Econ 2261B – Final Exam
Western University · Department of Economics · Bruno Salcedo · April 20th 2018
Read questions carefully. Answer all questions. Justify all your answers.
You have 120 minutes. Good luck!
1. [0 marks] What is your name? What is your student number?
2. [40 marks] There are two markets for a given commodity. The market demand in
each of these two markets is given by:
D1 (p1 ) = 60 − 3p1
and
D2 (p2 ) = 20 − p2 ,
respectively. All the firms have the same cost function. There are no fixed costs,
and the marginal cost is constant and equal to 5. Firms receive a subsidy of 2
dollars per unit sold.
For each of the following institutional arrangements, find the equilibrium price
paid by buyers and the quantity traded in each market, and determine the cost of
the subsidy.
(a) Both markets are competitive.
(b) Both markets are operated by a monopolist that can price discriminate by
setting a different price in each market.
(c) Both markets are operated by a monopolist that cannot price discriminate
across markets.
(d) Price discrimination is not possible, and there are two firms, j = 1, 2. Each
firm j chooses a quantity qj . Quantities are chosen simultaneously and independently. The market price is determined by the total inverse demand
function.
(e) There are two firms choosing quantities, and price discrimination is not pos-
sible. Firms choose quantities sequentially instead of simultaneously. Firm 1
chooses its quantity first. Firm 2 chooses its quantity after observing q1 .
3. [20 marks] The mechanism designer must allocate 10 identical objects. There is
no cost associated with allocating the objects. There are more than 10 individuals
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interested in receiving an object. Each individual i would like to receive at most
one object. The utility of individual i is given by
ui = vi qi − ti ,
where vi is i’s private value for receiving an object, and qi = 1 if i receives an
object and qi = 0 otherwise.
(a) Find all Pareto efficient outcomes.
(b) Find the VCG mechanism for this problem.
(c) Does the VCG mechanism run a deficit?
4. [20 marks] Anna initially has a banana, and Bob has an apple. Anna’s value for
her banana is 4, while Bob’s value for his apple is 6. This is public information.
Anna’s value for the apple is vA , while Bob’s value for the banana is vB . The
values vA and vB are private information: each person know his/her own value,
but not the value of the other person. Anna and Bob can consume at most one
fruit each. They must decide whether to trade their fruit with one another, or
not.
(a) Draw a graph illustrating when it is efficient for Anna to trade her banana
in exchange for Bob’s apple.
(b) Find the VCG mechanism for this problem.
(c) Does the VCG mechanism run a deficit?
(d) Find a second-best mechanism for this problem.
5. [20 marks] Consider a presidential election with three candidates. The winner of
the election is chosen by simple majority. The candidate that receives the most
votes will be elected president. In case of a draw, a winner will be chosen at
random among those candidates that have the most votes.
(a) Is this mechanism Pareto efficient?
(b) Is this mechanism incentive compatible?
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