matching markets

Homework

1. Chp 10. Exercise 1 - 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.

Suppose that a charges a price of 0 for his house, and b charges a price of 1 for his house. Is this set of prices market-clearing? Give a brief (1-3 sentence) explanation; as part of your answer, say what the preferred-seller graph is with this given set of prices, and use this in your explanation.

2. 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.

Suppose that sellers a and b each charge 2, and seller c charges 1. Is this set of prices market-clearing? Give a brief explanation.

3. 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.

Suppose that sellers a and c each charge 1, and seller b charges 3. Is this set of prices market-clearing? Give a brief explanation.

4. 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.

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. Is this set of prices market-clearing? If so, 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 of the bipartite-graph auction procedure from Chapter 10.

5. 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.

Suppose that 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. Is this set of prices market-clearing? Give an explanation for your answer, using the relevant definitions from Chapter 10.