EC9570
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University of Warwick
January 2021
EC9570: Microeconomics

Instructions
This is an OPEN BOOK examination.
Time allowed: 2 hours
Answer ALL questions from Section A and any TWO questions from Section B.
Section A is worth 30 marks and Section B is worth 70 marks



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SECTION A

Answer ALL of the following questions:

Q1. A lottery ℓ draws a prize from the interval [0,1] with equal probability (i.e. ̃~[0,1]). Give
an example of a lottery ℓ′ which first order stochastically dominates ℓ. Which kind of decision maker
would always prefer ℓ′ over ℓ? (10 marks)

Q2. Suppose that two agents have preferences satisfying completeness, transitivity and continuity
but not monotonicity. Is every Walrasian equilibrium a Pareto optimum in this case? (10 marks)

Q3. Evaluate the following statement: “Signals must be costly to convey information”. (10 marks)

SECTION B
Answer any TWO of the following questions:
Q4. Andrew goes to the supermarket and buys a new loaf of bread. When he gets home he
remembers that there is still 1/4 of a loaf of bread from four days ago.
He eats 1/4 of a loaf per day and prefers newer bread to older bread. If indicates bread of age
then (0) > (1) > (2) > ⋯ > (8) = 0.
Suppose we model Andrew as a utility maximiser and that he discounts future utility at rate > 0
per period.
(a) Which axioms does Andrew have to satisfy to be modelled using the utility function above?
(5 marks)

(b) Write down Andrew’s discounted stream of utility if he finishes the old bread first and then
eats the new bread. (5 marks)

(c) Write down Andrew’s discounted stream of utility if he eats the new bread first and then
eats the old bread. (5 marks)

(d) Is one consumption plan always better than the other? Explain your findings. (10 marks)

(e) Can it ever be optimal to throw the old bread away? (5 marks)

(f) Explain whether this is a ‘normative’ or ‘descriptive’ model. (5 marks)

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Q5. Consider a bargaining game between 2 players who must split a pie of size . Player 1 goes first
and specifies a share which can be either = 0, = /2 or = . Player 2 goes second and either
accepts or rejects the offer. If they accept the offer Player 2 gets and Player 1 gets − . If they
reject then both payoffs are 0.
(a) Draw the game tree for this game and find all pure strategy Subgame Perfect Equilibria (SPE)
(9 marks)

(b) Are there any Nash equilibria in this game which are not SPE? (10 marks)

(c) Are there any mixed strategy SPE? (8 marks)

Suppose that Player 2 has different actions and can no longer reject an offer. They must either
‘Accept Happily’ (AH) or ‘Accept Rudely’ (AR). If Player 2 picks AH the offer is accepted and payoffs
are as before. If Player 2 picks AR then the offer is accepted but Player 1 is upset and their payoff is
decreased by a fixed amount .

(d) Can Player 2 strictly increase their payoff compared to part (a)? (8 marks)

Q6. Consider the following model with two firms and one worker. The worker either has low
productivity = 1 or high productivity = 1 + , where is their education level which can be
either 0, 1 or 2 and is a positive constant. Each type is equally likely.
The cost of education is 2 for the low types and 2 for the high types. Utility for the workers is
given by = − 2 for low types and = − 2 for high types where < ≤ 1.
There are two identical firms who compete to attract workers. The firms simultaneously offer wages
to the worker to maximise profit = − and the worker then accepts the higher wage.
(a) What are the equilibrium wages as a function of the firms’ expectations of productivity? (5
marks)

(b) Can there be a Perfect Bayesian Equilibrium (PBE) in which the low type gets 0 years of
education and the high type gets 1 year of education? If there is then state it and explain it,
if not then explain why not. (12 marks)
Now assume a ‘high-tech’ industry also exists with two firms. Firms in the high-tech industry have a
unique production technology that increases the productivity of high type workers only. The high
type’s productivity is now ′ = 1 + 2 if the high type joins the high-tech industry. The previous
firms are still in the market for workers and all wages are posted simultaneously. All other details
remain the same.
(c) Can there be a separating PBE in this version of the model where the high types work in the
high-tech industry and the low types do not? (18 marks)

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Q7. Two players (called ‘1’ and ‘2’) play the following game. Player 1 has private information about
their type which takes the value = 10 with probability and = −10 otherwise.
Player 1 moves first by sending a costless message. The message can be either 1 or 2. Player 2
then observes the message and picks Action A or Action B.
The payoffs are given below where payoffs are displayed as (Payoff 1, Payoff 2):
Action A Action B
State = (20, 10) (, 10+)
State = (20, 10) (, 10+)


(a) Represent this game in extensive form. Write the payoffs in full. (10 marks)

(b) Can there be any separating equilibria in this game? Does your answer depend on ? (10
marks)

(c) Can there be any pooling equilibria in this game? Does your answer depend on ? (15
marks)

End of Paper