are the equilibrium values of x and y? What happens to total costpof-travel (the sum of total travel times for the 1000 cars) as a result of the availability of the new road? (c) Suppose now that conditions on edges CB and AD are improved so that the travel time on each edge are reduced to 5. The road from C to D that was constructed in part (b) is still available. Find a Nash equilibrium for the game played on the network with the smaller travel time for CE and AD. What are the equilirbium values of :r: and 3;? What is the total cost-of-travel'? What could happen to the c0It-of-travel if the government closed the road from C to D? 2 Auctions 2.1 Textbook Page 268, Chapter 9, 9.8 Exercise, Question 2 In this problem we will ask how the number of bidders in a secondprice, sealed-bid auction affects how much the seller can expect to receive for his object. Assume that there are two bidders who have independent, private values 1;,- which are either 1 or 3. For each bidder, the probability of 1 and 3 are both 1/2. {If there is a tie at a bid of z for the highest bid the winner is selected at random orn among the highest bidders and the price is :12.) (a) Show that the seller's expected revenue is 6/4. (b) Now let's suppose that there are three bidders who have independent, private values U, which are either 1 or 3. For each bidder, the probabilities of 1 and 3 are both 1 / 2. What is the seller's expected revenue in this case? (c) Briey explain why changing the number of bidders aHects the seller's expected revenue. 3 Matching Markets 3.1 Textbook Page 303, Chapter 10, 10.? Exercise, Question 4 Suppose we have a set of 3 sellers labeled a, b, and c, and a set of 3 buyers labeled at, y, and 2. Each seller is offering a distinct house for sale, and the valuations of the buyers for the houseI are as follows. Buyer Value for Value for Value for a's house b'a house '3 home I___ Suppose that a charges a price of 3 for his house, b charges a price of 1 for his home, 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 sellerI should raise their price(s) in the next round of the bipartite-graph auction procedure