Lemons market

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Lemons market [50 points]
Suppose there are three types of used cars, low quality cars orlemons(L),medium
quality cars or melons (M), and top quality cars or peaches (P). There is a continuum
of buyers and sellers. Potentialbuyersvalue lemons at $1200, melons at $2400, and
peaches at $2800. Thesellersvalue lemons at $800, melons at $2000, and peaches at
$2600. Everybody knows that 1/4 of the cars are lemons, the fractionλare melons, and the remaining fraction 3/4−λare peaches. Buyers and sellers are risk neutral. Prices are given exogenously.

Lemons market

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(a) 5 marks Which cars should be traded from an efficiency perspective?
(b) 15 marks Suppose that both buyers and sellers observe the quality of the cars
perfectly. How many different prices can coexist in the market?Determinethe
range of prices at which all cars can be traded.
(c) 15 marks Now consider the diametrically opposite case, where neitherbuyers nor
sellers can observe the quality of the cars at all. How many different prices can
coexist in the market now? Determine the range of prices at which all cars will be
traded in this case.
(d) 15 marks Finally, suppose that buyers still cannot observe the quality levels at
all, whereas sellers can identify lemons, but cannot tell melons apart from peaches.
How many different prices can coexist in the market now? For whatrangeofvalues
ofλwill there exist prices at which all types of cars are traded?
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EC3313: Winter 2016 Maris Goldmanis Spring Coursework
2. Sequential equilibrium [50 points]
Consider the following game (player 1’s payoffs are listed first and player 2’s payoffs are
listed second):
1
(5,5)
C
A (r)
(1,3)
L (t)
(7,5)
R
B (s)
(2,2)
L
(6,4)
R
2
(a) 5 marks How many subgames does this game have?
(b) 15 marks Find all pure strategy subgame-perfect Nash equilibria (SPNEs) of this
game.
(c) 15 marks Show that one of the SPNEs that you found in part (b) is not part of
any weak sequential equilibrium (Perfect Bayesian equilibrium or PBE). [Hint: By
looking at player 2’s choices, decide which SPNE from part (b) makes the least
sense. Assume that this SPNE is part of a PBE. Use sequential rationality and
consistency of beliefs to obtain a contradiction.]
(d) 15 marks Find a weak sequential equilibrium (Perfect Bayesian equilibrium) of
this game. [Hint: Start with the most reasonable of the SPNEs from part (b)
and add appropriate beliefs. Do not forget to check sequential rationality and
consistency of beliefs at all information sets