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Consider a financial market with two assets: peaches and lemons. The fraction of lemons in the economy is = 0 . 4 . Buyers value

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Consider a financial market with two assets: peaches and lemons. The fraction of lemons in the economy is =0.4. Buyers value peaches at vpb=$20 and lemons at vlb=$10. Sellers value peaches at vps=$16 and lemons at vls=$8. Sellers have all the bargaining power when setting prices at which assets trade.
a) Assume both buyer and sellers can perfectly observe the quality of assets in the market. At what price will lemons and peaches trade?
b) Now assume that the quality of assets is unobservable, but that buyers and sellers have symmetric information. That is, neither sellers or buyers can tell whether a particular asset is a lemon or a peach. What is the (pooling) price P** at which assets trade?
c) Now assume that only sellers can observe the quality of assets, so that there is asymmetric information between buyers and sellers. Explain (intuitively, without equations) why the quality of assets traded in equilibrium will now depend on the price.
d) Calculate the share of lemons that trade in the market as a function of the price, and buyers' expected valuation for the asset as a function of the price. Show that the pooling price P** clears the market.
e) Assume the fraction of lemons increases to =0.5. Show that the pooling price P** no longer clears the market. Calculate the new equilibrium price. Comment.
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