Week 2
The following question is a numerical illustration of Gresham's Law. The broader economics topic being applied here is adverse selection.
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Quality of coin
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# of Coins
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Value to the buyer
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Value to the seller
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High
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1
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$12,000
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$9,000
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Low
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1
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$800
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$600
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Consider a transaction between a maker of coins (a "seller" of coins, denoted as seller in the chart above) and a buyer of coins (a seller of goods, denoted as the (coin) buyer in the chart above). There are two types of coins manufactured by the coin maker: a high quality coin (more gold content, less silver) and a low quality coin (more silver content, less gold), with one of each coin type available for sale to the coin buyer in exchange for goods of some dollar value. The coin maker's valuations of the coins are lower than the coin buyer's valuations. Given the valuations of the two parties to the transaction, we are interested in coming up with a possible equilibrium market price or range of market prices for the coins. That is, we are looking for prices at which the coin maker would be willing sell a coin at the same time as the coin buyer is willing to buy the same coin (i.e. prices that would equate supply and demand for coins in this market).
a) If neither the coin buyer nor the coin seller knows the quality of the coins (that is, they know that there is one high quality coin and one low quality coin, but not which of the two is high quality - they are indistinguishable to both parties), what is the range of possible market prices (in other words, what dollar value of goods will the coin buyer have to exchange for the coin(s))? How many high quality coins will change hands? How many low quality coins will change hands?
b) Suppose now that this coin market is characterized by asymmetric information. More specifically, the coin maker knows which of the coins available for sale is the high quality coin and which is the low quality coin, but the coin buyer does not know which is which (again, he knows there is one high quality coin and one low quality coin but cannot distinguish between the two). What is the range of possible equilibrium prices in this market? How many high quality coins will be change hands? How many low quality coins will change hands? What is the issue here?
Hint: if the coin maker or coin buyer is uncertain about coin quality, his valuation of a coin will reflect that uncertainty. In other words, his valuation will be some weighted average of his two valuations.