information microecon.pdf

information microecon.pdf - Microeconomics 3.1 Private...

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Microeconomics - 3.1 Private Information Adverse Selection Signaling Microeconomics 3. Information Economics Alex Gershkov http://www.econ2.uni-bonn.de/gershkov/gershkov.htm 19. Dezember 2007 1 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling Information Economics We will apply the tools developed in game theory to analyse the effect of informational asymmetries in the models of: 1.a) adverse selection 1.b) signaling 1.c) screening. 2 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling 1.a Adverse Selection Definition Adverse Selection arises when an informed individual’s trading decision depends on privately held information in a way that adversely affects other uninformed market participants. When adverse selection is present, uninformed traders will be wary of any informed trader who wishes to trade with them, and their willingness to pay for the product offered will be low. Remark: This excludes first-best outcomes. 3 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling 1.a Adverse Selection Consider the following motivating example there is a large number of buyers and sellers each seller has one car each buyer is willing to buy at most one car suppose the quality of a car can be indexed by some number q [0 , 1] buyers are willing to pay 3 2 q for a car of quality q sellers are willing to sell a car of quality q for a price of q assume that q U [0 , 1] 4 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling 1.a Adverse Selection under perfect information, since 3 2 q q for all q , all cars of any quality are sold if q were mutually unknown (but the beliefs are the same for buyers and seller) any price between 1 / 2 and 3 / 4 will lead to efficient allocation Conclusion: Under symmetric information the outcome is efficient (first-best). 5 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling 1.a Adverse Selection now q U [0 , 1] : since the expected quality of a car for the whole market is ¯ q E [ q ] = 1 2 , only a ‘pooling’ price of p q 2 = 3 4 will be offered by the buyers but at this price, the top quarter of the whole market will not be supplied because their known valuation by the sellers is higher than the pooling price offered by the buyers therefore buyers need to re-calculate the expected market quality without the withdrawn top-quality quarter: The expected quality of the market is E [ q ] = ¯ q = 3 8 and prices up to p q 2 = 9 16 are offered at this price now only 9 16 < 3 4 of the whole market will be offered by the sellers 6 / 36
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Microeconomics - 3.1 Private Information Adverse Selection Signaling 1.a Adverse Selection therefore buyers again will re-calculate the expected quality and the market will shrink further as we can see below, this process is monotonic and will only stop at q = p = 0 hence the complete market unravels and no car (the probability of q = 0 is zero) is sold.
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