ECON 212 - Microeconomic Theory I - Winter 2015 - Section 2 - Quiz 1 - Solution
Question 1 (10 points) Market research has revealed the following information about the market for socks. The demand schedule can be represented by the equation Qd = 800 − 150p, where
Qd is the demanded quantity and p the price. The supply schedule can be represented by the
equation Qs = 700 + 350p, where Qs is the quantity supplied.
a) (5 points) Calculate the equilibrium price and quantity in the market for socks. (Show your
work, use fractions rather than decimals). Draw the demand and supply curves, and indicate
clearly the equilibrium price and quantity.
At equilibrium Qd = Qs . Then
800 − 150p = 700 + 350p
100 = 500P
1
p∗ = .
5
At p∗ we have Q∗ = 800 − 150p∗ = 700 + 350p∗ = 700 + 350(1/5) = 770. Graphically,
p
p=
p∗ =
16
3
1
5
Qd = 800 Qd , Qs
Qs = 700
p = −2
Figure 1: Equilibrium
Q∗ = 770
b) (5 points) What is the price elasticity of demand?.
The price elasticity of demand is given by
εQd ,p
∂Qd P
= −150
=
∂p Qd
P
Qd
Question 2 (10 points) For the following description of preferences, write a utility function that
could represent the preferences. Draw an indifference curve for that utility function, and label all
relevant points, including the level of utility associated with that particular indifference curve.
a) (5 points) A consumer is always willing to exchange one hour of swimming (S) for 45 minutes
of running (R).
A utility function that would describe the preferences is
U(S, R) = S +
4
60
R = S + R,
45
3
where S denotes hours of swimming and R denotes minutes of running. Notice that the consumer exchange 1hr S for 0.75 hr of running.
S
(0, 4) Ū = 4
(0, 2) Ū = 2
(1.5, 0)
(3, 0)
Figure 2: Indifference curve with perfect substitutes.
R
With these preferences, MUS = 1 and MUR =
The slope of the indifference curve is −(3/4).
60
45
= 34 . Thus, the MRSR,S = (4/3)/1 = −4/3.
Other representations for this preferences are valid, for example:
U(S, R) = 45S + 60R
3
U(S, R) = S + R
4
U(S, R) = 3S + 4R
All of them have the marginal rate of substitution given by MRSS,R = −4/3. Thus, all of them
have the same slope −(4/3).
b) (5 points) A consumer builds ultrasound computers and always requires two screens and one
system unit.
The utility function is given by
U(S, U) = min {2U, S} ,
where S denotes screens and U denotes system units.
S
4
Ū = 4
2
Ū = 2
12
Figure 3: Indifference curve with perfect complements.
Other representations for this preferences are valid, for example:
U(S, U) = min {4U, 2S}
1
U(S, U) = min U, S .
2
U