Download Solutions Homework 2 - Trinity College Dublin

EC2010-Intermediate Economics
Microeconomics Module
Lecturer: Martín Paredes
Trinity College Dublin
Department of Economics
Hilary Term 2007
SOLUTIONS FOR ASSIGNMENT # 2
1. Chapter 2, Problem # 2.12
a) More elastic in the long run as the theatre owner can increase space or add
another 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 price. However if the price remains high for a long time they will
consider giving up the habit as it becomes too expensive.
2. Chapter 2, Problem # 2.14
a) Since the two goods are rather close substitutes for each other, you would
expect that the demand for Tylenol would go up if the price of Advil increases
and vice versa. Therefore, the cross price elasticity will be positive.
b) Similar to part (a). Although VCRs and DVD players are not very close
substitutes, if the price of VCRs were to go up substantially, potential buyers
would probably decide to pay a little bit more and get the higher-end DVD
player. Similarly if the latter becomes expensive, some consumers will not be
able to afford it and will switch to the VCR instead. The elasticity will be
positive.
c) Since the two usually go together, a sharp increase in the price of one will lead
to a decline in the demand for the other, and the cross-price elasticity will be
negative.
3. Chapter 2, Problem # 2.16
We know that along a linear demand curve
P
 Q , P  b  
Q
Using the given information this implies
.05


.5  b 

 10, 000, 000 
b  100, 000, 000
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Plugging this result into a demand equation using the known price and quantity
then implies
Q d  A  bP
10, 000, 000  A  100, 000, 000(.05)
A  15, 000, 000
So a demand equation that fits this information is given by
Qd  15,000,000  100,000,000 P
Graphically, the demand curve looks like
P
0.15
Q
15,000,000
4. Chapter 2, Problem # 2.17
a) Butter has some reasonably close substitutes such as margarine or cheese, while
eggs have no immediate substitutes. Therefore we would expect the demand
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 fixed dates on
which to be in Washington and would be prepared to pay more to ensure that
he flies on the day of his choosing. Therefore, demand for vacation trips is likely
to be more elastic (i.e. the price elasticity will be more negative) than the
demand for trips by your congressman.
c) As discussed in the chapter, market level elasticities tend to be lower (less
negative) than the elasticity of a particular brand. Thus, expect the demand for
Tropicana to be more elastic than the demand for generic orange juice.
5. Chapter 2, Problem # 2.18
First, consider each demand curve in its “inverse” form: long run demand is P = 15
– 0.5Q, and short run demand is P = 30 – 2Q. Thus, the slope of the long run
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demand is –0.5, which is closer to zero than that of the short run demand, –2.
Thus, long run demand is flatter. 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.
Consider, for instance a price of $10. Quantity demanded is equal in both the long
and short runs at P = 10. However, consider increasing the price to, say, $15.
Although this will reduce quantity demanded in the short run by a little, it would
reduce quantity demanded all the way to zero in the long run.
6. Chapter 3, Problem # 3.2
The first figure below shows Jimmy’s utility function for hotdogs. You can see that
the point at which H = 5 corresponds to the flat portion of the utility function, i.e.
the point at which the marginal utility of hotdogs is zero, and beyond which the
marginal utility is negative. Alternatively using the second graph it is clear that
the point H = 5 is when the marginal utility intersects the x-axis, and beyond
which it is negative. Both graphs tell you that to maximize his utility Jimmy
should only consume 5 hotdogs and not more.
To answer this question algebraically, you should first recognize from the
marginal utility function that Jimmy has a diminishing marginal utility of
hotdogs. Therefore the point at which he should stop consuming hotdogs is the
point at which MU H  0, or 10  2H  0. This gives H = 5.
U(H) = 10H – H2
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MUH = 10 – 2H
7. Chapter 3, Problem # 3.5
a) Three indifference curves corresponding to U = 2, 5 and 10 are shown in the
figure. The direction of increasing utility is down and to the right.
U=2
U=5
U=10
Increasing
utility
b) Note the negative sign for MUy. This means that an increase in the consumption
of y would decrease the consumer’s utility. This violates the basic assumption
that more is better for this utility function.
8. Chapter 3, Problem # 3.6
Indifference curves corresponding to U = 2 are shown for both Julie and Toni in
the graph below. Notice that the indifference curves are parallel everywhere –
indeed, MRSx,y = 1 for both Julie and Toni, for all values of x and y. Toni’s
indifference curve for the utility level UToni = 2 is the same as Julie’s indifference
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curve for the utility level UJulie = 4. So whenever Julie ranks bundle A higher than
bundle B, Toni would have the same ranking, and vice-versa. So Julie and Toni
will have the same ordinal ranking of bundles of x and y. (Julie will associate each
bundle with a higher utility level than Toni will, but that is a cardinal ranking.)
UToni = 2
UJulie = 2
9. Chapter 3, Problem # 3.10
In the following pictures, U2 > U1.
a)
Jelly
4
2
U1
U2
1
2
Peanut Butter
b)
Jelly
U1
U2
Peanut Butter
5
c)
U1
Jelly
U2
Peanut Butter
d)
Jelly
U1
U2
2
1
2
4
Peanut Butter
10. Chapter 3, Problem # 3.12
a) Yes, the “more is better” assumption is satisfied for both goods since both
marginal utilities are always positive.
b) The marginal utility of x remains constant at 3 for all values of x.
c) MRS x , y  3
d) The MRS x , y remains constant moving along the indifference curve.
e) & f)
See figure below
Y
U1 U2
X
11. Chapter 3, Problem # 3.14
a) Yes, the “more is better” assumption is satisfied for both goods since both
marginal utilities are always positive.
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b) The marginal utility of x remains constant as the consumer buys more x.
y 1
c) MRS x , y 
x
d) As the consumer substitutes x for y , the MRS x , y will diminish.
Y
e) & f)
See figure below. The indifference curves intersect the x-axis, since it is
possible that U > 0 even if y = 0.
20
18
16
U2
14
12
10 U1
8
6
4
2
0
0
5
10
15
20
25
30
35
X
12. Chapter 3, Problem # 3.15
a) Yes, the “more is better” assumption is satisfied for both goods since both
marginal utilities are always positive.
b) The marginal utility of x diminishes as the consumer buys more x .
.4( y 0.6 / x 0.6 ) 0.4 y
c) MRS x , y 

.6( x 0.4 / y 0.4 ) 0.6 x
d) As the consumer substitutes x for y , the MRS x , y will diminish.
See figure below. The indifference curves do not intersect either axis.
160
140
U2
120
100
Y
e) & f)
80
U1
60
40
20
0
0
5
10
15
20
25
30
35
X
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