EconS 301 – Intermediate Microeconomics
Study Guide for the Final Exam
Material: Chapters 12, 13, 14 and 17 from Besanko and Braeutigam.
This study guide provides a short summary of the main topics we have been discussing in class. You
should be confident in all of them before the exam, and know how to apply them to specific exercises.
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You can find additional practice in the handouts posted for the weekly Review Sessions (they
contain detailed answers to all exercises).
CHAPTER 12 – Capturing surplus
1. First-degree price discrimination. Perfect price discrimination.
a. Price=marginal cost.
b. Subscription fee=Consumer surplus.
2. Second-degree price discrimination (Quantity discounts).
a. Recall the exercise we did in class about block pricing (a form of quantity discount,
where you pay p1 for the first Q1 units, and p2 for the remaining units from Q1 to Q2).
b. Learning-by-doing 12.3 and your lecture notes.
3. How to identify the nonlinear outlay schedule: total expenditure divided over Q. It is nonlinear
because of the quantity discount.
4. Third-degree price discrimination: setting different price for different market segments.
a. Example in class: railroad transportation offering their services to coal and grain
producers.
b. Each producer has a different demand curve (and as a consequence a different MR
curve). Determining profit-maximizing prices in this context is equivalent to two
different monopoly exercises, each for a different MR function.
c. Intertemporal price discrimination is a form of third degree price discrimination, where
the two market segments are defined temporarily, e.g., new i-pad.
d. Coupons and rebates. Another form of third-degree price discrimination.
5. Third-degree price discrimination with capacity constraints: not explained in class, but short and
easy in the textbook, pages 475-477 (especially including learning-by-doing exercise 12.6).
6. Bundling: only profitable for the firm if consumer’s willingness to pay for the different goods
conforming the bundle is negative correlated, i.e., individual 1 is the person with the highest
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willingness to pay for the monitor, but he is not the person with the highest willingness to pay for
the computer as well.
7. Advertising: a non-pricing technique that firms use in order to increase demand and thus raise
profits. Advertising is, however, costly. What level of advertising does a profit-maximizing firm
select?
a. We identified a condition similar to the IEPR in which the elasticity of demand to
advertising was playing a role. Refresh.
b. Also have a look at learning-by-doing exercise 12.7/
CHAPTER 13 – Market Structure and Competition
1. If firms compete in quantities: Cournot model.
a. First you write firm 1’s profit-maximization problem. Then you take first order
conditions with respect to q1. This will give you an expression of q1 as a function of q2.
This is what we referred as firm 1’s best response function. Draw it in a figure with q1 on
the vertical axis and q2 on the horizontal axis. What is the economic intuition behind its
negative slope?
b. Then you repeat the same process for firm 2, obtaining firm 2’s best response function.
Draw it in the same figure as you started above. You can rotate your piece of paper, it
will help.
c. The point where both of your best response functions cross determines the Cournot
equilibrium in this oligopoly.
2. Are firms maximizing their joint profits by acting like the Cournot model predicts? No! If they
collectively acted as a cartel, their profits would go up. How to show that? We did an example in
class. Think about it, you just need to write down a joint profit-maximization problem, taking first
order conditions with respect to q1 and q2. Then solve for both. In a context where both firms’
costs coincide each firm should produce half of the monopoly output in order to maximize the
cartel profits. Otherwise, the firm with the lowest costs should produce more. Sounds familiar?
You were right… like a multiplant monopolist. (Recall that a cartel operates as a multiplant
monopolist).
3. What if we have more than two firms? For simplicity, we assume that all firms were symmetric in
costs.
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a. We showed in class how to find every firm’s equilibrium output, the aggregate output,
and equilibrium price. We also analyzed how these results vary as we increase the
number of firms in the industry, N.
b. Cool result: when you increase N to infinity your oligopoly results exactly coincide with
the results we had under perfectly competitive markets. In contrast, when N is reduced to
N=1 (a single firm in the industry) our results coincide with those under monopoly.
4. We also identified an IEPR (like that under monopoly) for the Cournot model, for N firms. It was
almost the same!! Do you remember the difference? The right-hand side was multiplied by 1/N.
What if N=1? Of course, we would be back at the standard IEPR under monopoly.
5. If firms compete in prices: Bertrand model.
a. Every firm undercuts each other price because the increase in profits from stealing the
other firm’s customers exceeds the reduction in profits due to charging a marginally
lower price than its competitor.
b. But the other firm will then react undercutting its competitor, argument that can be
repeated until the point in which both firms are charging a price=MC, and hence no firm
has incentives to undercut each other’s price any further (otherwise it will be losing
money).
6. In the Cournot model of quantity competition and in the Bertrand model of price competition
firms choose either quantities or prices simultaneously. But what if firms compete sequentially?
Stackelberg model.
a. A leader and a follower.
b. The leader can anticipate that, regardless of its production in the first stage, the follower
will respond by selecting the output that maximizes its profits given the leader’s output.
In other words, the follower will respond using its best response function.
c. Given that, the leader can introduce the follower’s best response function into its own
profit-maximization problem. Then the leader takes first order conditions with respect to
q1. This gives you a number for q1 right away. Then you can plug that number into the
follower’s best response function in order to know the follower’s production level.
d. As a double check, the leader’s (follower’s) profits under the Stackelberg model of
sequential quantity competition should be larger (lower, respectively) than its profits
under the Cournot model of simultaneous quantity competition.
7. Dominant firm markets. A dominant firm with a competitive fringe of firms.
a. Recall the exercise we did in class.
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b. First you find the supply curve for the competitive fringe.
c. Then you find the dominant firm’s residual demand (subtracting the supply curve of the
competitive fringe).
d. Then you find the MR associated to this residual demand, making it equal to MC. This
gives you the output level for the dominant firm.
e. Map this output into the market (not residual) demand in order to determine the
equilibrium price.
f.
Then plug this price into the competitive fringe’s supply curve in order to find the output
supplied by the fringe.
8.
Product differentiation.
a. Horizontal versus Vertical differentiation.
b. Effect of horizontal differentiation on the demand curve.
c. Bertrand price competition with horizontally differentiated products.
i. Practice about this? Learning-by-doing 13.4. You had an exercise similar to this
in the review session corresponding to chapter 13.
9. Monopolistic competition.
a. Many firms, but all selling products which are horizontally differentiated. Examples:
restaurants in a large metropolitan area.
b. In the short run every individual firm can make profits, but not in the long run. Firms’
entry reduces the demand of customers to restaurant X until the point in which it makes
no profits.
CHAPTER 14 – Game Theory and Strategic Behavior
1. Games as representations of strategic situations, where an agent’s action affects other players’
payoff. “No man is an island.”
2. When players act simultaneously, we represent their interaction in a matrix. Within every cell, the
payoff on the left-hand side denotes the payoff accruing to the row player, while the payoff on the
right-hand side denotes the payoff accruing to the column player.
3. How can we predict the way in which a particular game will be played? In simultaneous-move
games we can use the Nash equilibrium solution concept.
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a. First, concentrate only on the row player. If the column player chose the action
represented in the first column, what is the best response for the row player? In order to
answer that question, cover the second column, so you focus your attention to the first
column alone. Within the first column, you should only pay attention to the first
component of every pair of payoffs, since that number is the one corresponding to the
row player’s payoff. Underline the highest one of the two.
b. Now repeat this process but covering the first column. This allows you to determine what
the row player’s best response is to the column player choosing the action represented in
the second row.
c. Second, put yourself in the shoes of the column player. If the row player were to choose
the action represented in the first row, what is the column player’s best response? You
can answer that question by covering the second row with your hand, so you only pay
attention to the payoffs in the first row. In particular, you just have to look at the second
component within every cell. What is the highest? This is the column player’s best
response to the row player’s choosing the action in the first row.
d. Repeat the process, but now covering the first row. This helps you determine which the
column’s player best response is to the row player choosing the action represented in the
second row.
e. Is there any cell in the matrix where both payoffs are underlined? This is the Nash
equilibrium of your simultaneous-move game.
f.
You can find one or more Nash equilibria. What if I don’t find any? (See point 7 below).
4. Prisoner’s Dilemma.
a. Every prisoner has individual incentives to defect (by confessing to the police), but they
both agree that they could be collectively better off if they both didn’t confess. That is,
there is a conflict between individual and group incentives.
5. Dominant strategy:
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a. A strategy that is selected by a player regardless of the action chosen by his opponent.
b. Example: confess in the prisoner’s dilemma game gives you a higher payoff than not
confess, both when your opponent confesses and when he does not. Hence, confess
constitutes a dominant strategy for you.
6. Dominated strategy:
a. A strategy that is never selected by a player regardless of the action chosen by his
opponent.
b. Example: do not confess gives you a lower payoff than confess, both with your opponent
confesses and when he does not. Hence, do not confess is dominated by confess.
c. In relatively large games with three or more rows and three or more columns, starting by
deleting dominated strategies is usually very convenient, since it allows you to focus on
much more reduced game.
7. What if you use the methodology described above to find the set of Nash equilibria in a game,
and you don’t find any?
a. Then it means that players don’t want their actions to be predictable, so they are exploited
by their opponent. Example: penalty kicks in soccer.
b. In order to maintain the suspense, players do not choose the same strategy 100% of the
times, but instead randomize among their available actions.
c. How to find the precise randomization pattern of every player?
• First, make a player indifferent between choosing each of his/her available
actions, by doing EUA(Left)=EUA(Right) for player A. This should depend upon
the probability with which player B randomizes. For simplicity, denote p as the
probability that the row player chooses the action in the first row, and 1-p the
probability that he selects the action in the second row. Similarly, let q denote the
probability that the column player chooses the action in the first column, and 1-q
the probability that he selects the action in the second column. Hence,
EUA(Left)=EUA(Right) for player A should depend on q. Solve for q to find the
probability with which player B randomizes.
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• Second, make player B indifferent between his two available actions,
EUB(Left)=EUB(Right). This equality should depend upon p. Solve for p to find
the probability with which the row player randomizes.
8. So far the equilibrium prediction of the Prisoner’s Dilemma game is pretty sad: both players
confess, and they end up many years in jail. Can we modify some environmental conditions in
which the game is played in order to avoid that unfortunate outcome?
a. Yes, repeated the game a sufficient number of times.
b. Players play a grim-trigger strategy (a tit-for-tat strategy would also work): I start
cooperating but revert to defection thereafter –punishing you— if I observe you defected
in the previous period (or revert to defection as long as I observe you previously defected
in the tit-for-tat strategy).
c. Which elements help sustain cooperation along time?
• Players’ patience: they care about future payoffs. If they didn’t they would defect
today.
• Cheating is easy to detect, so that the gains from teaching are short-lived.
• The one-time gain from cheating is relatively small.
9. Sequential-move games.
a. Represented in a game tree form.
b. How to predict the way in which rational players behave in this type of games? By using
backward induction.
c. Start from the last player called to move, and determine which best action is given that
the game reached the point where he/she is called to move. Mark the branch of the tree
that he/she would choose in order to keep track of your results.
d. Given your results for the last movers in the game, determine which the best action that
the player moving before him is, anticipating the best response of the players acting after
him.
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e. Continue until you reach the root of the tree, where the first mover is called to move. By
now you should have identified an equilibrium path that determines how the game
progresses at every stage: the first mover starts by choosing X, the second mover
responds to such action by selecting Y, etc.
CHAPTER 17 – Externalities and Public goods
1. A negative externality arises when an agent’s actions impose a negative effect on the well-being
of other agents, beyond the effects transmitted by changes in prices.
a. Example: a firm emitting pollution to the atmosphere, rivers, etc.
2. The equilibrium occurs at the point where demand=supply, where supply reflects the MPC from
the activity that generates the externality.
3. The social optimum, however, occurs at the point where demand=MSC, where MSC embodies
both the MPC and the MEC that the polluter imposes on other agents not directly involved in the
production activities of the firm.
4. Too many units of pollution are hence provided at equilibrium, relative to the social optimum.
5. How can we restore efficiency?
a. By imposing emission standards, obliging firms to produce no more than Q* units of
pollution.
b. By setting emission fees, whereby the polluter pays a tax equal to P*-Ps (Recall the
figure).
c. You went over a relatively long exercise with the TA last week (based on the learningby-doing exercise 17.2). This is important…
6. Why does a policy declaring pollution illegal reduce social welfare?
a. In short, because the socially optimal amount of pollution is not zero. It would only be
zero if the MEC was super high.
7. Common property resources.
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a. Resources that every agent can have access to. Example: fishing grounds, forests, certain
mineral reservoirs, aquifers, etc.
b. In class we examined the example of a freeway where the decision of an additional driver
to enter causes a negative externality on current drivers: their driving time increases
because of congestion. The new driver, however, does not take into account the external
effect that he imposes on current drivers, i.e., he does not internalize the effect of the
externality.
c. How to restore efficiency? By setting a toll equal to the MEC that the new driver imposes
on current drivers at the socially optimal number of cars: segment BE in the peak period,
or segment MN in the off-peak period (see your lecture notes and figure 17.5).
8. Positive externalities:
a. In this case an agent’s action produces a positive effect on the well-being of others.
Example: vaccination program, research and development, etc.
b. The agent producing the positive externality does not take into account the MEB that his
actions causes, producing too few units of it relative to the social optimum. The
equilibrium is determined by setting MPB (reflecting market demand) equal to the supply
curve (MC). The socially efficient amount is determined, instead, by setting MSB
(embodying both MPB and MEB) equal to the MC.
c. How to restore efficiency? Through a subsidy program that pays the agent producing the
positive externality a subsidy equal to Ps-P* (which intuitively measures the extent of the
MEB that his action causes, if he were to exactly produce the socially optimal amount).
9. Property rights and the Coase theorem.
a. If agents can costlessly bargain over the amount of the externality, then a socially
efficient amount of the externality will be produced, regardless of how property rights are
assigned.
b. Steel producer (upstream) and Fishing farm (downstream). It doesn’t matter who owns
the river, the amount of pollution will be socially efficient.
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c. Caveat: bargaining must be costless, which is only applicable to situations involving few
agents.
10. Public goods.
a. Rival vs. Nonrival goods.
b. Exclusive vs. Nonexclusive goods.
c. Combining all of the above in a very simple table (lecture notes).
d. How can we determine the efficient amount of public good to be provided?
i. First, sum the individuals’ willingness to pay for the public good (their inverse
demand curves) vertically. This is what we refer as the MSB from the public
good.
ii. Then draw MSB, with Q on the horizontal axis and prices on the vertical axis.
MSB should have a kink. Find it.
iii. Then set MSB equal to the MC from providing additional units of the public
good. Which of the three segments of the MSB curve I should use? Be careful.
The figure will help you in that.
Good luck!! This course prepared you for all elective courses in Econ pretty well. I am not kidding. This
course gave you the tools that you will be using later on in all other courses. Now let the fun begin!!
If you are interested in Environmental Economics…………….. EconS 330. (Fall)
If you are interested in Strategy and Game Theory…………….. EconS 424. (Fall)
If you are interested in Industrial Organization …………….. EconS 425. (Spring).
If you are interested in Public Finance………………….. EconS 322 (Spring).
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