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Suppose we have a set of 2 sellers labeled a and b, and a set of 2 buyers labeled x and y . Each seller

Suppose we have a set of 2 sellers labeled a and b, and a set of 2 buyers labeled x and y. Each seller is offering a distinct house for sale, and the valuations of the buyers for the houses are as follows.

Buyer Value for a's house Value for b's house
x 4 1
y 3 2

In general, there will be multiple sets of market-clearing prices for a given set of sellers, buyers, and valuations: any set of prices that produces a preferred-seller graph with a perfect matching is market-clearing.

As a way of exploring this issue in the context of the example above, give three different sets of market-clearing prices for this matching market. The prices should be whole numbers (i.e. they should be numbers from 0, 1, 2, 3, 4, 5, 6, . . .). (Note that for two sets of market-clearing prices to be different, it is enough that they not consist of exactly the same set of numbers.) Explain your answer.

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