Problem 1 (Auctions).
A developer of a new technology τ can use the technology to produce an output with market value equal to 45. However, she wants to sell the rights of use of the technology at auction to reach a higher profit. She is considering sellign the technology and has hired the company you work for to help her decide how to sell it. You suggest she should use a sealed-bid first-price auction or a seald-bid second-price auction to allocate the technology. There are three potential buyers of the technology in the auction: Firms 1, 2 and 3. Their profit functions are:
respectively, where C(τ) is the cost of using technology τ in the production process. This profit functions are private information, that is, a firms knows only its own profit function, and the seller does not have access to this information. Answer the following items assuming the seller and all firms are profit maximisers.
Should the auctioneer set a reserve price? If so, what should the reserve price be for this auction? (5 marks)
If the selling mechanism is a 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)
If the selling mechanism is a 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)
What will be the profits net of investment made by the seller? (10 marks)
Sample Solution
