Download Answers to Homework #2

Homework 2: Demand
1.
ANSWERS
The market demand curve is the horizontal summation of the individual demand
curves. The graph of market demand shows the relation between each price and
the sum of individual quantities. Because price elasticities of demand may vary
by individual, the price elasticity of demand is likely to be greater than some
individual price elasticities and less than others.
Individual brands compete with other brands. If the two brands are similar, a
small change in the price of one good will encourage many consumers to switch
to the other brand. Because substitutes are readily available, the quantity
response to a change in one brand’s price is more elastic than the quantity
response for all brands. Thus, the demand for Head skis is more elastic than the
demand for downhill skis.
2.
3.
a)
Books are a normal good since his consumption of books increases with
income. Coffee is a normal or neutral good since consumption of coffee
did not fall when income increased.
b)
Books and coffee are both normal goods since his response to a decline
in purchasing power is to decrease consumption of both goods.
The price of food doubles from $2 to $4, so arc elasticity should be used as it is a
large price change:
 P1  P2

Q

 2
EP  

 P   Q1  Q2

 2





We know that E P = -1, P1 = 2, P2 = 4;  P = 2, and Q1 = 5000. We need to solve
for Q2. Given the Ep = -1, and the formula above, we can write:
3(Q2 – 5000) = - 2 [(Q2/2) + 2500)]
Thus, 3Q2 – 15000 = -Q2 – 5000
4Q2 = 10000
Q2 = 2,500
4.
a.
The data only allows us to look at 50-cent changes in price. Computing
arc elasticities would be best. At I = $20,000:
Q P  1,000  900  0.75 
 

  0.16 from P = 0.50 to 1.00.
P Q  0.50  1.00  950 
 900  800  1.25 
EP  

  0.29 from P = 1.00 to 1.50.
 1.00  1.50  850 
EP 
At I = $30,000:
 1,500  1, 000   0.75 
EP  

  0.46 from
 0.50  1.00   1,300 
P = 0.50 to 1.00.
 1,100  900   1.25 
EP  

  0.50 from
 1.00  1.50   1, 000 
P = 1.00 to 1.50.
Therefore, demand is inelastic. However, demand is less inelastic at
higher income levels.
b.
Income
P = 1.50
P = 1.00
P = 0.50
30,000
20,000
Hamburgers
800
900
1000
1100
1500
5.
If the household does not change its consumption of gasoline, it will be
unaffected by the tax-rebate program, because in this case the household pays
0.10*500=$50 in taxes and receives $50 as an annual tax rebate. The two effects
would cancel each other out. To the extent that the household reduces its gas
consumption through substitution, it must be better off. The new budget line
(price change plus rebate) will pass through the old consumption point of 500
gallons of gasoline, and any now affordable bundle which contains less gasoline
must be on a higher indifference curve. The household will not choose any
bundle with more gasoline because these bundles are all inside the old budget
line, and hence are inferior to the bundle with 500 gallons of gas.
6.
We know that the indifference curves for perfect substitutes will be straight lines.
In this case, the consumer will always purchase the cheaper of the two goods. If
the price of orange juice is less than that of apple juice, the consumer will
purchase only orange juice and the price consumption curve will be on the
“orange juice axis” of the graph. If apple juice is cheaper, the consumer will
purchase only apple juice and the price consumption curve will be on the “apple
juice axis”. If the two goods have the same price, the consumer will be indifferent
between the two; the price consumption curve will coincide with the indifference
curve.
Apple Juice
PA  PO
PA  PO
E
PA  PO
U
F
Orange Juice
Assuming that the price of orange juice is less than the price of apple juice, so
that the consumer is buying orange juice, the consumer will maximize her utility
by consuming only orange juice. As the level of income varies, only the amount
of orange juice varies. Thus, the income consumption curve will be the “orange
juice axis”.
Apple Juice
Budget
Constraint
Income
Consumption
Curve
U1
U2
U3
Orange Juice
7.
a.
Toll
12
10
8
Consumer
Surplus
6
P = 12 – 2Q
4
2
Crossings
1
8.
2
3
4
5
6
7
b.
At a price of zero, the quantity demanded would be 6.
c.
The consumer surplus with no toll is equal to (0.5)(6)(12) = 36. Consumer
surplus with a 36 toll is equal to (0.5)(3)(6) = 9. Therefore, the loss of
consumer surplus is $27.
Vera is consuming under the influence of a positive network externality. When
she hears that there are limited software choices that are compatible with the
Linux operating system, she decides to go with Windows (inherently more
valuable). If she had not been interested in acquiring much software, she may
have gone with Linux. In the future, however, there may be a bandwagon effect
the other way, in that as more people use Linux, manufacturers might introduce
more software that is compatible with the Linux operating system. As the Linux
based software section at the local computer store gets larger and larger, this
prompts more consumers to purchase Linux. Eventually, the Windows section
shrinks as the Linux section becomes larger and larger.