Download Solutions for HW #5

Solutions for HW #3
Economics 301
Chapter 4 Problems
7.
(a) P = $3  Q = 7000  Revenue = P*Q = $21,000
(b)
E
Q, P

Q P
3
 3 
 1000
    .429
P Q
7
 7000 
(c) Yes, since the price elasticity of demand is below one in absolute value, they
can increase revenue by increasing price (since quantity will fall by less than price
rises).
(d) Since substitution opportunities are greater, demand for the bridge will
become more elastic.
10.
First we need to determine the inverse slope of the demand curve (which will be
constant since we are told that the demand curve is linear).
inverse slope 
Q Q2  Q1

P P2  P1
P1  $400 Q1  300
P2  $600 Q2  280
Thus,
Q Q2  Q1 280  300
20
1




P P2  P1 600  400
200
10
When P1  $400 , Q1  300
E
Q, P

Q P
1  400 
 
  .133
P Q
10  300 
When P1  $600 , Q1  280
E
11.

Q, P
Q P
1  600 
 
  .214
P Q
10  280 
P = 100 – Q
If P = $30  Q = 70  Revenue = P*Q = $2100
E
Q, P

Q P
 30 
 1 *    .429
P Q
 70 
Since demand is inelastic at the current price, they can increase revenue by
increasing price.
13.
(a) Q = 300  P = 100 cents / $1.00 (Be careful here; even though the elasticity
itself is a unit-less measure, the demand curve is based on a price measured in
cents, so you need to maintain this as the unit of measurement when calculating
the elasticity).
 Revenue = P*Q = 30,000 cents (or $300)
(b)
E
Q, P

Q P
 100 
 15 * 
  5
P Q
 300 
(c) Since demand is elastic, he can increase revenue by reducing price.
(d) Maximum revenue occurs where
P
  1   1  15 
Q, P
Q

Q  15P
E
Substituting this into the equation for the demand curve Q = 1800 – 15P and
solving yields
P *  60 cents
16.
(a) Complements  cross-price elasticity < 0
(b) Complements  cross-price elasticity < 0
(c) Substitutes  cross-price elasticity > 0
Chapter 5 Problem
4. The maximum membership fee you would be willing to pay is equal to the consumer
surplus that you receive from being able to rent all the movies you want at a price of $4
per rental. Rearranging the demand curve to express quantity as a function of price yields
Q = 10 - (1/2)P
Thus, at a price of $4, you will rent 8 videos. Since the vertical intercept for this demand
curve is 20, the consumer surplus received from renting 8 videos at a price of $4 is
CS = ½*(20 – 4)*8 = $64
Additional Problems
1.
Since the budget line shifts inward, consumption of both goods will decline if
both are normal.
2.
False. By definition, an increase in price increases consumption of a Giffen good.
Thus, demand curves for Giffen goods will be upward sloping.
3.
True. If X is normal good, then the income effect of a price increase will reduce
demand for good X. Since the substitution effect is always away from the good
whose price has risen, the total effect of the price increase will reduce demand for
good X.
4.
False. By definition, an increase in income will reduce consumption of an inferior
good. Thus, Engel curves for inferior goods will be downward sloping.
5.
True. By definition, an increase in income will increase consumption of a normal
good. Thus, Engel curves for normal goods will be upward sloping.
6.
Please consult your class notes for the correct diagram.
7.
Please consult your class notes for the correct diagram.
8.
True. Giffen goods are the subset of inferior goods for which the income effect is
larger than the substitution effect.
9.
False. An inferior good for whom the substitution effect is larger than the income
effect will not be Giffen.
10.
First, we must find the optimal consumption bundles at each of the three prices.
When the price of X is $2, we obtain the tangency / optimality condition
Y 2

X 1
which can be rewritten as 2X = Y. Substituting this into the budget constraint
2X + Y = 36,
and solving, we obtain an optimal bundle of X = 9, Y = 18.
When the price of X is $4, we obtain the tangency / optimality condition
Y 4

X 1
which can be rewritten as 4X = Y. Substituting this into the budget constraint
4X + Y = 36
and solving, we obtain an optimal bundle of X = 4.5, Y = 18.
When the price of X is $6, we obtain the tangency / optimality condition
Y 6

X 1
which can be rewritten as 6X = Y. Substituting this into the budget constraint
6X + Y = 36
and solving, we obtain an optimal bundle of X = 3, Y = 18.
This leads to the following table, which can be used to plot a demand curve.
11.
Price of X
Quantity of X
$2
$4
$6
9 units
4.5 units
3 units
Solving for the vertical intercepts (choke prices) for each demand curve, we
obtain
Kubik: P = 50
Black: P = 100
Thus, for P greater than or equal to 100, market demand is zero. For P between 50
and 100, market demand is equal to Professor Black’s individual demand curve,
and for P below 50, market demand is equal to the (horizontal) sum of both
professor’s individual demand curves. Thus, market demand is given by
0
for


Q   100  P
for
125  (3 / 2) P for

P  100
50  P  100
P  50
12.
Since the income elasticity of demand for the product is negative, the projected
increase in consumer incomes will decrease the demand for the product. Thus,
you should order less PVC pipe.
13.
This is just a thinly disguised version of the ``shipping the good apples out''
paradox that we discussed in class. Here the per-unit cost (which is independent
of which good is purchased) is the cost of the babysitter. Adding this constant cost
to the price of both goods reduces the relative price of the more expensive good
for the Andersons, but not for the Smiths. Since both couples are sufficiently
wealthy that their expenditure on movies and plays is a negligible fraction of their
total expenditures, there will be no income effect and the total effect of the price
differential will be determined by the substitution effect (which always causes
consumers to substitute away from the good whose relative price has risen). As a
result, all other things equal, the Andersons will go to relatively more plays and
fewer movies than the Smiths.
14.
To illustrate why this is so, consider the case where the price of good X rises
while the price of good Y remains the same.
Y
D
A
U2
U0
U1
C
E
B
X
In the above diagram, budget line AB represents the prices faced by the consumer
in the base year, while budget line AC represents the prices faced by the
consumer in the following year (after the price of good X has risen). Recall the
CPI cost of living adjustment gives consumers an income transfer that allows
them to purchase their original (pre-inflation) bundle at the new (higher) prices
(represented by the budget line DE in the diagram). This over compensates
consumers in the sense that it allows them to achieve a higher level of utility than
prior to the price increase (U2 vs. U0).