Student Number :
Student Name
ECON 212 - Winter 2017 - Section 002 - Quiz 1 - Solution
1.) Suppose the demand for ECON 212 course is given by equation Q = 90 − 15 P , where P
denotes the price of taking one course of ECON 212.
1.a.) (3 points) Calculate the price elasticity of demand for ECON 212 given P = 2.
First, calculate the quantity demanded: Q = 90 − 15 P = 90 − 15 (2) = 90 − 30 = 60
εQ,P =
dQ P
dP Q
=
d(90−15 P ) P
dP
Q
= (−15)
2
60
30
= − 60
= − 12
1.b.) (1 point) Is the demand elastic or inelastic?
Since εQ,P = − 12 > −1, or |εQ,P | = − 12 =
1
2
< 1, the demand is inelastic.
1.c.) (2 points) At what price is the demand elastic? Hint: Calculate the unit price elasticity
of demand.
εQ,P = −1 occurs at the mid-point of the demand curve. The mid-point of the demand
curve is a2 , where a is the intercept of the demand curve.
Thus,
a
2
=
90
2
= 45 = Qunit−elastic .
Then set Qunit−elastic = 90 − 15 Punit−elastic
=⇒ 45 = 90 − 15 Punit−elastic
=⇒ −45 = −15 Punit−elastic
=⇒ Punit−elastic =
−45
−15
=3
The results from Parts (1.a.) and (1.b.) tell us that the demand is inelastic when P = 2,
which is less than 3. Hence, the demand is elastic if P > 3.
1
1.d.) Suppose Mary consumes good x and good y, and her utility function is U (x, y) = x y 1/3 .
2.a.) (2 points) Does Mary believe that consuming more of good x and more of good y
gives her more utility?
Marginal utility of x = M Ux =
∂U (x, y)
∂x
=
∂(x y 1/3 )
∂x
= y 1/3 > 0
Marginal utility of y = M Uy =
∂U (x, y)
∂y
=
∂(x y 1/3 )
∂y
=
1
3
x y −2/3 > 0
Since M Ux > 0 and M Uy > 0, Mary will be better off (having more utility) if she
consumes more of good x and more of good y.
2.b.) (2 points) What is the marginal rate of substitution of good x for good y (M RSx, y )?
M RSx, y =
M Ux
M Uy
=
1
3
y 1/3
x y −2/3
=
3 y 1/3 y 2/3
x
2
=3
y
x