ECON 100 Tutorial: Week 10
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Question 1
Classify each of the following markets as highly contestable,
moderately contestable, slightly contestable or non-contestable. If it
depends on the circumstances, explain in what way.
Key characteristic of a contestable market:
Firms are influenced by the threat of new entrants into a
market.
(a) satellite broadcasting
highly / moderately / slightly / non
(b) hospital cleaning services
highly / moderately / slightly / non
(c) banking on a uni campus
highly / moderately / slightly / non
(d) piped gas supply
highly / moderately / slightly / non
(e) parcels delivery
highly / moderately / slightly / non
(f) siting for the Olympic games highly / moderately / slightly / non
(g) bus service to the area where you live
highly / mod./ slightly / non
Question 2
Why, under oligopoly, might a particular industry
be collusive at one time and yet highly price
competitive at another?
Because the market environment, or the firm’s
assessment of it, may well change.
For example, if just one firm in an oligopoly introduces a
price cut, the other firms may feel obliged to follow suit,
with the result that collusion breaks down. Alternatively,
a new firm may enter the market (e.g. a foreign
multinational), or costs may change, or rivals develop
new varieties of the product, etc.
Question 3
Explain under what conditions collusion is likely to
a) collapse
Collusion is likely to collapse in a single game, or
in a finite number of games.
b) be maintained, in a prisoners’ dilemma model
If the game is repeated and the players do not
know how many games are left (i.e. an “infinite”
number of games), collusion can continue
How do we know that collusion could be maintained in an “infinite” repeated
game? Let’s look at the following game:
We are going to play a card game in which groups of students will form teams. Each
team gets a pair of playing cards, one red card (Hearts or Diamonds) and one black
card (Clubs or Spades). The numbers or faces on the cards do not matter, just the
color.
Each team will be asked to play one of these cards by holding it to your chest (so we
can see that you have made your decision, but not what that decision is).
Your earnings are determined by the card that you play and by the card played by
your opposing team. If you play your red card, then your earnings in pounds will
increase by £2, and the earnings of the person matched with you will not change. If
you play your black card, your earnings do not change and the dollar earnings of your
opposing team go up by £3.
So,
If you each play your red card, you will each earn £2.
If you each play the black card, you will each earn £3.
If you play your black card and the other person plays his or her red card, then you
earn zero and the other person earns the £5. If you play red and the other person
plays black, you earn the £5, and the other person earns zero.
All earnings are hypothetical.
Here are the
payoffs, written as
a normal-form
game.
black
black
(£3, £3)
red
(£0, £5)
Red
Player ONE
First we’ll play one
round. Talk about
your strategies
quietly with your
teammates before
you make your
decision.
Player TWO
(£5, £0)
(£2, £2)
Player TWO
black
black
(£3, £3)
red
(£0, £5)
Red
Player ONE
Now we’ll move
the teams around,
so you have a new
opposing team.
Same rules.
Keep adding up
your winnings if
we play more than
one round.
(£5, £0)
(£2, £2)
Player TWO
black
black
(£3, £3)
red
(£0, £5)
Red
Player ONE
For a final round, let’s
have the two highestscoring teams play a
single game against
each other, and the
two lowest-scoring
teams play a single
game against each
other.
(£5, £0)
(£2, £2)
Question 4(a)
The following information
describes the demand schedule
for a unique type of apple.
This type of apple can only be
produced by two firms because
they own the land on which
these unique trees
spontaneously grow.
As a result, the marginal cost of
production is zero for these
duopolists, causing total
revenue to equal profit.
Price Quantity
per
of Boxes
Box (£)
12
11
10
9
8
7
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
45
50
55
60
Total
Revenue
(Profit)
0
55
100
135
160
175
180
175
160
135
100
55
0
Question 4(b)
If the market were
characterised by Bertrand
competition, what price and
quantity would be generated by
this market? Explain.
In a Bertrand competition
model, Competition reduces the
price until it equals marginal
cost (which is zero in this case),
therefore P = £0 and Q = 60.
(See Tutorial 9, Slides 14 and 15 for a
detailed explanation of why P = MC in
Bertrand competition.)
Price Quantity
per
of Boxes
Box (£)
12
11
10
9
8
7
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
45
50
55
60
Total
Revenue
(Profit)
0
55
100
135
160
175
180
175
160
135
100
55
0
Question 4(c)
If these two firms colluded and formed a cartel, what price
and quantity would be generated by this market?
These duopolists would behave as a
monopolist, produce at the level that
maximises profit, and agree to divide the
production levels and profit.
According to the table, Profit is
maximised at where P = £6, Q = 30 for
the market.
What is the level of profit generated by
the market?
Profit = £6 x 30 = £180.
And what is the level of profit generated
by each firm?
Each firm produces 15 units at £6 and
receives profit of £90 (half of the £180).
Price
Price
per
per
Box
Box (£)
(£)
Quantity
Quantity
of
of Boxes
Boxes
Total
Total
Revenue
Revenue
(Profit)
(Profit)
12
11
10
9
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
5
10
15
20
25
25
30
30
35
35
40
40
45
45
50
50
55
55
0
55
100
135
160
175
175
180
180
175
175
160
160
135
135
100
100
55
55
Question 4(d)
If one firm cheats and produces one additional
increment (five units) of production, what is the level of
profit generated by each firm?
When the two firms are colluding, they produce 15
units each, for a total output of 30 and a price of £6.
If the Cheating firm produces 5 more units, the total
output will be 35, which will cause the price to drop to
£5.
Price Quantity
Total
Cheating firm: 20 x £5 = £100
Other firm: 15 x £5 = £75
per Box
(£)
of Boxes
Revenue
(Profit)
6
5
30
35
180
175
Question 4(e)
If both firms cheat and each produces one
additional increment (five units) of production
(compared to the cooperative solution), what is the
level of profit generated by each firm?
Both firms have moved from 15 units to 20 units
each. Total output will be 40, which causes price to
drop to £4.
Each firm: 20 x £4 = £80.
Question 4(f)
If both firms are cheating and producing one additional increment of
output (five additional units compared to the cooperative solution), will
either firm choose to produce an additional increment (five more units)?
Why? What is the value of the Nash equilibrium in this duopoly market?
FIRM TWO
Produce 25
Produce 20
Produce 20
FIRM ONE
Price
Quantity
Total
No,
because
the profit
per Box of Boxes
Revenue
would
fall
for
the
(£)
(Profit)
cheater
to 25
12
0 x £3 = £75
0
which
the £80
11 is below
5
55
profit
part (e). 100
10 from10
9
15
Therefore,
the Nash135
8
20is each firm
160
equilibrium
7
25
175
producing
20 units (40
30
for6the market)
at a 180
price
5
35
175
of £4,
creating
£160
of
4
40
160
profit
and
3 for the
45 market135
each
2 duopolist
50 receives
100
£801 profit. 55
55
£80, £80
£75, £60
Produce 25
£60, £75
£50, £50
Question 4(g)
Compare the competitive equilibrium to the Nash
equilibrium. In which situation is society better off?
Explain.
The Nash equilibrium has a higher price
(£4 compared to £0) and a smaller quantity
(40 units compared to 60 units).
Society is better off with competitive equilibrium
(Bertrand equilibrium).
Question 4(h)
Describe what would happen to the price and
quantity in this market if an additional firm were
able to grow these unique apples.
(Do not attempt to calculate quantitative changes –
the direction of change is all that is required.)
The new Nash equilibrium would have a lower price
and a larger quantity. It would move toward the
competitive solution.
Question 4(i)
Use the data from the duopoly example above to fill in
the boxes of a prisoners' dilemma normal form game.
Place the value of the profits earned by each duopolist
in the appropriate boxes.
FIRM ONE
Payoffs are Revenue (PxQ) for each
firm.
Price is determined by the total
market quantity in the Table (part a).
Market Quantity is the sum of the
quantities of the two firms.
Example:
Firms 1 chooses Q = 15 and
Firm 2 chooses Q = 20.
Market Q = 15+20 = 35 units,
therefore Market P = £5
Payoff for each firms is PxQ
Firm 1: 15 x £5 = £75
Firm 2: 20 x £5 = £100
Price
per
Box (£)
Quantity
of Boxes
Total
Revenue
(Profit)
6
5
30
35
180
175
FIRM TWO
Question 4(i)
Use the data from the duopoly example above to fill in the boxes of a
prisoners' dilemma normal form game. Place the value of the profits
earned by each duopolist in the appropriate boxes.
FIRM TWO
collude (15)
collude (15)
cheat (20)
FIRM ONE
Payoffs are Revenue (PxQ) for each
firm.
Price is determined by the total
market quantity in the Table (part a).
Market Quantity is the sum of the
quantities of the two firms.
Example:
Firms 1 chooses Q = 15 and
Firm 2 chooses Q = 20.
Market Q = 15+20 = 35 units,
therefore Market P = £5
Payoff for each firms is PxQ
Firm 1: 15 x £5 = £75
Firm 2: 20 x £5 = £100
£90, £90
£100, £75
cheat (20)
£75, £100
£80, £80
Question 4(j)
What is the solution to this prisoners' dilemma? Explain.
FIRM TWO
collude (15)
cheat (20)
FIRM ONE
collude (15)
£90, £90
£100, £75
cheat (20)
£75, £100
£80, £80
The dominant
strategy for each is to
cheat and sell 20
units because each
firm’s profit is
greater when it sells
20 units regardless of
whether the other
firm sells 15 or 20
units.
Question 4(k)
What might the solution be if the participants were
able to repeat the "game?" Why? What simple
strategy might they use to maintain their cartel?
They might be able to maintain the cooperative
(monopoly) production level of 30 units and each
produce 15 units because if the game is repeated,
the participants can devise a penalty for cheating.
This is because if the game is repeated, the
participants can devise a penalty for cheating. The
simplest penalty is "tit-for-tat."
Question 5
An alternative to the Cournot model, where firms choose q’s,
is the Betrand model (see above), where firms choose p’s. Of
course firms can only have different p’s if they are selling
differentiated products.
Gasmi et al (J Econ & Man 1992) estimated the demand for
coke as
QC=58-4PC + 2PP where C=coke and P=pepsi.
If MC = AC = 5 then profits are given by
C=(PC-5)(58-4PC+2PP)
where the first bracket is per unit profit and the second
bracket is the number of units sold.
The slope of this profit function shows how C’s profits vary
with PC.
Multiply out the brackets in the profit function and then
apply the rule to get the slope. Hence show what C’s best
response function is (ie how Pc depends on Pp).
Question 5
We have:
QC=58-4PC + 2PP where C=coke and P=pepsi.
If MC = AC = 5 then profits are given by
C=(PC-AC)(QC)
C=(PC-5)(58-4PC+2PP)
We want to find the slope of the profit function, or take the
derivative of it.
Before we do that, we need to multiply out the brackets in
the profit function and then apply “the rule” to get the slope.
This will give us C’s best response function is (ie how Pc
depends on Pp).
C=(PC-5)(58-4PC+2PP)
C=58PC-4PC2+2PCPP-290+20PC-10PP
C=-4PC2+2PCPP+78PC-290-10PP
continued on next slide
Question 5
We left off with:
C=-4PC2+2PCPP+78PC-290-10PP
To find the slope of C, we are going to take the derivative
with respect to PC:
dC/dPC=-8PC+2PP+78
Profits are maximised when the slope is 0, so the next step is
to set dC/dPC equal to zero and solve for PC:
0=-8PC+2PP+78
8PC=2PP+78
PC=(2PP+78)/8
PC=PP/4+9.75
So, PC=PP/4+9.75 is C’s best response function to Pepsi’s price
choice.
Question 5 ctd.
They also estimate that the demand curve for pepsi was QP =
63.2 - 4PP + 1.6PC. Using the same approach derive the best
response for Pepsi.
We have:
QP = 63.2 - 4PP + 1.6PC where C=coke and P=pepsi.
If MC = AC = 5 then profits are given by
P=(PP-AC)(QP)
P=(PP-5)(63.2 - 4PP + 1.6PC)
Next, we’ll multiply out the brackets in the profit function and
then apply “the rule” to get the slope of the profit function.
This will show us what P’s best response function is (ie how PP
depends on PC).
P=(PP-5)(63.2 - 4PP + 1.6PC)
P=63.2PP-4PP2+1.6PCPP-316+20PP-8PC
P=-4PP2+1.6PCPP+83.2PP-316-8PC
continued on next slide
Question 5 ctd.
In the previous slide, we left off with:
P=-4PP2+1.6PCPP+83.2PP-316-8PC
To find the slope of P, we are going to take the
derivative with respect to PP:
dP/dPP=8PP+1.6PC+83.2
Profits are maximised when the slope is 0, so the next
step is to set dP/dPP equal to zero and solve for PP:
0=8PP+1.6PC+83.2
8PP=1.6PC+83.2
PP=(1.6PC+83.2)/8
PP=PC/5+10.4
So, PP=PC/5+10.4 is Pepsi’s best response function to
any price that Coke may choose.
Question 5 ctd.
Show what the equilibrium prices are.
In the previous slides, we found best response functions for each
firm:
PP=PC/4+9.75 and PC=PP/5+10.4
A Nash Equilibrium can be found by finding the intersection of
these two lines (i.e. where both players play their best response
strategy). To find this, we can plug the second function into the
first:
PP=(PP/5+10.4)/4+9.75
PP=(PP/5)/4+10.4/4+9.75
PP=PP/20+2.6+9.75
PP=PP/20+12.35
PP-PP/20=12.35
19PP/20=12.35
PP=12.35*20/19
PP=13
continued on next slide
Question 5 ctd.
Show what the equilibrium prices are (ctd).
In the previous slides, we found best response
functions for each firm and we found PP by plugging
one function into the other:
PP=PC/4+9.75 and PC=PP/5+10.4 and PP=13
Now, to find PC, we can plug PP=13 into PC=PP/5+10.4:
PC=PP/5+10.4
PC=13/5+10.4
PC=2.6+10.4
PC=13
So, the best response functions intersect at PC = 13 and
PP = 13
Have a nice Holiday!
(Also, don’t forget to start studying for Exam 2 (it’s on
24/01/2014) and check Moodle for the Week 11 worksheet.)