Economics 102
Principles of Microeconomics
Introduction to Economics
Juha Seppälä
Fall 2003
Solutions to Midterm
1
The Economics of Baby-Sitters
A temporarily high birth rate in the year 2005 leads to opposite effects on the price of babysitting services
in the years 2010 and 2020. In the year 2010, there are more 5-year olds who need sitters, so the demand
for babysitting services rises. The result is a higher price for babysitting services in 2010. However, in the
year 2020, the increased number of 15-year olds shifts the supply of babysitting services to the right. The
result is a decline in the price of babysitting services.
2
Elasticity and Its Application
Pharmaceutical drugs have an inelastic demand, and computers have an elastic demand. Suppose that
technological advance doubles the supply of both goods (that is, the quantity supplied at each price is twice
what it was).
(a) In both markets, the increase in supply reduces the equilibrium price and increases the equilibrium
quantity.
(b) In the market for pharmaceutical drugs, with inelastic demand, the increase in supply leads to a
relatively large decline in the price and not much of an increase in quantity.
(c) In the market for computers, with elastic demand, the increase in supply leads to a relatively large
increase in quantity and not much of a decline in price.
(d) In the market for pharmaceutical drugs, since demand is inelastic, the percentage increase in quantity
will be less than the percentage decrease in price, so total consumer spending will decline. In contrast,
since demand is elastic in the market for computers, the percentage increase in quantity will be greater
than the percentage decrease in price, so total consumer spending will increase.
3
Subsidies and Welfare
Suppose that the demand and supply functions as the function of market price, P , are
QD (P ) = a − bP
QS (P ) = c + dP,
respectively.
(a) To solve for the equilibrium price, set supply and demand equal to each other, or
QD (P ) = QS (P )
a − bP = c + dP
=⇒
=⇒
a − c = (b + d)P
a−c
.
P =
b+d
=⇒
Hence, the equilibrium quantity is just going to be
QD (P ) = a − bP a−c
=a−b
b+d
ab − bc
=a−
b+d
ab + ad − ab + bc
=
b+d
ad + bc
=
.
b+d
(b) b and d must positive (downward-sloping demand curve and upward-sloping supply curve). Also, a > c
because the equilibrium price must be positive. Finally, ad + bc > 0 because the equilibrium quantity
must be positive. Notice that this means that at least a > 0.
(c) Suppose that the government pays the consumers a subsidy of S for each unit they purchase. Therefore,
the effective price for the buyers is going to be P − S and the new demand function is
QD (P − S) = a − b(P − S) = a + bS − bP.
Solve for the equilibrium price in an economy with subsidy,
QD (P − S) = QS (P )
=⇒
a + bS − bP = c + dP
a + bS − c = (b + d)P
a + bS − c
.
P =
b+d
In other words, the sellers are going to receive a price
P =
a + bS − c
bS
= P +
> P
b+d
b+d
2
=⇒
=⇒
in the equilibrium which is stricly more than what they obtained in the equilibrium without subsidies.
Also, the buyers are going to pay
P − S =
a + bS − c − bS − dS
a − c − dS
a + bS − c
dS
−S =
=
= P −
< P
b+d
b+d
b+d
b+d
in the equilibrium which is stricly less than what they paid in the equilibrium without subsidies.
Finally, the equilibrium quantity with subsidies
QD (P − S) = a − b(P − S)
a − c − dS
=a−b
b+d
ab − bc − bdS
=a−
b+d
ab + ad − ab + bc + bdS
=
b+d
ad + bc + bdS
=
b+d
is going to be
ad + bc + bdS
bdS
= Q +
> Q ,
b+d
b+d
which is strictly more than in the equilibrium with subsidies.
Q =
(d) To summarize, with subsidies the sellers are receiving
P =
a + bS − c
,
b+d
the buyers are paying
P − S =
a − c − dS
,
b+d
and the quantity traded is going to be
Q =
ad + bc + bdS
.
b+d
Producers and consumers are better off, the government is worse off.
4
Quotas and Welfare
See Figure 9-7 in Mankiw (2004, p. 186).
3