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3. Matching Markets Suppose we have a set of 3 sellers labeled a, b, and c, and a set of 3 buyers labeled x, y, and z. Each seller is offering a distinct house for sale, and the valuations of the buyers for the houses are as follows. Buyer x y z Value for Value for Value for a's house b's house c's house 12 9 8 10 3 6 8 6 5 Suppose that a charges a price of 3 for his house, b charges a price of 1 for his house, and c charges a price of 0. 1. When the payoff is no smaller than 5, the buyer regard the house to be acceptable. Plot the bipartite graph where the buyers are connected with the acceptable houses. Is there a perfect matching? 2. Is this set of prices market-clearing? If yes, explain which buyer you would expect to get which house. If not, say which seller or sellers should raise their price(s) in the next round. 3. Now a house retail policy is announced, and each buyer raises their price. Currently a charges a price of 4 for his house, b charges a price of 3 for his house, and c charges a price of 1. Please follow the procedure, and figure out a set of market-clearing prices. With the prices you found, figure out which buyer would get which house. 3. Matching Markets Suppose we have a set of 3 sellers labeled a, b, and c, and a set of 3 buyers labeled x, y, and z. Each seller is offering a distinct house for sale, and the valuations of the buyers for the houses are as follows. Buyer x y z Value for Value for Value for a's house b's house c's house 12 9 8 10 3 6 8 6 5 Suppose that a charges a price of 3 for his house, b charges a price of 1 for his house, and c charges a price of 0. 1. When the payoff is no smaller than 5, the buyer regard the house to be acceptable. Plot the bipartite graph where the buyers are connected with the acceptable houses. Is there a perfect matching? 2. Is this set of prices market-clearing? If yes, explain which buyer you would expect to get which house. If not, say which seller or sellers should raise their price(s) in the next round. 3. Now a house retail policy is announced, and each buyer raises their price. Currently a charges a price of 4 for his house, b charges a price of 3 for his house, and c charges a price of 1. Please follow the procedure, and figure out a set of market-clearing prices. With the prices you found, figure out which buyer would get which house

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