ECF5040 Industry Economics Assignment 1 solution / answers
1 Proving efficiency
Draw a linear demand curve P = D(Q) (downward sloping) and a linear supply curve
P = S(Q) (upward sloping) in the space of quantity (x axis) and price (y axis). Both
should have an intersection with the y axis at a positive value. This market represents
the total market supply and total market demand for a good produced in a perfectly
competitive industry.
1. Label the market clearing price and quantity Pc, Qc.
2. Show clearly what is Consumer Surplus and what is Producer Surplus on the graph.
3. Recall the definition of Efficiency: a market outcome is efficient if we cannot find an
allocation of inputs or outputs which would increase the well-being of at least one
participant in the market without decreasing the well-being of others.
4. Show what would be the consumer surplus and producer surplus at quantity, Qg,
such that Qg > Qc, and at price Pg = D(Qg). Please show these on the graph.
5. Is consumer surplus under 4) larger or smaller than under 2)?
6. Is producer surplus under 4) larger or smaller than under 2)?
7. Show what would be the consumer surplus and producer surplus at quantity, Qf > 0,
such that Qf < Qc, and at price Pf = D(Qf ). Please show these on the graph.
8. Is consumer surplus under 7) larger or smaller than under 2)?
9. Is producer surplus under 7) larger or smaller than under 2)?
10. What can you conclude about the efficiency properties of the perfectly competitive
market equilibrium? Why?
2 Government as the sole provider of electricity
The government is the exclusive seller of electricity in the country. Demand is characterized
by: Q=50-2P. The total cost curve of the government electricity production is TC
(Q)=100+10Q
1. What is the average cost curve AC(Q)?
2. What is the marginal cost curve MC(Q)=dTC(Q)
dQ
3. What price should the government set to achieve the efficient allocation of electricity?
Please derive your answer in detail and draw a graph.
4. If the government wants to maximize its profit, what price should it set? Please
derive your answer in detail and draw a graph.
5. What is the size of the efficiency loss in moving from 3) to 4)? Show on a graph
and give the number.
6. What is the efficiency loss derived in point 5 called? What does “loss” refer to in
its name?
3 Network externalities
Imagine you live in a small town. In this small town every house is very far from the
next one, and so it is quite time costly to go visit anyone. You would like to be able to
keep in touch with as many people as possible, even when you do not meet in person.
There are two landline providers in the town (we are in pre internet and pre mobile phone
era). Every person in the town has a landline phone. Company A has 300 subscribers
and Company B has 700. Unfortunately neither of the two is very sophisticated and once
you are in one of the networks, you can only make calls within that network. You just
moved to the town and need to choose which Company to subscribe with. There is no
price consideration for you, it will be a gift to you (this is because you are the 1001st
inhabitant of the town and the mayor decided to celebrate surpassing the 1000 size by
gifting you the subscription).
• Which company do you choose? Why? You can only choose one.
Suppose a few decades later you still live in the town. We have the same two landline
provider companies, with the same number of subscribers, 300 and 700. (It is not possible
to switch providers, so it is actually the same people that are the subscribers that were
the subsribers a few decades ago.) The companies have become more sophisticated, and
figured out how to make calls across networks. So no matter which network you are in,
you can call anyone in the town now.
Whichever company is your landline provider gifts their landline subscribers a tablet. The
tablets look the same and feel the same to the user, but applications and games available
are different on the two tablets (an app or a game is not compatible between the two
tablets for technical reasons). Suppose people in this town like games and apps quite
a bit. Games and apps are complementary goods to the tablet. The next town has a
very high concentration of software engineers, and they are the ones writing the apps
and games for the two companies. Engineers choose which company to write for based
on the expected number of users (they get paid based on how many people use their
apps/games). Notice that sophistication of the companies is still low, so these are all
individual apps and games, you cannot play with someone in the network of the company
you chose.
• If you could go back in time, would you change which company to choose A or B
considering now the softwares and apps?
• Why or why not?
• Why does the size of the network matter here even if for the apps and games you
do not interact with the people in the network?
• What do you think network externality means? How is it related to complementary
goods?
4 Oligopoly 1
When we are looking at markets in which there is more than one seller, but not a very
large number of sellers, the action of one company (what quantity they bring to the market
or what price they sell their good for) changes profits of another company on the market.
For this reason, when companies make their decisions, they take account of the other
company’s/companies’ expected action, and in general expected strategy. In equilibrium
it has to be true that all companies choose a strategy which is the best response to the
other companies’ strategy. (This is review from the prerequisite course.)
1. Suppose there are two firms on the market, they produce homogeneous goods and
their cost curves have the exact same shape, with constant marginal costs. Their
is a linear market demand curve for this homogeneous good. The firms can quickly
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adjust production quantities, so they choose prices to compete on, not quantities.
They set their prices simultaneously and they face no capacity constraints.
2. If MC=c for both firms, what happens if firm 1 sets a higher price than firm 2?
Does firm 1 want to change the price they set? Why?
3. What happens if firm 1 sets a lower price than firm 2? Does firm 1 want to change
the price they set? Why? What about firm 2?
4. Draw the best response function of firm 1 to the price of firm 2 (p1*(p2)). Please
draw it in the space of p2 (x axis) p1 (y axis). Add the marginal cost function to
the graph.
5. Add (p2*(p1)) to the graph.
6. Find the equilibrium.
7. What are firms’ profit levels compared to a world with not two firms on the market,
but a very high number and perfect competition as market structure?
8. This is called the Bertrand trap. There are several ways to avoid the Bertrand trap:
• differentiated product oligopoly price competition
• dynamic competition on prices (where firms interact in more than one period)
• capacity constrains (as we saw in class with the electricity price graph during
the Chicago polar vortex week)
• asymmetric marginal costs
9. Assume now that MC1 < MC2 and answer questions 2)-7) from above applied to
the asymmetric marginal cost case.
5 Oligopoly 2
Read the setup part of Q4 again. Now instead of firms setting prices simultaneously, they
will simultaneously set quantities. The market demand is characterized by P(Q) = a−bQ,
both firms have TC(q) = cq, and Q = q1 + q2.
1. Please write down firm 1’s profit function, as a function of q1 and q2.
2. What’s the first order condition of firm 1 with respect to q1?
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3. Rearrange this first order condition to obtain firm 1’s best response function to firm
2’s output, i.e. q∗
1(q2)?
4. What is q∗
2(q1)? Remember, the firms are identical, so their problems are symmetric.
5. In equilibrium, neither of the two firms want to change their quantity decision by
deviating to produce a lower or higher quantity. What condition characterizes the
equilibrium? We are looking for two equations here with two unknowns.
6. Solve this system of two equations for q∗
1 and q∗
2.
7. What’s the profit level of both firms in equilibrium? π∗
1, π∗
2?