EconS 301 – Intermediate Microeconomics with Calculus
Homework #0 – ANSWER KEY
Exercise #1: Exercise 2.18 from Besanko and Braeutigam
a) When the price of gasoline goes up, it becomes more expensive to drive a private automobile;
because private automobiles and taxis are substitutes, the demand for taxi service should increase
(shift to the right). On the other hand, when the average speed of a trip by automobile increases,
commuters are more likely to use their cars instead of public transportation; the demand for taxi
service should shift to the left. On the supply side, a higher price of gasoline increases to cost of
providing taxi service; the supply curve for taxi service should shift to the left.
b) Substituting G = 4 and E = 30 into equations for the supply and demand curves we have:
Qs = 200 – 30 (4) + 100P
Qd = 1,000 + 50 (4) – 4 (30) - 400P
Qs = 200 – 120 + 100P
Qd = 1000 + 200 – 120 – 400P
Qd = 1,080 – 400P
Qs = 80 + 100P
Solving equation Qd = Qs we have P = 2, Q = 280:
80 + 100P = 1,080 – 400P
500P = 1,000
P* = 2
Q = 1,080 – 400 (2)
Q* = 280
Supply and demand curves are graphed below.
c) In equilibrium Qd = Qs, solve for P, allowing the other variables to remain unknown:
200 - 30G + 100P = 1000 + 50G - 4E - 400P
500P = 800 + 80G – 4E
P = 8/5 + 4/25G - 1/125E
.
The equilibrium taxi fare goes up as gasoline price increases (P and G are the same sign) and
goes down when it private automobiles can travel faster (P and E are opposite signs).
Exercise 2.19 from Besanko and Braeutigam
a) Since the two goods are rather close substitutes for each other, you would expect that the
demand for Tylenol would go up if the price of Advil increases and vice versa. Therefore, the
cross price elasticity will be positive (price increase results in demand increase for the other
product).
b) Similar to part (a). Although VCRs and DVD players are not very close substitutes, if the
price of VCRs were to go up substantially, potential buyers would probably decide to pay a little
bit more and get the higher-end DVD player. Similarly if the latter becomes expensive, some
consumers will not be able to afford it and will switch to the VCR instead. The elasticity will be
positive.
c) Since the two usually go together, a sharp increase in the price of one will lead to a decline in
the demand for the other, and the cross-price elasticity will be negative (price increase results in
demand decrease for the other product).
Exercise #2:
a) Set the equations equal to solve for Q:
3+0.2𝑄𝑄 = 120 − 0.7𝑄𝑄
0.9𝑄𝑄 = 117
Q* = 130
Substitute the Q you found into either of the equations above to solve for p (the answers should
be the same here):
𝑝𝑝=120−0.7(130)
𝑝𝑝=3+0.2(130)
𝑝𝑝=120−91
𝑝𝑝=3+26
P* = 29
p* = 29
b) Calculate the area of the triangle made by the supply and demand curves. Above the
equilibrium price is consumer surplus, below is producer surplus:
Consumer:
(120 – 29) x ½ x 130 = 5,915
Producer:
(29 – 3) x ½ x 130 = 1,690
c) If 𝑝𝑝 is given, substitute it into the demand equation:
36 = 120−0.7𝑄𝑄𝑑𝑑
0.7𝑄𝑄𝑑𝑑 = 84
𝑄𝑄𝑑𝑑 = 120
d) For consumer surplus, calculate the triangle above the price line and below the demand curve
as before:
(120–36) x ½ x 120 = 5,040
For producer surplus, calculate the area under the price line and above the supply curve, then
subtract the area of deadweight loss (see DWL calculation in part e).
((36–3) x ½ x 120)–35 = 1,945
e) Deadweight loss is the area of the triangle made by the change in quantity and change in price
(Q* - Q`) x (p` - p*) x ½:
(130–120) x (36–29) x ½ = 35
f) First, find the amount of surplus quantity is available. This is where we substitute the price
floor amount into the supply equation, and subtract the amount purchased by consumers:
36 = 3 + 0.2𝑄𝑄𝑠𝑠
33 = 0.2𝑄𝑄𝑠𝑠
𝑄𝑄𝑠𝑠 = 165
Surplus = 𝑄𝑄𝑠𝑠 – 𝑄𝑄𝑑𝑑 = 165 – 120 = 45
Money spent = 36 cents x 45 million litres = 0.36 x 45,000,000 = €16,200,000
Price
120
Consumer surplus
100
80
60
p’
Deadweight loss
S
40
Price floor
p*
20
D
Producer
surplus
0
20
40
60
80
100
120
Q`
140
Q*
160
180
200
Quantity