Economics 2022/23 – Group
assignment
Question 1
(a) Can you charge a different price to different segments? If yes, how? [5
marks]
It is possible to charge different prices to different segments. In particular,
third-degree price discrimination enables the monopoly to charge different prices or
set quantities for each segment. Given that each market has different demand
functions, where each segment is further divided by the time of the week, there will
be different optimal bundles of price and quantity choice for each demand function.
Furthermore, as MC=0, these bundles will differ. Thus, the monopoly can extract the
maximum amount of consumer surplus through price discrimination such that they
charge a higher price to those with higher consumer surplus and vice versa.
(b) Find the profit maximizing prices for Seniors and for the general public
both for peak and off-peak concerts. [10 marks]
Given 100 identical venues, the transformation of the demand function should not
change the optimal bundle of price and quantity for each market. Thus, in this case,
we will consider a single monopoly case in which we denote the optimal price as p*
and quantity q* of the monopoly.
As shown above, in (peak, general public) case, we see that the optimal quantity is
greater than the capacity. Intuitively, the monopoly has the incentive to raise the price
just enough that the demand will equal to the capacity of 1400. Therefore, the
monopoly will choose the optimal price and quantity as shown above.
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(c) Live Nation Entertainment has a contract with Pulito, a firm that cleans
the venues at the end of the concerts. Initially, Live Nation Entertainment
paid Pulito a fee of $3 per person for their services. How does your
answer to (b) change? [5 points]
With a $3 per person cleaning fee, the linear cost function for total cost will be equal
to TC=3Q. This function is added to each of the profit functions of (b).
Apart from the (peak, general public) case, we see that optimal quantity is reduced
compared to the case where there was no linear total cost. This makes sense because,
as they produce tickets, it incurs more costs, and therefore, the monopoly has the
incentive to reduce the quantity sold and increase the price instead.
For the over-capacity case, the optimal quantity is still above the capacity, and
therefore, the monopoly has the incentive to increase the price until the demand for
the concern equals the capacity, as it has done in part (a).
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(d) Upon renewal of the contract, the owner of Pulito argues it is increasingly
more expensive to clean venues with larger audiences. You agree to pay
Pulito 4Q2 for cleaning, where Q is the total number of people in a given
audience. What are the new profit maximising prices for Seniors and for
the general public for off-peak concerts?[10 marks]
With 4Q2 the total cost function is now TC=4Q2
With strictly convex total cost, i.e., increasing marginal cost, the negative effect of
increasing the quantity sold on profit is greater than the case of part (b), which
indicates that the firm is reluctant to increase the quantity sold. Thus, reducing the
quality and increasing the price significantly compared to the no marginal cost
optimal bundle is the ideal option to maximize profits.
*
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Question 2.
(a) If the families were to interact only once (compete on one day only), what
price would you expect to prevail for a gram of cocaine in New Jersey?
Explain your answer. [6 marks]
The competition on price indicates that the firms are in Bertrand's competition. We
use conventional Bertrand competition assumptions such that products and costs
functions for each firm are homogenous, the firms choose the prices simultaneously,
each firm has the perfect information about what other firms’ strategies are, no
transaction and search costs, and a firm that undercut the other firms will obtain 100%
of the market.
The price of a gram of cocaine in New Jersey will be equal to MC, i.e., P=MC=$50
per gram. Suppose all the other four firms are charging a monopoly price; the fifth
firm has the incentive to undercut the price by a small amount and collect the entire
market share. Given the strategy of the fifth firm and perfect information, the best
response for the four firms is to undercut the fifth firm by a tiny amount. Given the
best response of the other four firms, the fifth firm’s best response is to undercut theirs
undercutting-price by a small amount, and so forth. This undercutting continues until
the price is equal to the marginal cost. This is because if P > MC, then the other firm
has the incentive to undercut, and if P < MC, the firm is making a loss. Therefore, the
only Nash Equilibrium is all five firms setting the price equal to the marginal cost.
This is consistent with the Bertrand model with two firms.
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(b) Compute the price that would be charged for cocaine if the market were a
monopoly. How many grams of cocaine would the monopolist sell daily
and what profits would it make? [6 marks]
If the 5 firms worked as a monopoly instead of an oligopoly, the total quantity and
price would be the following:
* wrt: with respect to
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(c) Now, suppose the five families interact indefinitely. They wish to collude
to price cocaine at the monopoly level. Suppose families have a discount
factor of δ = 0.7. There is an understanding that if any family undercuts,
the rest will punish by reverting to the price set in (a) forever. Is collusion
sustainable amongst the five families? What is the maximum number of
families that could sustain collusion? [10 marks]
Based on the assumption that under collusion, each firm would split the profit evenly,
and each firm would get $140,000.
If a firm decides to cheat, the firm will decrease the price by ε (epsilon) amount, i.e., a
very small amount, and set the price equal to P - ε and earn very close to a monopoly
profit of $700,000 for a deviating period. After that, the grim trigger strategy by the
non-cheating firms resulted in π (profit) = 0 for all of the five firms onwards. Thus,
from one firm perspective, this can be illustrated as:
Thus, a firm has the incentive to remain in the collusion iff:
The left-hand side illustrates the perpetuity payoffs from colluding, and the right-hand
side shows the payoff when a firm deviates.
The answer illustrates the colluding condition such that if the discount factor is
greater than 0.8, i.e., if a firm is sufficiently patient, the collusion sustains.
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However, given the discount factor is δ=0.7, the collusion will not sustain, i.e., firms
are not patient enough to remain in the collusion.
The maximum number of families that can sustain collusion
A firm will remain in collusion iff:
This is the generalised colluding condition where n illustrates the number of firms
colluding. The 700k/n is the one-period payoff for a firm under the assumption that
monopoly profits will be distributed evenly under collusion with n firms.
Substituting δ and solving for n state that as long as the number of firms within the
collusion is under 3, the collusion will be sustained. This is because a one-period
payoff with collusion is large enough to sustain the collusion, but with more than
three firms, the payoff will not be large enough and incentivises cheating.
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(d) Imagine now there is a newcomer (Valletti family) whose marginal cost of
providing cocaine is $40 dollars. How do your answers to (a), (b), and (c)
change? Discuss in particular how collusion among asymmetric firms can
be orchestrated and sustained. [8 marks]
Changes to a:
Given that the Valletti family knows the other 5 firms can only undercut the prices as
low as P=MC=$50, the Valetti family would undercut by ε (very small) amount, i.e.,
setting the price equal to 50 - ε, and obtain 100% of the market,. This means that the 5
families would not make a profit and would likely exit the market, leaving the Valetti
family the only player left in the market.
Changes to b:
If the 6 firms act as a monopoly, the optimal monopoly P* and Q* would not change,
i.e., P=100, Q=14,000, π=$700,000. Whether a monopoly can be sustained or not
depends on the assumptions which we discuss below.
Changes to c:
Based on the assumption that under collusion, the 6 firms would split the quantity
evenly, the Valetti family would achieve the profit shown below:
Valetti family’s payoff for colluding and cheating given other players deploy grim
trigger strategy would be:
Thus, when the Valletti family cheats, they would earn greater profit in each of the
punishing periods, and therefore it is no credible threat for the Valletti family when
they cheat. The collusion would not sustain under any number of interactions.
However, it may be possible to collude among asymmetric firms; for example, the
Valletti family could share information about how they got a lower marginal cost of
$40, allowing other firms to have a marginal cost of $40. Under this assumption,
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collusion may be sustainable, with sufficiently patient firms, just as in the case of part
(c) in question 2.
Another possible solution is an uneven distribution of quantity or profit under
collusion. If the Valletti family is offered enough quantity distribution under
collusion, there may be some δ that collusion is more attractive than cheating such
that the collusion payoff is greater than the one in the punishment phase.
There is also a way to introduce a credible threat. Given that we are talking about the
Mafia in this scenario, the old-fashioned Mafia style of threatening to kill family
members if a firm chooses to cheat may reduce the punishment phase payoffs for
Valetti when they decide to deviate from collusion. The effectiveness of the threat
increases when transparency increases as it will make other firms easier to find out
when one firm cheats.
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Question 3
(a) Draw up the decision tree representing the choice facing your company.
Do you recommend to build the network or not? Why? [10 marks]
Assuming that if Outback Cables does not build, they receive revenue of 0.
Using backwards induction, when Outback Cables choose to ´build´, the Expected
Value (EV) after they built the network is:
EV (build, t = 2) = 320M * 0.5 + 140M * 0.5 = AUD$ 230M
Given that if Outback Cables choose to ´build´, the EV at a time period of 1 (before
building a network) is:
EV(build, t = 1) = 230M- 200M= AUD$ 30M
Where EV (build, t = 1) denotes the choice of Outback Cables at the time period of 1.
Given that EV(not build, t = 1) = 0 > 30M, Outback Cables should build the network.
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(b) Suppose that KangaTel must decide whether it wants to use the Outback
Cables network before you build your network. Thus, if it wants to use
your network it must tell you before you build the network. Will
KangaTel decide to use your network, or not? Will Outback Cables build
the network, or not? Explain your answer. [10 marks]
Payoff = (KangaTel, Outback Cables)
Assuming that if KangaTel does choose to ´not use´ the network, Outback cables will
still be able to generate the revenue as in the case of (a).
By backwards induction, when KangaTel chooses to use the network EVs for Outback
are:
EV (build, Outback) = 0.5*40M + 0.5*(-50M) = -5M
EV (not build, Outback) = 0 > -5M
So Outback Cables choose ´not build´ when KangaTel chooses to ´use´ the network
When KangaTel ‘does not use´, the same tree as part (a) and thus Outback Cables will
´build´.
Given the Outback Cables choice, KangaTel payoff will be indifferent, i.e. receives 0
in either case.
SPE: {Indifferent; not build if use ´build´, otherwise}.
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(c) Suppose that KangaTel only has to decide whether or not it wants to use
the Outback Cables network after it has seen whether pay-TV is
successful or unsuccessful. If it decides to use your network, it only has to
pay you AUD$100m after it makes its decision. Draw the game tree
representing the interaction between your firm and KangaTel. When, if
ever, will KangaTel want to use your network? Will you build the network
or not? Is your decision the same or different to your decision in part (b)?
Explain. [10 marks]
Payoff= (Outback, KangaTel)
By backwards induction, focus on KangaTel’s choice first. When Outback Cables
´build´ and ´success´, KangaTel’s EVs are:
Similarly, when Outback Cables ´Build´and ´fail´:
Thus, KangaTel choose to ´use´ network iff Outback Cables ´build´ and ´succeed´.
Given KangaTel’s choices, Outback’s EVs for choosing each choice will yield:
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Outback Cables does ´not build´.
SPE: {Not build; ´use´ if ´build´and ´succeed´, not use´ otherwise}
Difference between B and C:
For Outback Cables, as they are the first-mover, they decided not to invest regardless
of the choices KangaTel makes, given Outback Cables know KangaTel only enters
when the network is successful.
KangaTel, on the other hand, decided to use the network only when it saw Outback
succeed i.e, utilizing second-mover advantage. Whereas before, part (b), it was
indifferent when it was the first-mover.
(d) It is sometimes argued that regulation which improves competition can
reduce risky investment. Does your answer to this question confirm or
rebut this claim? Briefly explain why regulation might influence risky
investment. [10 marks]
The answer confirms the claim that regulation which improves competition can
reduce risky investments, assuming building a network by Outback Cables is a risky
investment. By itself, with no regulation, Outback Cables should and will build the
network, which leads to a risky investment.
However, Outback Cables choose not to build the network when KangaTel chooses
´use´ in the case of part (c), and Outback Cables will not invest in a risk asset
regardless of what KangaTel chooses in the case of part (b). The reluctance to invest
in the risky project was due to the increase in the competition introduced by the
regulation.
The reason why regulation influences risky investment is that it introduces
interdependence between the firms, and Outback Cables has to respond in a strategic
way, according to this newly-created environment by the regulation.
For example, in part (c), the competition introduced by the regulation made risky
investments unprofitable, and in part (d), KangaTel’s second-mover advantage made
Outback Cables not invest in the risky investment. Thus, regulation changes the best
response for firms and influences investment decisions.
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