Econ 101
Answers to Homework 5
Fall 2005
1.
(a) In perfect Competition P=MC, so PPC=2.
QPC=80.
1
CS  (14  2)80  6  80  480
2
PS=0
DWL = 0
(b) QM=40, PM=8.
1
CS  (14  8)40  3  40  120
2
PS  (8  2)40  6  40  240
1
DWL  (8  2)(80  40)  3  40  120
2
(c) P(last unit)=MC, so P(last unit)=2. Q1=80.
CS=0
1
PS  (14  2)80  6  80  480
2
DWL=0
2.
(i) Third-degree
(ii) Second-degree
(iii) First-degree
3.
(a) MR1=MR2=MC
 24  2Q1  6,  2Q1  18  Q1  9. So P1=15
Also  12  Q2  6,  Q2  6. So P2=9
(b) T  1   2  TR1  TC1  TR2  TC2  ( P1  ATC)Q1  ( P2  ATC)Q2
So T  (15  6)9  (9  6)6  81  18  99
1
(c) Solving the demand equations for price: P1  24  Q1 and P2  12  Q2 .
2
So the horizontal intercepts for the two markets are different. For a price
higher than 12, only consumers in the 1st market demand the good. So for
1
price higher than 12, the aggregate demand function is given by P1  24  Q1
(just the demand of the 1st market). For price lower than 12, aggregate
demand is given by the sum of the two separated demands: Q=Q1+Q2 . So
1
Q=48-3P or P  16  Q .
3
24
24
12
12
24
24
P1  24  Q1
48
For P>12, P1  24  Q1
1
For P<12, P  16  Q
3
1
P2  12  Q2
2
2
2
(d) MR=MC. So 16  Q  6  Q  10  Q  15. So 3P=33, so P=11.
3
3
(e)   TR  TC  ( P  ATC )Q  (11  6)15  75 . So 75<99=Profits in the case
where the monopolist could charge different prices.
4.
The firm can choose A1, A2, P1, P2 to make the buyers separate themselves.
The high-demand consumers will choose the T1 pricing schedule and the lowdemand consumers will choose the T2 pricing schedule.
The following graph is helpful to understand why the types have an incentive to
separate themselves:
Tariff
T2
T1
P2
p1
A1
A2
Q2
Q1
Q
2
[Monopolistically Competitive Market]
5.
a. With the demand curve P=100-Q, we have MR=100-2Q as Marginal Revenue.
b.
MC
$
100
4
MR
50
D
Q
c. From MR=MC, we have 100-2Q=4+10Q, or Q=8.
d. When Q=8, the price will be P=100-8=92. Total Revenue is 92*8=736. Total
Cost is 320+4*8+5*8*8=672. So the profit=736-672=64.
e. With positive profit, there will be more beer firms due to entry. Then the
demand curve for the firm shifts to the left until the profit goes down to zero. ATC
Curve meets Demand Curve tangentially at the quantity where MR=MC.
3
$
MC
ATC
4
MR
D
Q
[Game Theory]
6.
a. For Player 1, there’s no dominant strategy. For Player 2, Down is dominant
strategy as it gives more payoff regardless of player 1’s action.
b. For player 1, Up is dominant strategy. There’s no dominant strategy for
player 2.
c. Up is dominant strategy for Player 1, and Up is dominant strategy for player 2.
d. Up is dominant strategy for player 1, and Center is dominant strategy for
player 2.
7.
c) (Up, Up) is the chosen outcome, since this is the combination that represents
the dominant strategy for each player.
d) (Up, Center) is the chosen outcome, as this is the combination that represents
the dominant strategy for each player.
4
8.
a.
OfficeMin
WorstBuy
Regular
Discount
Regular
(500, 500)
(800, 200)
Discount
(200, 800)
(300, 300)
b. (i), (ii) False. Discount is the dominant strategy for WorstBuy, so WorstBuy
definitely will choose Discount.
(iii) True.
(iv) Discount is the dominant strategy for OfficeMin.
c. (iv) (Discount, Discount) is the chosen outcome for this game since Discount
is the dominant strategy for each firm.
9.
A. d) If x>4, A will choose Down regardless of B’s choice.
B. a) If y<3, B will choose Left definitely.
C. d) If x=5, Down is the dominant strategy. If A chooses Down, then B’s payoff
is 3 with Left, while y with Right. When y>4, (Down, Right) becomes a Nash
Equilibrium.
5