Final
Examination
FALL 2015
ECON 302
D100 (LU)
MICROECONOMIC THEORY II:
STRATEGIC BEHAVIOR
Dec e mbe r 17, 2015
IN ST RUCTIONS & FOR MAT
DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO DO SO.
1. On the cover of the answer booklet, write your name, your SFU ID number
and the day of your tutorial (Tu or Th).
2. Simple (non-graphing, non-programmable) calculators are permitted.
3. Use a pen (not pencil) for regrade eligibility. No other aids are allowed.
4. Label the axes and curves in any graph you draw.
5. Make sure that your solutions are legible and, when asked to show your
work, that the order of your reasoning is clear.
6. Remaining students must stay seated for the last ten (10) minutes.
7. At the end of the exam, stay seated and quiet while material is being
collected. Hand in the answer booklet. You may keep this questionnaire.
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This exam is out of one hundred and twenty-five (125) points.
There is no choice of questions.
The point value of each question is shown in brackets.
DURATION: 169 minutes
1. (40 points) Consider a market with the following characteristics:
- Two firms produce a good at a constant marginal cost of 12, with no fixed cost.
- The good may be of high (H) or low (L) quality. It is indivisible.
- Firm A’s goods are of type H with probability 0.8, and type L with probability 0.2.
- Firm B’s goods are of type H with probability 0.6, and type L with probability 0.4.
- No one (buyer or seller) knows the quality of the good at the time of purchase.
- However, consumers can tell if a good is from firm A or firm B.
- Consumers are divided into two types, rich (R) and poor (P). Let 𝑤 denote wealth. Both
R and P have utility:
o 𝑤 if they do not own the good,
o 𝑤 + 𝑣𝐻 if they own at least one unit of the type H good (regardless of whether
they own any type L good), and
o 𝑤 + 𝑣𝐿 if they do not own any type H good and own at least one unit of the type
L good.
- For type R, 𝑣𝐻 = 50 and 𝑣𝐿 = 40. The proportion of rich consumers is 60%.
- For type P, 𝑣𝐻 = 35 and 𝑣𝐿 = 30.
- The firms cannot tell apart the types of consumers.
- There is no time-discounting.
a) [4] Suppose that the firms do not sell any unit at a loss. Explain why no consumer would
purchase more than one unit of the good (either at the same time, or by acquiring a
second unit after finding out the quality of the first unit purchased).
b) i.
ii.
[7] In general, what is second-degree price discrimination? How can it increase a
firm’s profit compared to the no-price-discrimination situation? Why,
nevertheless, does it typically not allow the firm to achieve its first-best profit?
[4] Suppose, in the above setting, that no consumer buys more than one unit of the
good. Can the firms engage in second-degree price discrimination? If so, how?
(You may describe what would be done in the monopoly case.) If not, why not?
For the remainder of this problem, assume that consumers are not allowed to purchase more
than one unit of the good.
c) [6] Let 𝑤0 be a consumer’s initial wealth. Write down the consumer’s expected utility
from buying one unit from firm A at price 𝑃𝐴 (in terms of 𝑤0 , 𝑣𝐻 , 𝑣𝐿 and 𝑃𝐴 ). Write down
the analogous expression for buying one unit from firm B at price 𝑃𝐵 . Use your answers
to derive each consumer type’s value for each firm’s product.
d) [7] What is adverse selection? Is it a problem in this setting? Why?
e) [12] Suppose firms choose price simultaneously and seek to maximize profit. Assume
that consumers: i) buy when indifferent between buying and not buying, and ii) buy from
each firm with probability 50% when buying from either firm is equally appealing (and is
better than not buying).
For every firm B price 𝑃𝐵 ∈ (0, ∞), find firm A’s best response(s). Show your work.
Hint: Use your work from part c to think carefully about how consumers would respond
to each pair of prices.
2. (48 points) A firm hires Tracy for a project. Tracy is one of two types (𝑤 denotes wage):
- Enthusiastic (E): always chooses effort 𝑒 = 1, has utility √𝑤 and outside option $44,100;
- Bored (B): chooses 𝑒 = 0 or 𝑒 = 1, has utility √𝑤 − 20𝑒 and outside option $40,000
with 𝑒 = 0.
The project generates revenue $90,000 if successful, $70,000 if OK, and $0 if abandoned.
If 𝑒 = 0, the project is successful with probability 0.25 and OK with probability 0.75.
If 𝑒 = 1, the project is successful with probability 0.75 and OK with probability 0.25.
If Tracy quits to take the outside option, the project is abandoned.
a) [10] What is the firm’s first-best expected profit if Tracy is of type E? Of type B? Justify
your answers by exhibiting the contracts used by the firm and by showing that they are
indeed first-best (make sure to justify the form they take).
For the rest of this problem, suppose that 𝑒 is not observable or verifiable by the firm.
b) [14] Find the second-best contract offered by the firm if Tracy is of type B. Justify your
answer by writing down the firm’s maximization problem, explaining the steps for
carrying out the maximization, and explicitly showing any relevant comparisons.
For the rest of this problem, suppose that, in addition to 𝑒, Tracy’s type is also not observable
by the firm, and denote the probability that Tracy is of type E as 𝑝 ∈ (0,1).
c) [9] Find the second-best contract offered by the firm as a function of 𝑝 ∈ (0,1). Justify
your answer.
d) [6] Find the type(s) of workers that benefit(s) from the firm’s inability to observe type,
compared to the case where type is observable. How does your answer depend on 𝑝?
Explain the economic intuition for this result.
Now suppose that the firm can observe signs of enthusiasm from Tracy before offering a
contract.
e) [5] Assume that type E automatically shows (and cannot hide) signs of enthusiasm, and
that type B can fake them at a monetary cost of 𝑐 > 0. For what values of 𝑐, if any, does
there exist a separating equilibrium? Justify your answer.
f) [4] Assume instead that type E can choose whether to exhibit signs of enthusiasm (at no
cost), while type B can still fake them at a monetary cost of 𝑐 > 0. For what values of 𝑐,
if any, does there exist a separating equilibrium? Justify your answer.
3. (25 points) Consider a world with two countries and a single good. The production of each
unit of the good emits one ton of CO2, and each ton of CO2 causes a negative externality of
$60 on the world (thus $30 on each country). For simplicity, assume that the externality is
entirely immediate.
In each country and in every period, the demand for the good is Q = 10,000 – 10P, and the
supply for the good is Q = 20P – 2,000. There is no international trade.
Assume that each country maximizes its net social surplus (i.e. consumer surplus plus
producer surplus plus government revenue minus negative externality) and has discount
factor 𝛿 ∈ (0,1). Countries are assumed to be infinitely lived.
a) [7] For each country, find the market quantity, the efficient quantity from a global
perspective (Qeff), and the quantity that maximizes the country’s own net social surplus
(Q*).
b) [4] If a country tries to achieve a reduction in emissions through assigning a limited
number of permits for producers, is it desirable that these permits be tradable? Explain
your answer, with respect to both surplus and Pareto efficiency.
c) [4] If Q* tradable permits are assigned, what will be the market price of a permit? Justify
your answer by briefly explaining how the demand for permits is derived.
Suppose the countries sign a treaty stating that each would limit its production to Qeff every
period. However, this treaty cannot be enforced by the courts (e.g. there is no way to levy
fines against a country that violates the treaty). Assume that the countries observe each
other’s quantity at the end of every period, and that, in each period, they choose either Q* or
Qeff.
d) [10] Find the range of 𝛿 ∈ (0,1) for which there exists a subgame-perfect equilibrium
where the countries will abide by the treaty in every period. Carefully justify your answer.
4. (6 points) Briefly explain how international trade can significantly reduce the impact of
carbon pricing (whether through a tax or permits) on global carbon emissions, if carbon
pricing is adopted by only one country (or a small group of countries). Address both
production-based and consumption-based carbon pricing.
5. (6 points) Briefly explain the significance of the von Neumann—Morgenstern Expected
Utility Theorem for game theory. (You do not need to formally state the theorem, but you
should describe the broad content of the theorem and explain why it is important.)