1. (M21) A new technology (X) can be used to produce an output with market value equal to 80. The owner wants to sell the rights of use of the technology at auction to reach a higher profit. You have been asked to advise if she should run a sealed bid first price auction or a sealed bid second price auction to sell the technology. There are three that will participate in the auction: Firms 1, 2 and 3. Their valuations are v1 = 80, v2= 100 and v3 = 120 respectively. The amount paid in the auction for the technology (X) is Px. This profit functions are private information, that is, each firm knows its own profit function but not the ones of the other participants in the auction, and the seller does not have access to this information. What they know is that the profit functions (valuations) come from a uniform distribution and that the values are independent. Answer the following items assuming the seller and all firms are profit maximisers.

a) If the selling mechanism is a sealed bid first price auction, who will win the auction? What will be the winner's bid? How much will the winner pay? And what will be the winner's profit when it starts using the technology? (15 marks)

b) If the selling mechanism is a sealed bid second price auction, who will win the auction? What will be the winner's bid? How much will the winner pay? And what will be the winner's profit when it starts using the technology? (15 marks)

c) Assume that the highest valuation is always v1= 120, and the second highest valuation is always v2= 100 regardless of the number of bidders. Show how many more bidders are at least needed to make the sealed bid first price auction a mechanism that provides a higher revenue for the auctioneer? Evaluate the mechanism behind this (10 marks)