CHAPTER 1
Answers to Questions for Review
1. The opportunity cost of reading a novel this evening is not being able to do whatever you
would have done instead. If you would have watched TV, then your opportunity cost is not
watching TV; if you would have studied economics, then your opportunity cost is not
studying economics.
2. The tuition is a sunk cost and so your roommante should consider only costs and benefits
relevant now and in the future. If he will be better off in life by leaving school now, he should
not let the tuition make the rest of life less meaningful.
3. Driving an automobile (which pollutes the atmosphere) imposes an external cost on others.
Building a house which others admire presents an external benefit. Inventing something
which is new and useful but which cannot be patented presents another external benefit.
4. A 50 year old presumably is in a higher pay bracket than a 20 year old so the opportunity cost
of leaving the job is greater for the older person.
5. By definition, a sunk cost is a cost that is incurred regardless of one's current decisions.
6. Economists generally argue that people act in their own self-interest even if they do not
consistently evaluate costs and benefits. The analogy most frequently used (from Milton
Friedman) is that of a pool player who knows how to sink his shots without having studied
physics.
Answers to Chapter 1 Problems
1. Let $X be the amount Chris earns in a day on his job. The cost to Chris of going to the park is
then $15 (admission fee) + $5 (gas & parking) + $10 (the lost satisfaction from not working)
+ $X (lost salary) = $30 + $X. The benefit of going to the park is $45. He should go to the
park if his salary is $10/day, and shouldn't go if his salary is $20/day. At a salary of $15/day,
he is indifferent between going and not going.
2. If Tom kept the $200 and invested it in additional mushrooms, at the end of a year's time he
would have an additional $400 worth of mushrooms to sell. Dick must therefore give Tom
$200 of interest in order for Tom not to lose money on the loan.
3. It is reasonable to assume that everybody has decreasing satisfaction from each pound of
food as consumption level increases. In University A, everybody will eat until the benefit
from eating an extra pound of food is equal to $0, since this is the cost of each pound of food.
In University B, people will eat until the benefit decreases to $2. Thus, everybody will eat
less if they are at University B. So, not just average consumption but also each individual’s
personal consumption will be lower. Note that to reach this conclusion we need the
assumption that the students at both universities have the same appetites.
4. The only costs that vary with mileage are fuel, maintenance, and tires, which average
$0.25/mile. The cost of driving will thus be $250, and since this is less than the cost of the
bus, you should drive.
5. The band and hall rental fees are fixed costs. The caterers charge at the rate of $7/guest ($5
catering bill/$2 drink). So an extra 10 guests will increase total costs by only $70.
6. You gave up the $60 you wold have earned if the money was in your savings account. This
assumes that your tax rate on interest earned is zero
7. Bill has already bought his ticket, so his cost-benefit calculation when it is time to go is as
follows: benefit of seeing game vs. cost of the drive + time costs, etc. Joe, not having bought
his ticket, faces a different calculation: benefit of seeing game vs. $30 + cost of the drive +
time costs, etc. Since the benefits are the same in each case, but the costs are larger for Joe at
the moment of decision, he is less likely to go.
8. A plane of either type--large or small--should use the state-of-the-art device if the extra
benefits of that device exceed its extra costs. Because the device will save more lives in large
planes than in small planes, its benefits are larger in large planes than in small ones. Your
original recommendation was presumably based on the calculation that the benefits for the
larger planes justified the extra cost, but did not do so in the case of the smaller planes.
Airline passengers are like other people insofar as their willingness to invest in extra safety is
constrained by other pressing uses for their scarce resources. Where extra safety is relatively
cheap, as in large planes, they will rationally choose to purchase more than when it is
relatively more expensive, as in small planes.
9. With more than a week to go, the $100 driver's fee and the $50 bus cancellation fee are sunk
costs. If the trip takes place, the additional costs will be the remaining $450 of the bus fee
plus the $75 in tolls, for a total of $525 in additional costs. If at least 30 tickets will be sold,
it makes sense to continue the trip, since total revenue ($540) will exceed the additional cost.
10. Assuming that residents are required to recycle cans, they simply cannot put them with the
regular trash. In the first case, the fixed cost of $6/week is a sunk cost. Therefore, for the
residents, the cost of disposing an extra can is $0. In the tag system, the cost of disposing an
extra can is $2, regardless of the number of cans. Therefore, since the costs are higher and the
benefit of setting out a can is assumed to be the same in both cases, you expect less cans to be
collected in the tag system.
11. The benefit of the 1st gigabyte is $800, the 2nd is $400, the 3rd is $200, the 4th is $100, the
5th is $50, the 6th is $25, the 7th is $12.50 and the 8th is $6.25. You should purchase 4
gigabytes. At higher levels of benefit, the benefit is less than the cost. At lower levels, benefit
exceeds the cost.
Price
800.00
400.00
200.00
100.00
1
2
3
4
5
6
7
8
9 Memory (GB)
12. When the price falls to $50/GB, you consume 5 GB (rather than 4 GB at the higher price.)
When your benefit rises also, you consume 6 GB of RAM.
Price
800.00
The curve to the right shows
the new benefit function.
400.00
200.00
100.00
50.00
1
2
3
4
5
6
7
8
9 Memory (GB)
13. False. The fact that she would have chosen the party before she bought her ticket means that
she prefers a party to an event that costs $40. Now her choice is between two events that she
can attend with no further payment.
14.
Benefit
Ani DiFranco
Bp
Dave Matthews
Br
Cost (initial)
Cost (final)
$75
$75
$75
$50
In the problem, we are given that
Bp - $75 > Br - $75
or
Bp > Br
(*)
Now, we need to find out whether the following is true or not:
Bp - $75 > Br - $50
which is the same as
Bp > Br + $25
(**)
Notice that (*) does not necessarily imply (**). For example, if Bp=$80 and Br=$60, then (*)
holds while (**) does not. So we can conclude that you should not go to the Ani DeFranco
concert in the above scenario if you are a rational utility maximizer.
Your decision will depend on the relative values of Bp and Br. The fact that you would have
bought a Ani DeFranco ticket means that the benefit of attending the Ani DeFranco concert,
denoted Bp, must be greater than $75. Let Bs denote the benefit of going to the Dave
Matthews concert. The fact that you would have chosen the Ani DeFranco concert before
receiving your Dave Matthews concert ticket means that Bp > Bs. But this does not imply that
you should go to the Ani DeFranco concert. Suppose Bp = $80 and Bs = $60. When you
now choose between the two concerts, the opportunity cost of attending the Dave Matthews
concert is $50, so the net benefits of attending each concert are given by Bd - $75 =$5 and Bs
- 50 = $10, which means you should go to the Dave Matthews concert. So FALSE.
15. Safari provides $10,000+/yr more enjoyment than a business job. $70,000 = gross benefit of
business job salary.
Costs of Business Job
10,000 opportunity cost of loan
50,000 lost salary as safari leader
10,000+ lost enjoyment from safari job
$70,000+ total cost of taking of business job > benefit, so don't take the job.
If business salary was $70,001/yr, he would have taken it.
16. True. If you got $15,000 for the Taurus and paid that plus $5,000 more for the Camry, the
entire Camry expense would have cost you $25,000. Since you have already shown that you
did not want the Camry for $25,000, why would you spend that for it now?
CHAPTER TWO
Answers to Questions for Review
1. A shortage occurs when, at a given price, quantity demanded exceeds quantity supplied.
Scarcity implies that not everyone can consume as much of a good as he wants. A good can
be scarce without a shortage occurring if the price of the good is set at the market
equilibrium.
2. The supply curve would be a horizontal line where the price equals zero. The demand curve
would be a typical demand curve. If the price is greater than zero, then the market system is
acting to allocate resources; not everyone can have as much as they want.
3. Some examples: Parking places for the president of the college; giving seniors priority in
class assignments. Shortage of parking spaces and students being bumped from
preregistration.
4. The former implies a shift in the supply curve; the latter a movement along the supply curve.
5. a. Shift in demand
b. Change in quantity demanded (shift in supply)
c. Change in the quantity demanded (shift in supply)
d. Shift Because consumers prefer to pay a lower price.
6. The allocative function of price is not important with vertical, or nearly vertical, supply
curves, e.g., land.
7. For the tax burden to fall mostly on consumers rather than producers (buyers rather than
sellers), you want to find a product (or products) for which the quantity supplied is very
responsive to price but quantity demanded is less responsive to price. Addictive goods like
cigarettes and alcohol may fit this description.
8. If a poor person were given $50,000 in cash, it is unlikely he would spend it on a Mercedes,
since he probably has other, more pressing wants. Since the gift Mercedes would fetch less
than the cash gift, most poor persons would choose the cash.
Answers to Chapter 2 Problems
1. a) The imposition of the ceiling price on tea causes a reduction in the quantity of tea bought,
from Q1 to Q2 (left panel). The result is a leftward shift in the demand for lemons, resulting
in a reduction in both price and quantity (right panel).
Price
Price
S
S
P 1l
t
P1
P 2t
P2l
D1
D
Q2 t Q1 t
D2
Tea
Q2 l Q1 l
Lemons
1. b) The ceiling price for tea lowers the quantity people are able to buy from Q1t to Q2t. There
is excess demand for tea at the ceiling price P2t, and some of this excess demand spills over
to substitute products such as coffee. The result is that the equilibrium price of coffee rises.
(Note: This result may seem inconsistent with the claim that a fall in the price of a good's
substitute reduces the demand for that good. But this claim refers to a fall in the equilibrium
price of the good, not a price reduction caused by a ceiling. Because of the quantity reduction
caused by the ceiling, tea buyers would be willing to pay P3t for tea. So the price ceiling
actually raises the opportunity cost of additional units of tea.)
P tea
Pcoffee
St
Sc
P3t
P1t
Pt
2
Pc
2
c
P
1
D
Qt Qt
1
2
D
1
Qc Q c
1
2
Q tea
D2
Q coffee
2. a) At prices of 35 and 14, there will be 7 DVDs traded in the market. At P=35, sellers are
dissatisfied. At P=14, buyers are dissatisfied.
2. b) The supply and demand curves, shown in the diagram, intersect at P=28, Q=14
Price
42
S
35
28
21
14
7
D
Quantity
7
14
21
28
35
42
2. c) Total revenue is (28)(14) = 392.
3. a-b) A reduction in the price of hardware would raise demand for software and thus cause
equilibrium price and quantity of software to rise. On the other hand, a rise in the price of
software would reduce demand for hardware and thus cause the equilibrium price and
quantity of hardware to fall.
4. a) Both price and quantity drop.
P(toys)
S
P1
P2
D1
D2
Q2
Q(toys)
Q1
4. b) Both quantity and price drop.
P(battery)
S
P1
P2
D1
D2
Q2
Q(battery)
Q1
4. c) Both price and quantity go up.
P(yo-yos)
S
P2
P1
D2
D1
Q1
Q2
Q(yo-yos)
5. a) The price goes up, the quantity goes down.
P(oil)
S2
S1
P2
P1
D
Q(oil)
Q2
Q1
5. b) The price and the quantity go down.
P(air)
S
P1
P2
D1
D2
Q2
Q(air)
Q1
5. c) The price and the quantity go up.
P(rail)
S
P2
P1
D2
D1
Q1
Q2
Q(rail)
5. d) The price and the quantity go down.
P(hotel)
S
P1
P2
D1
D2
Q2
Q(hotel)
Q1
5. e) The price goes down, the quantity goes up.
P(milk)
S1
S2
P1
P2
D
Q(milk)
Q1
6.
6.
6.
6.
6.
a)
b)
c)
d)
e)
Q2
In quantity demanded.
In demand.
In demand.
In demand.
In quantity demanded.
7.
a) The equilibrium quantity is Q = 90,000 seats and the equilibrium price is P = 1900 –
(1/50)(90,000) = 1900 – 1800 = $100.
7.
b) At a price ceiling of P = $50, quantity demanded is found by solving 50 = 1900 – (1/50)Q
for Q = 92,500 seats. Since the stadium only holds Q = 90,000 seats, there will be 92,500 –
90,000 = 2,500 dissatisfied fans who want to buy a ticket at P = $50 but cannot find one
available.
7. c) Quantity demanded for the higher demand is found by solving 50 = 2100 – (1/50)Q for
Q = 102,500 seats. Now there will be 102,500 – 90,000 = 12,500 dissatisfied fans who want
to buy a ticket at P = $50 but cannot find one available. The excess demand is
12,500 – 2,500 = 10,000 seats more than for the not so big game.
7. d) Normally a price ceiling both raises quantity demanded and lowers quantity supplied.
Here, only the first effect is present because the stadium capacity is fixed.
Problem 2-17
S
Price ($)
350
300
D’
D
100
50
0
80
90
92.5
Quantity of seats per game (000)
102.5
105
8. a) Under the original demand curve, quantity demanded was Q = 900 units and quantity
supplied Q = 300 units, so excess demand was 900 – 300 = 600 units. With the larger
demand, quantity demanded becomes Q = 1100 units, so excess demand becomes
1100 – 300 = 800 units. Excess demand has grown by 800 – 600 = 200 units.
8. b) Quantity demanded is Q = 1400 – P; quantity supplied is Q = P. Subtracting quantity
supplied form quantity demanded gives excess demand of 1400 – 2P units. Set excess
demand equal to the original level of 600 and solve 600 = 1400 – 2P for the required price
floor of P = $400. If the government accommodates the increase in demand by raising the
rent control form $300 to $400, the degree of excess demand will be unchanged.
Price ($)
600
S
D
D’
400
300
0
300
400
Quantity (units/month)
900
1000 1100
1400
9. a) With a price support of P = $500/ton and the original supply of P = Q, quantity supplied
must be Q = P = 500 tons. Meanwhile, quantity demanded is Q = 100 tons, so excess supply
is 500 – 100 = 400 tons. With the expanded supply of P = (1/2)Q, quantity supplied grows to
Q = 2P = 1000 tons. Quantity demanded is still Q = 100 tons, so excess supply grows to
1000 – 100 = 900 tons.
9. b) The extra 900 – 400 = 500 tons the government has to buy of excess supply costs the
government $500/ton, so the added expenditure is 500(500) = $250,000.
Price ($)
600
S
500
S’
D
0
100
500
Quantity (tons/yr)
1000
10. The supply curve becomes P = 2 + 2Q and the demand remains P = 8 – 2Q. By setting the two
equations equal to each other and solving for Q we have Q = 1.5. Substituting 1.5 into the
demand equation results in a price of 5.
Answers to Appendix Problems
1. The supply curve after the tax is shown as S' in the diagram. The new equilibrium quantity
will fall to 2. The equilibrium price paid by the buyers is now $4/oz. The price received by
the sellers is now $2/oz.
Price ($/ounce)
6
S'
S
5
4
3
2
1
D
1
2
3
4
5
Quantity
6 (tons/year)
2. The supply curve tells us that at a quantity of 2 tons/yr, suppliers will be willing to supply
additional titanium at a price of $2/oz. At that same quantity, buyers are willing to pay $4/oz.
Suppose a supplier sells one ounce to a new buyer at a price of $3. This will make the
supplier better off by $1. The buyer will also be better off by $1.
3. With the tax of T = $2/oz on sellers, the supply curve shifts up by the amount of the tax from
P = Q to P = 2 + Q. The intersection of the tax-ridden supply curve and the new demand
curve is found by solving 8 – Q = 2 + Q for Q = 3 tons. Inserting the quantity into the
demand curve yields a price buyers pay of P = 8 – 3 = 5 an ounce and hence a price sellers
receive of P = 5 – 2 = 3 an ounce. The government collects revenue of TQ = 2(3) = $6. Prior
to the increase in demand, the government collected the tax on only 2 ounces, so its total
revenue collected was $4. Thus, government revenue has grown by 6 – 4 = $2 due to the
expansion in demand for titanium. See the graph below
Price of Titanium ($)
8
S’
S
5
3
0
3
8
Quantity of Titanium (tons/yr)
4. At a price floor of P = $4/oz, quantity supplied would be Q = 2 tons. Using demand P = 6 – Q
and P = $4/oz, quantity demanded is also Q = 2 tons. Thus, the reduction in supply raises the
equilibrium price to the level of the price floor, so the price floor is no longer binding.
Price of Titanium ($)
S’
6
S
4
D
0
2
4
6
Quantity of Titanium (tons/yr)
5. a) The effect of the tax is to shift the supply curve upwards by $9 as shown in the diagram on
the next page. The quantity sold falls to 11 units.
5. b) The new market price is 31, of which the seller gets to keep only 22.
3. c)Buyers now spend 11(31)=341.
5. d)The government collects 11(9) = 99.
5. e)
s'
Price
42
S
35
28
21
14
7
D
Quantity
7
14
21
28
35
42
6. a-b) The seller's share is the fall in price received by the seller divided by the total tax:
ts = 6/9=2/3. The buyer's share is the increase in price divided by the total tax: tb = 3/9=1/3.
7. In the diagram below, P* and Q* are the original equilibrium price and quantity of Japanese
cars sold in the U. S. If a quota of Q1 is imposed, Japanese car makers will be able to charge
P1 for their cars. To get the same quantity reduction by means of a tax, the after tax supply
curve must intersect the demand curve at Q1 . The result is a price to the U. S. buyer of P1,
the same as in the quota case. The difference in the two policies is that in the quota case the
price increase goes to Japanese car makers, while in the tariff case it goes to the U. S.
government.
S'
Price
S
P1
P*
P1-T
D
8.
Quantity
Q*
Q1
Price
S(tax)
S
120
90
60
45
30
D
15
30
60
Quantity
8. a) Before tax: 120-2Q=30+Q (in equilibrium)
Q=30
P=60
8. b) After tax supply curve: P = 60 + 2Q
Equilibrium: 120 - 2Q = 60 + 2Q
Q = 15
Price, including tax = 90
Price received by seller (net of tax) = 45.
8. c) Sellers share = 60 – 45 = 15
Buyer’s share = 90 – 60 = 30
9. a-c) With the tax on sellers, supply rises by the amount of the tax to P = 4 + 4Q. the
equilibrium is found by solving 20 = 4 + 4Q for Q = 4 units. Buyers pay P = $20 and sellers
receive 20 – 4 = $16. Sellers pay the full tax because demand is perfectly elastic, which
means that buyers cannot be forced to pay any of the tax.
Supply + tax
Supply
Price ($) 28
20
16
D
0
4
5
Quantity (units/wk)
10. a-c) With the tax on buyers, demand falls by the amount of the tax to P = 24 – Q. The
equilibrium is found by solving 20 = 24 – Q for Q = 4 units. Sellers receive P= $20, and
buyers pay 20 + 4 = $24. Buyers pay the full tax because supply is perfectly elastic, which
means that sellers cannot be forced to pay any of the tax.
Problem A2-10
Price ($)
28
24
D
20
S
D’
=
0
Quantity (units/wk)
4
8
CHAPTER THREE
Answers to Questions for Review
1. You will be as well off as a year ago; your budget line will remain the same.
2. False. The slope of the budget constraint tells us only the ratio of the prices of the two goods.
3. False. Diminishing MRS explains the convexity of the indifference curve, but not the
downward slope.
4. You prefer Coke to Diet Coke, Diet Coke to Diet Pepsi, but prefer Diet Pepsi to Coke.
5. The slope of an indifference curve indicates how much of a good one is willing to give up to
get one unit of another and be at the same level of satisfaction. Thus the more of one good
that one is willing to give up, the less important is that good relative to the other.
6. One bundle may be within the individual's opportunity set while the other is not.
7. If the relative price of the two goods is not the same as the slope of the indifference curve,
then one will always get a corner solution.
8. True. The corner solution (a) is on a higher indifference curve than the corresponding
tangency (b). Which corner becomes the solution depends on the slope of the budget
constraint. There can be a solution in either corner, as shown in the graphs below. Quantity
discounts will not change this outcome scenario.
Y
a
Y
B
b
a
X
X
9. Suppose that Ralph's current consumption bundle is given by the point A in the diagram. The
information given tells us that on the budget with M+10 units of income, Ralph would
consume at the point B, and that B is equally preferred to C. This can happen only if the
indifference curve passing through B and C does not have the usual convex shape. His
indifference curve through B and C could, for example, be a straight line, indicating that tuna
fish and Marshallian money are perfect substitutes in this region. (If the indifference curve
through B and C were convex, then Ralph's optimal bundle would lie between B and C,
which means that he would spend some of the extra $10 on tuna fish.)
Y
M + 10
M
B
A
C
Answers to Chapter 3 Problems
1.
Y($/wk)
100
80
60
40
20
20
40
60
80
100
Seeds (lbs/wk)
2.
Y($/wk)
100
80
60
40
20
20
40
60
80
100
Seeds (lbs/wk)
3. a) Pecans are equally preferred to macadamias, which are preferred to almonds, which are
preferred to walnuts, so by transitivity it follows that pecans are preferred to walnuts.
3. b) Macadamias are preferred to almonds and cashews are preferred to almonds. Transitivity
tells us nothing here about the preference ranking of macadamias and cashews.
4. True (see diagram on next page). Each price increases by 15%, so that – Px/Py is unchanged.
Y
M/80
M/92
slope = 120/80 = 3/2
Slope = 138/92 =3/2
M/138 M/120
X
5. a)
Y
150
60
Milk Balls
5. b) The opportunity cost of an additional unit of the composite good is 1/2.5 = 0.4 bags of milk
balls.
6. a)
Y
150
100
60
Milk Ball
6. b) The opportunity cost of a unit of the composite good is now 0.6 bags of milk balls.
7. a)
Y
150
90
Milk Balls
7. b) The opportunity cost of a unit of the composite good is again 0.6 bags of milk balls.
8. a) To get any enjoyment from them, Picabo must consume skis and bindings in exactly the
right proportion. This means that the satisfaction Picabo gets from the bundle consisting of 4
pairs of skis per year and 5 pairs of bindings will be no greater than the satisfaction provided
by the bundle (4, 4). Thus the bundle consisting of 4 pairs of skis per year and 5 pairs of
bindings lies on exactly the same indifference curve as the original bundle. By similar
reasoning, the bundle consisting of 5 pairs of skis per year and 4 pairs of bindings lies on this
indifference curve as well. Proceeding in like fashion, we can trace out the entire
indifference curve passing through the bundle (4, 4), which is denoted as I1 in the diagram.
b) Skis (pairs/yr)
20
16
I4
12
I3
8
I2
4
I1
0
4
8
12
16
18
20
Bindings (pairs/yr)
9. Picabo's budget cnstraint is B = 15 - 2S. Initially, she needs the same number of pairs of skis
and bindings S = B. Inserting this consumption equation into her budget constraint yields B =
15 - 2B, or 3B = 15, which solves for B = 5 pairs of bindings (and thus S = 5 pairs of skis).
As an aggressive skier, she needs twice as many skis as bindings S = 2B. Inserting this
consumption equation into her budget constraint yields B = 15 - 4B, or 5B = 15, which solves
for B = 3 pairs of bidings (and thus S = 6 pairs of skis). She consumes more skis and fewer
bindings as an aggressive skier than as a recreational skier. See graph below.
Pairs of Bindings per Year (B)
15
B = 15 – 2S
B+S
5
B = S/2
3
0
5
6
Pairs of Skis per year (S)
7.5
10. Alexi's budget constraint is T = 75 - (3/4)C. Her perfect substitute preferences yield linear
indifference curves with slope equal to negative one, such as T = 75 - C and T = 100 - C. By
consuming 90/0.90 = 100 cups of coffee each month, she reaches a higher indifference curve
than consuming 90/1.20 = 75 cups of tea (or any affordable mixture of coffee and tea). Thus
Alexi buys 100 cups of coffee and no tea. Any increase in the price of coffee would force
Alexi to a lower indifference curve, and thus lower her standard of living.
Cups of Tea/month
(T)
100
T = 100 – C
75
T = 75 – (3/4)C
0
100
Cups of Coffee per month (C)
11. In the diagram, suppose we start at bundle A and then take away ΔP units of pears. How
many more units of apples would we have to give Eve to make her just as happy as at A?
The answer is none, because she didn't care about pears in the first place, and therefore
suffered no loss in satisfaction when we took ΔP units of pears away. Bundle B is thus on the
same indifference curve as bundle A, as are all other bundles on the horizontal line through
A. All of Eve's indifference curves are in fact horizontal lines, as shown.
Apples (lbs/wk)
Increasing satisfaction
⇑
B
ΔP
A
Pears (lbs/wk)
12. Again start at a given bundle, such as A in the left panel of the diagram below. Then take
away a small amount of food, ΔF, and ask what change in smoke, ΔS, would be required to
restore Koop's original satisfaction level. In the standard case, when we take one good away
we need to add more of the other. This time, however, we compensate by taking away some
of the other good. Thus, when we take ΔF units of food away from Koop, we must reduce
the smoke level by ΔS in order to restore his original satisfaction level. This tells us that the
indifference curve through A slopes upward, not downward. Koop would be just as happy
with a smaller meal served in a restaurant with a no-smoking section as he would with a
larger meal served in a restaurant without one.
It is usually possible to translate the consumer's indifference curves into ones with the
conventional downward slope by simply redefining the undesirable good. Thus, if we might
focus not on smoke, an undesirable good, but on cleanliness (the absence of smoke), which is
clearly desirable. So doing would recast the indifference map in the left panel of the diagram
as the much more conventional-looking one in the right panel.
Food (lbs/wk)
Increasing Satisfaction
⇑
Food
Increasing Satisfaction
⇑
B
A
ΔF
I3
I2
I1
ΔS
I3
I2
I1
Smoke (micrograms/wk)
Cleanliness
13. You prefer to maximize profit, which is the same under the two rate structures, making you
indifferent between them.
14. a)
Movies
36
30
24
21
15
B
0
B
1
5
7
10
12 Plays
14. b) If plays cost $12 and movies cost $4, the budget line is Bo, which has exactly the same
slope as Paula's indifference curves. She will be indifferent between all the bundles on B0.
14. c) On B1, she will consume 10 plays.
15.
Y
Increasing
satisfaction
Y
Increasing
Satisfaction
Garbage
Garbage
16. Let C = coffee (ounces/week) and M = milk (ounces/week). Because of Boris's preferences,
C = 4 M. At the original prices we have:
4M(l) + M(0.5) = 9
4.5M = 9
So M=2 and C=8
Let M' and C' be the new values of milk and coffee. Again, we know that C'=4M'. With the
new prices we have:
(4M')(3.25) + M'(.5) = 9
13M' + 0.5M' = 9, 13.5M' = 9, M' = 2/3
C = 8/3
17. An unrestricted cash grant would correspond to the budget B1 in the diagram. On B1 the
university would want to spend more than 2M on non-secular activities anyway, so the
restriction will have no effect. This result is analogous to the result in the text concerning the
restriction that food stamps not be spent on cigarettes. Provided the recipient would have
spent more on food than he received in stamps, such a restriction has no effect.
Non-secular Activities
14
12
10
B0
B1
8
6
4
2
0
2
4
6
8
10
18.
19 a) 10(0) + 10(0.25) = 2.50
19. b) 10(0.25) + 10(0.50) = 2.50 + 5.00 = 7.50.
12
14
16 Secular Activities
20. Your budget constraint is Y = 360 - 40C for 0 < C < 5 days of car rental (when you pay the
daily rate), constant at Y = 160 for 5 < C < 7 days of car rental (when you switch to the
weekly rate and thus additional days up to one week are free), and then Y = 160 - 40(C - 7) =
440 - 40C for 7 < C < 11 (when again you have to pay by the day for each day beyond the
one week). a) If y = 140C, then inserting this equation into the first leg of the budget
constraint yields 140C = 360 - 40C or 180C = 360, which solves for C = 2 days of car rental
and thus Y = 280 worth of other goods. b) If instead you will trade a day of car rental for $35,
then you would consume a week's rental C = 7 and thus Y = 160 worth of other goods. Your
seven days of car rental are equivalent to 7(35) = $245 according to your preferences, which
when added to the $160 remaining, yields $405. This beats the $360 if you consume no rental
days and also beats the 11(35) = $385 if you consume the maximum rental days you can
afford (as well as beating any other affordable combination of C and Y.
Composite Good
per trip (Y)
360
Problem 20a
Y = 140C
280
Y = 360 – 40C
Y = 160
160
Y = 440 – 40C
0
2
Composite Good
per trip (Y)
360
5
7
11
Days of Car Rental per trip (C)
Problem 20b
Y = 405 – 35C
Y = 360 – 40C
Y = 160
160
Y = 440 – 40C
0
5
7
11
Days of Car Rental per trip (C)
21. With diminishing MRS, to decrease pizza consumption from 3 to 2 slices, the consumer has
to be given more than 1 beer (since that was the amount needed to decrease pizza
consumption from 4 to 3 slices and stay on the same indifference curve). So he would be
indifferent between the bundles (3 slices of pizza, 2 beers) and (2 slices of pizza, X beers)
where X>3. However, we know that he prefers (1 slice of pizza, 3 beers) to (3 slices of pizza,
2 beers), so he should also prefer that bundle to (2 slices of pizza, X beers). But this violates
the more-is-better assumption.
22. Budget set under Plan A:
composite($/week)
12
calls(number/wk)
240
Budget set under Plan B:
composite($/week)
12 .
10
.
calls(number/wk)
30
230
Notice that Plan A is superior to Plan B since its budget constraint is above the budget
constraint of Plan B.
23.
composite good
12
11
.
.
10 .
9
8
7
6
5
4
3
2
1
.
.
.
.
.
.
.
.
.
.
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Quantity of Soft Drinks
Note that the budget constraint is not a line but rather the set of points that are shown in the
diagram and the ones that are below them. To construct this, for each level of composite
good, from 0 to 12, determine the maximum number of bottles you can buy with the leftover
money. For example, for Y=4, you have $8 left. The best you can do is 1 large and 1 small,
which gives 11 tickets. Remember that you can't buy a fraction of a set. Notice that point
(0,12) is also on the budget constraint.
24. Assume that the quality of the food is the same in both restaurants, so that price is the only
difference that matters to consumers. In the first restaurant, the $15 flat tip is a fixed cost: it
does not affect the cost of additional items ordered from the menu. In the second restaurant,
by contrast, the price will be 15 percent higher for each extra item you order. The marginal
cost is higher. The average meal is $100 in the first restaurant, which with tip comes to $115.
The same amount of food would cost the same in the second restaurant. But because the cost
of each additional item is higher there, we expect that less food will be consumed in the
second restaurant. Note the similarity of this problem to the pizza experiment described in
Chapter 1.
25. Bo is Plane's budget constraint last year. By selling all his grapes he would have an income of
$14,000. By spending all his income on grapes he would have 7000 bu. This year's budget
constraint is B1. It starts at 16 on the Y axis and hits the grapes axis at 16/3, passing through
Y = 10, G = 2, last year's bundle. Since last year's indifference curve (ICo) was tangent to B0
at Y = 10, G = 2, and since this year's budget constraint is steeper than last year's, we know
that some part of last year's IC lies within B1. In particular, a part of ICo that lies above Y =
10, G = 2 is within B1. This means that Plane will consume more Y and less G than he did
last year. (See graph on next page.)
Y (1000s)
16
14
10
IC0
B1
2
B0
5.33
7 Grapes (1000 bu/yr)
CHAPTER FOUR
Answers to Questions for Review
1. a) Salt is generally considered a necessity.
1. b) As the text points out, the income effect for salt is extremely small.
2. Unlike salt, education at a large private university has a large income effect.
3. See Figure 4-5 in the text.
4. Some examples: hamburger, generic beer, bus tickets, almost anything purchased at stores
selling "as is" damaged or discontinued merchandise..
5. Yes. A downward-sloping PCC simply implies that as the price of a good falls, the consumer
purchases so much more of the good that the proportion of income spent on the good actually
increases.
6. Vertical summation would mean that each good could be jointly consumed. Horizontal
summation means each person consumes their commodity and excludes others from it.
7. An elastic demand leads to revenue increases if price falls. An inelastic demand leads to
revenue increases if the price increases. A unitary demand curve results in constant revenue
no matter what price does. If price goes the opposite direction from that listed above, the
revenue moves in the opposite direction also.
8. The slope of the demand will give only an absolute change number. It does not give a
proportionate change. Since price sensitivity has little meaning apart from the proportion of
change, elasticity is far better than slope at showing a useful responsiveness of demand to
price.
9. Unitary
10. Since other good substitutes abound, a school will likely have a fairly elastic demand curve.
11. If income is shifted from the rich to the poor, those products consumed by poor people and
not by rich will increase in demand and those goods consumed by the rich and not the poor
will have a decrease in demand.
12. Companies that produce more necessary items rather than luxuries would be better to invest
in than companies that produce luxury items since people will be paring down their
expenditures.
13. False. In the diagram below, an increase in the price of X leads to a reduction in the amount
of X consumed, but an increase in the quantity of Y.
Y
Positive income effect for both X and
Y because the quantity of both X and
Y increase when income is increased
.
Change
in Y
X
Change in X
14. The demand for tennis balls is elastic. When its price goes up, the total expenditure on the
balls goes down. Thus, the share of income available for tickets increases. Since their price is
constant, he consumes more tickets.
15. False. Look at Figure 4-13 in the text. Both individuals have linear demand curves, but the
aggregate demand curve is kinked, not straight.
16. No. If bread is an inferior good, then as income increases, quantity demanded of bread
decreases. If butter were an inferior good also, then likewise, quantity demanded of butter
would decline as income grows. However, spending on both goods cannot decline, because
there would be no way of spending the added income. Thus, not all goods can be inferior.
Answers to Chapter 4 Problems
1. Sam’s budget constraint is 2OJ + AJ = 6 or OJ = 3 – (1/2)AJ. Sam’s indifference curves are
straight lines with constant MRS = 1/3. Sam’s optimal bundle is to consume no apple juice
and three cups of orange juice. When the price of apple juice doubles, Sam would not need
any additional income to afford his original consumption bundle, since he does not consume
any apple juice.
Orange Juice in
Cups
3
B0
ICs
3
6
9
Apple Juice in cups/week
2. Bruce’s budget constraint is the same as Sam’s, but his indifference curves have constant
MRS = 1. Thus Bruce’s optimal bundle is to consume six cups of apple juice per week and no
orange juice. To afford his original consumption bundle, Bruce would need additional income
(P’AJ – PAJ)AJ = (2 – 1)6 = $6/wk. At his new income of $12/wk and facing the higher price
of apple juice, Bruce’s budget constraint would become OJ + 2AJ = 12 or
OJ = 6 – AJ,
which contains Bruce’s original consumption point of six cups of apple juice and no orange
juice.
0
Bs’ = B1
Orange Juice in
cups/week
6
ICB = BB’
3
B1
0
3
Apple Juice in cups per week
B0
6
3. Maureen’s budget constraint is the same as Sam and Bruce’s but her indifference curves are
right angles (L-shaped) at bundles where the cups of orange juice and apple juice consumed
are the same. Setting OJ = AJ in her budget constraint gives OJ = AJ = 2 as her optimal
consumption bundle: two cups of orange juice and two cups of apple juice per week. To
afford her original consumption bundle, Maureen would need additional income (P’AJ – PAJ)A
= (2 – 1)2 = $2/wk. At her new income of $8/wk and facing the higher price of apple juice ,
Maureen’s budget constraint would become OJ + 2AJ = 8 or OJ = 4 – AJ, which contains
Maureen’s original consumption point of two cups of apple juice and two cups of orange
juice per week.
Orange Juice
in cups/week
4
OJ = AJ
3
2
1
B1
0
1
B0
BM’
2
3
4
Apple Juice in cups/week
5
6
4. First solve the demand curve for Q and multiply the result by 10. Then solve back in terms of
P to get P = 101 – Q for the market demand. At price $1/cup the individual consumes 10 cups
and the market consumes 100 cups.
Price
101
10.1
5. a) P=10, Q=100;
5. b)
101 Cups
So h = (P/Q)(1/slope) = (10/100)[1/(-0.5)] = -0.2
P
.
.
Q
P stays the same, Q increases, and the slope stays the same. Therefore, elasticity
decreases.
6. a)
P
2
elastic
unit-elastic
.
1
inelastic
50
Q
100
6. b) At (1, 50), total revenue is maximized since this is the unit-elastic point. At higher prices,
revenue decreases since it is the elastic region. At lower prices, revenue again decreases since
it is the inelastic region.
7. a) P=$3, Q=8000, Revenue=$21,000
7. b) Ep = (P/Q)(1/slope) = (3/7000)(-1000) = - 3/7
7. c) A price increase will increase revenue since current price is in the inelastic region.
7. d) Since substitution chances are increased, demand for the bridge will become more elastic.
8. We can’t know. We are only given that income elasticity of demand for safety (Ei) is positive.
For necessities, we have 0 < Ei< 1, and for luxury goods we have Ei> 1.
We need more information to determine whether Ei> 1 or not.
9. QA=25-0.5P, QB=50-P, So Q=QA+QB=75 + 1.5P and hence P=50-(2/3)Q.
Price
Price
50
Price
50
DA
25
+
50
DB
QA
50
=
D
QB
75 Q
10. Elasticity at A =(PA/QA)( Δ Q/ Δ P)=(400/300)(-20/200)=-40/300=-2/15. Elasticity at
B=(PB/QB)( Δ Q/ Δ P)=(600/280)(-20/200)=-60/280=-3/14.
Price
B
600
Change in P = 200
400
A
Change in quantity = 20
280 300
Quantity
11. Price elasticity = -CE/AC =-3/7 (using segment-ratio method). Because demand is inelastic
with respect to price, total revenue will go up with an increase in price.
Price ($/calculator)
100
A
total revenue = $2100/mo.
30
C
A
Q (calculators/mo.)
12. Total expenditure = PQ=27Q-Q3, which is shown in the diagram on the next page. It attains
its maximum value, 54, when Q=3.
Total Expenditure
54
Quantity
1
2
3
4
5
For students who have had calculus, an easier approach is to set d(PQ)/dQ=0:
d(PQ)/dQ=27-3Q2=0,
which solves for Q=3. Plugging Q=3 back into the equation for the demand curve, we
have P=27-32=18, and this is the price that maximizes total expenditure.
13. a) 300 = 1800 - 15P, so P = 100, which gives TR = 100(300) = 30000 cents/day.
13. b) Expressing the demand curve in terms of price, we have P = 120 - Q/15. Price elasticity =
(P/Q) (1/slope) = (1/3)(-15) = -5 .
13. c) Since demand is elastic with respect to price, a reduction in price will increase total
revenue.
13. d) Maximum total revenue occurs where price elasticity = -1.
(P/Q)(1/slope) = (P/Q)(-15) = -1, so maximum TR will occur when P = Q/15.
Substituting P = Q/15 back into the demand curve we get Q/15 = 120 - Q/15, or
2Q/15 = 120, which solves for Q = 900. At Q = 900, we have P = 60.
14. In absolute value terms, where price elasticity = Ep
Ep A = Q2A/AP2 = 2
Ep B = Q2B/P2B = 1
Ep C = Q1C/P1C = 1
Ep D = Q1D/P1D = 3
Ep E = Q1E/P2E = 1
So Ep D > Ep A > Ep B = Ep C = Ep E
15. The income elasticity for food is positive but less than 1; for Hawaiian vacations, greater than
1; for cashews probably greater than 1; and for cheap sneakers, less than 0. These elasticity
values are reflected in the Engel curves shown below.
food in general
cashews
Y
Y
food
Y
vacations
cheap sneakers
16. a) Tennis balls and tennis racquets are complements, so negative.
16. b) Negative, same reason.
16. c) Hot dogs and hamburgers are substitutes, so positive.
17. The cross price elasticity of good X with respect to good Y is – 4/5 for the point represented
by 2001. This is calculated by taking the location and slope of a function representing the
quantity of X in terms of the price of Y and putting that data into the standard elasticity
equation. Accordingly, EpXY = (Py/X)(dQx/dPy) = (Py/X)(1/slope) = 10/400)[1/(–1/50)] = –
5/4. The graph below illustrates this situation, but it is an unusual graph which can not be
interpreted as a typical demand curve since the price of the vertical axis is not for the product
on the horizontal axis.
Py
12
14
300 400
Quantity of X
18. Wheat and rice are perfect substitutes for Smith, and her indifference curves are shown as the
heavy downward-sloping 45° lines in the diagram. The lighter downward-sloping straight
lines, B1_B4, are the budget constraints that correspond to four arbitrarily chosen prices of
wheat, namely, $12/lb, $4/lb, $2/lb, and $1.50/lb, respectively. The first two of these prices
exceed the price of rice, so Smith ends up spending all of her food budget on rice. Bundle A
denotes the optimum purchase of wheat when the price of wheat is $12/lb (budget constraint
B1); and bundles C, D, and F are the corresponding bundles for the remaining prices (budget
constraints B2, B3, and B4, respectively). As noted, the amount of wheat in both A and C is
zero. Once the price of wheat falls below the price of rice, Smith does best to spend all of her
food budget on wheat. When wheat costs $2/lb, for example, she will buy
($24/wk)/($2/lb)=12 lbs/wk (bundle D on B3); and at $1.50/lb, she will buy 16 lbs/wk
(bundle F on B4). The heavy line labeled PCC is Smith's price-consumption curve.
Rice (lbs/wk)
18
16
14
12
PCC
10
8
AC
6
4
B1
2
0
B4
B3
B2
2
4
6
8
F
D
10
12
14
16
18
20
Wheat (lbs/wk)
To construct Smith's demand curve for wheat, we can retrieve the price-quantity pairs
from her PCC and plot them in a separate diagram, just as before. But an even easier way
is available in this particular case. It is to note that her behavior may be summarized by
the following purchase rule: when the price of wheat, PW, is below the price of rice, she
will buy $24/PW pounds of wheat, and when PW is above the price of rice, she will buy
no wheat at all. The demand curve that corresponds to this purchase rule is plotted as the
heavy line in the diagram below
22
P ($/lb)
W
Demand curve for wheat
6
5
4
Price of rice =
3
2
1.5
1
0
19.
D
Wheat (lbs/wk)
4
8
12
16
20
24
.
Rice (lbs/wk)
12
PCC
10
8
6
4
2
0
24/9
2
24/5
24/3
Wheat (lbs/wk)
24/2
3 4 5
Price of Wheat ($/lb)
D
9
8
7
6
5
4
3
2
D
1
Wheat (lbs/wk)
0
1
2
3
4
5
6
7
20. a) The new policy represents a decline in the price of cappuccino by less than 20% (the
nominal price, including the $.50 for the milk, declines by exactly 20% but the implicit cost of the
effort of buying the milk separately must now be added to the nominal price), accompanied by a
quantity increase of 60%. It follows that the absolute value of the price elasticity of demand for
cappuccino is greater than 3. So false.
20. b) The policy has the effect of making milk more valuable to those users who supply their
own milk to receive the discount. At a given price of milk, the quantity demanded will rise,
and hence total revenue will rise, no matter what the value of the price elasticity of demand
for milk. So false.