q x . 2
b. Notice that when P x '03, Q x =300−2 ( 45 )=210 units. 5lso, from part a, we *now the vertical intercept of the inverse demand e#uation is 13. hus, consumer surplus is '11,$3 (computed as (.3)('13'03)$1 '11,$3). c. 6hen price decreases to ', #uantity demanded increases to $0 units, so consumer surplus increases to '10,0 (computed as (.3)('13')$0 '10,0). d. So long as the law of demand holds, a decrease in price leads to an increase in consumer surplus, and vice versa. 7n general, there is an inverse relationship between the price of a product and consumer surplus. d
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-. a. 8#uating #uantity supplied and #uantity demanded yields the e#uation 60− P = P− 20 . Solving for 9 yields the e#uilibrium price of '0 per unit. 9lugging this into the demand e#uation yields the e#uilibrium #uantity of $ units (since #uantity demanded at the e#uilibrium price is Q d =60−( 40 )=20 ). b. 5 price floor of '3 is effective since it is above the e#uilibrium price of '0. 5s a result, #uantity demanded will fall to 1 units ( Q d =60−50 ), while #uantity supplied will increase to units ( Qs=50 −20 ). hat is, firms produce units but consumers are willing and able to purchase only 1 units. herefore, at a price floor of '3, 1 units will be e&changed. Since :d ; :s there is a surplus amounting to 1 $ units. c. 5 price ceiling of '$ per unit is effective since it is below the e#uilibrium price of '0 per unit. 5s a result, #uantity demanded will increase to $ < units ( d Q =60−32 =28 ), while #uantity supplied will decrease to 1$ units ( s Q = 32−20=12 ). hat is, while firms are willing to produce only 1$ units consumers want to buy $< units at the ceiling price. herefore, at the price ceiling of '$, only 1$ units will be available to purchase. Since :d = :s, there is a shortage amounting to $<1$ 1- units. Since only 1$ units are available at a price of '$, the full economic price is the price such that #uantity demanded e#uals the 1$ available units4 1$ - > 9/. Solving yields the full economic price of '0<. ?. 1
1
2
4
a. 8#uate #uantity demanded and #uantity supplied to obtain 14 − P x = P x −1 . Solve this e#uation for 9& to obtain the e#uilibrium price of 9& $. he e#uilibrium #uantity is 0 units (since at the e#uilibrium price #uantity de manded is
d
1
Q x =14 − (20 )= 4 ). he e#uilibrium is shown in /igure $. 2
Managerial Economics and Business Strategy, 8e
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$30 $25 $20
Price of X
$15 $10 $5 $0 0
1
2
3
4
5
6
Quantity of X
Figure 2-
b. 5 '1$ e&cise ta& shifts the supply curve up by the amount of the ta&. %athematically, this means that the intercept of the inverse supply function increases by '1$. @efore the ta&, the inverse supply function is P= 4 + 4 Qs . 5fter the ta& the inverse supply function is P=16 + 4 Q s , and the after ta& supply function (obtained by solving for :s in terms of 9) is given by s
1
Q = P −4 . 8#uating #uantity demanded to afterta& #uantity supplied yields 4 1
1 14 − P = P− 4 . Solving for 9 yields the new e#uilibrium price of '$0. 2 4
9lugging this into the demand e#uation yields the new e#uilibrium #uantity, which is $ units. c. Since two units are sold after the ta& and the ta& rate is '1$ per unit, total ta& revenue is '$0. <. a. he shortage is units (since at a price of '-, Q economic price is '1$.
d
−
Qs
=
0
−
1
=
(
s d Q Q $.3 1 b. he surplus is 1.3 units (since at a price of '1$, cost to the government is '1< (computed as ('1$)(1.3) '1<). −
=
−
units). he full =
1.3
units. he 1
c. he e&cise ta& shifts supply vertically by '-. hus, the new supply curve is S and the e#uilibrium price increases to '1$. he price paid by consumers is '1$ per unit, while the amount received by producers is this '1$ minus the per unit ta&. hus, producers receive '- per unit. 5fter the ta&, the e#uilibrium #uantity sold is 1 unit. d. 5t the e#uilibrium price of '1, consumer surplus is .3 ( '1
−
'$ ) $
=
.3 ( '10
−
'1 ) $
=
'0
.
'<
9roducer surplus is . e. No. 5t a price of '$ no output is produced. Page !
Baye & Prince
A. a. he inverse supply curve is P=26 + 0.05 Q . b. 6hen Q x 0, producer surplus is (0-$-)B0C$ '0,. 6hen Q x 1$, producer surplus is (<-$-)B1$C$ '-,. 1. a. he cost of purchasing the surplus is '0B($01$) '0<. b. he deadweight loss resulting from a '0 price floor is 0.5∗( 40 −28 )∗( 20 −12 )= $ 48.00 . 11. Dising input prices that increase production costs will lead to a leftward shift in the supply curve for D5% chips, resulting in a higher e#uilibrium price of D5% chips. 7f in addition, income falls, the demand for D5% chips will decrease since they are a normal good. his decrease in demand would tend to decrease the price of D5% chips. he ultimate effect of both of these changes in supply and demand on the e#uilibrium price of D5% chips is indeterminate. Eepending on the relative magnitude of the decreases in supply and demand, the price you will pay for chips may rise or fall. 1$. he tariff reduces the supply of raw sugar, resulting in a higher e#uilibrium price of sugar. Since sugar is an input in ma*ing generic soft drin*s, this increase in input prices will decrease the supply of generic soft drin*s (putting upward pressure on the price of generic soft drin*s and tend to reduce #uantity). Fo*e and 9epsiGs advertising campaign will decrease the demand for generic soft drin*s (putting downward pressure on the price of generic soft drin*s and further reducing the #uantity). /or these reasons, the e#uilibrium #uantity of generic soft drin*s sold will decrease. However, the e#uilibrium price may rise or fall, depending on the relative magnitude of the shifts in demand and supply. 1. No. this confuses a change in demand with a change in #uantity demanded. Higher cigarette prices will not reduce (shift to the left) the demand for cigarettes. 10. o find the e#uilibrium price and #uantity, e#uate #uantity demanded and #uantity supplied to obtain $1 > 1.39 $.39 > 13. Solving yields the new e#uilibrium price of 'A per pint. he e#uilibrium #uantity is ?3 units (since Qd $1 > 1.3BA ?3 units at that price). Fonsumer surplus is surplus is
1 2
1 2
( $ 140 −$ 90 )∗75 = $ 1,875 . 9roducer
( $ 90− $ 60 )∗75= $ 1,125 . See /igure $0.
Managerial Economics and Business Strategy, 8e
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160 140 120
Supply
100 Fonsumer Surplus
Price
80 9roducer Surplus 60
Eemand
40 20 0 0
20
40
60
80
100
Quantity
Figure 2-!
13. his decline represents a leftward shift in the supply curve for oil, and will result in an increase in the e#uilibrium price of crude oil. Since oil is an input in producing gasoline, this will decrease the supply of gasoline, resulting in a higher e#uilibrium price of gasoline and a lower e#uilibrium #uantity. /urthermore, the higher price of gasoline will increase the demand for substitutes, such as small cars. he e#uilibrium price of small cars is li*ely to increase, as is the e#uilibrium #uantity of small cars.
1-. 8#uating the initial #uantity demanded and #uantity supplied gives the e#uation4 > 09 9 > 1$. Solving for price, we see that the initial e#uilibrium price is '- per month. 6hen the ta& rate is reduced, e#uilibrium is determined by the following e#uation4 > 09 .$9 1$. Solving, we see that the new e#uilibrium price is about '3<. per month. 7n other words, a typical subscriber would save about '1.-? (the difference between '-. and '3<.). 1?. Ery beans and rice are probably inferior goods. 7f so, an increase in income shifts demand for these goods to the left, resulting in a lower e#uilibrium price. herefore, .D. Ery /oods will li*ely have to sell its products at a lower price. 1<. /igure $3 illustrates the relevant situation. he e#uilibrium price is '., but the ceiling price is '1.$3. Notice that, given the shortage of 10 million transactions caused by the ceiling price of '1.$3, the average consumer spends an e&tra 10 minutes traveling to another 5% machine. Since the opportunity cost of time is '$0 per hour, the non pecuniary price of an 5% transaction is '3.- (the '$0 per hour wage times the fractional hour, 10C-, spent searching for another machine). hus, the full economic price under the price ceiling is '-.<3 per transaction. 5% /ee Page #
Supply Baye & Prince
'-.<3
'. Feiling 9rice
'1.$3
Shortage 10$ million 3
Eemand
1A
:uantity (%illions of ransactions) Figure 2-"
1A. he unusually cold temperatures have caused a decrease in the supply of grapes used to produce Fhilean wine, resulting in higher prices. hese grapes are an input in ma*ing wine, so the supply of Fhilean wine decreases and its price increases. Since Falifornia and Fhilean wines are substitutes, an increase in the price of Fhilean wine will increase the demand for Falifornian wines causing an increase in both the price and #uantity of Falifornian wines. d
$. Substituting 9des*top A< into the demand e#uation yields Qmemory =9240−100 Pmemory . Similarly, substituting N 1 into the supply e#uation yields s Qmemory =1100 + 25 Pmemory . he competitive e#uilibrium level of industry output d s and price occurs where Q memory =Qmemory , which occurs when industry output ¿ ¿ Qmemory =2728 (in thousands) and the mar*et price is Pmemory =$ 65.12 per unit. Since 1 competitors are assumed to e#ually share the mar*et, Ii*ing should d produce $?.$< thousand units. 7f 9des*top '1,<, Qmemory =9040−100 Pmemory . Jnder this condition, the new competitive e#uilibrium occurs when industry output is $-<< thousand units and the perunit mar*et price is '-.3$. herefore, Ii*ing should produce $-.<< thousand units. Since demand decreased (shifted left) when the price of des*tops increased, memory modules and des*tops are complements.
Managerial Economics and Business Strategy, 8e
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$1. %id owne 75 aimed to educate consumers that its contract with Kocal -33 union members was different than its rivals, so it engaged in informative advertising. %id owne 75Gs informative advertising increases demand (demand shifts rightward) resulting from (1) Kocal -33 union members loc*ed out of rival supermar*ets ($) consumers who are sympathetic to the Kocal -33 union, and () consumers who do not li*e the aggravation of pic*eting employees and other disruptions at the supermar*et. his shift is depicted in /igure $-, where the e#uilibrium price and #uantity both increase. 7t is unli*ely that demand will remain high for %id owne 75. 5s contracts are renegotiated and Kocal -33 union members are ba c* to wor*, demand will li*ely settle bac* around its original level. Price
1
P2
P1 %2
%1 Q1
Q2
Quantity
Figure 2-#
$$. he price gouging statute imposes an effective price ceiling on necessary commodities during times of emergenciesL legally retailers cannot raise prices by a significant amount. 6hen a natural disaster occurs, the demand for necessary commodities such as food and water can dramatically increase, as people want to be stoc*edup on emergency items. 7n addition, since it can be difficult for retailers to receive shipments during emergency periods, the supply of these items is often reduced. iven the simultaneous reduction in supply and increase in demand, one would e&pect the price to increase during times of emergencies. However, since the price gouging statute acts as a price ceiling, the price will probably remain at its normal level, and a shortage will result.
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$. 6hile there is undoubtedly a lin* between unemployment and crime, the governorGs plan is li*ely flawed since it only e&amines one side of the mar*et. Daising the minimum wage will ma*e the prospect of wor*ing more appealing for teenagers, but it will also have an effect on business owners and managers in the state. he minimum wage is a price floor. Daising the minimum wage will reduce the #uantity demanded for labor within the state, and result in a labor surplus. %ore teenagers will see* Mobs, but fewer businesses will hire teenagers. 7n all li*elihood, the governorGs plan will result in greater Muvenile delin#uency.
Managerial Economics and Business Strategy, 8e
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