Question

Two firms sell an identical product and engage in simultaneous-move price competition (i.e., Bertrand competition). Market demand is Q = 20 – P. Firm A has marginal cost of $1 per unit and firm B has marginal cost of $2 per unit. In equilibrium, firm A charges PA = $1.99(…) and firm B charges PB = $2.00 A clever UNC alum has patented a cost-saving process that can reduce marginal cost to zero. The UNC alum is willing to license her invention to one (and only one) of the firms. She will invite the firms to bid for the license. The firms submit their bids simultaneously to the inventor. The firm with the higher bid wins the license and pays its bid, and the losing firm keeps its old technology and pays nothing. The firm that wins the auction gets MC = 0. The firm that loses keeps its original marginal cost (MCA = 1 or MCB = 2). After the auction, the firms engage in one additional round of price competition.

a. What is the maximum each firm is willing to pay for the license? In other words, how much value does each firm get from winning the auction instead of losing it? Explain and/or provide sufficient calculations to support your answer.

b. Which firm do you expect will win the auction? At what price (bid)? Assume that each firm is willing to pay (bid) a price that could be as high as its value from the license, i.e. the values you found in part (a), but each firm would prefer a lower price to win if possible.

Answer 1

An auction is usually a process of buying and selling goods or services by offering them up for bid, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition exist and are described in the section about different types. The branch of economic theory dealing with auction types and participants' behavior in auctions is called auction theory.

Two firms sell an identical product and engage in simultaneous-move price competition (i.e., Bertrand competition). Market demand is Q = 20 – P. Firm A has marginal cost of $1 per unit and firm B has marginal cost of $2 per unit. In equilibrium, firm A charges PA = $1.99(…) and firm B charges PB = $2.00 A clever UNC alum has patented a cost-saving process that can reduce marginal cost to zero. The UNC alum is willing to license her invention to one (and only one) of the firms. She will invite the firms to bid for the license. The firms submit their bids simultaneously to the inventor. The firm with the higher bid wins the license and pays its bid, and the losing firm keeps its old technology and pays nothing. The firm that wins the auction gets MC = 0. The firm that loses keeps its original marginal cost (MCA = 1 or MCB = 2). After the auction, the firms engage in one additional round of price competition.

a. What is the maximum each firm is willing to pay for the license? In other words, how much value does each firm get from winning the auction instead of losing it? Explain and/or provide sufficient calculations to support your answer.

b. Which firm do you expect will win the auction? At what price (bid)? Assume that each firm is willing to pay (bid) a price that could be as high as its value from the license, i.e. the values you found in part (a), but each firm would prefer a lower price to win if possible.

The open ascending price auction is arguably the most common form of auction in use throughout history.[1] Participants bid openly against one another, with each subsequent bid required to be higher than the previous bid.[2] An auctioneer may announce prices, bidders may call out their bids themselves or have a proxy call out a bid on their behalf, or bids may be submitted electronically with the highest current bid publicly displayed.[2]

Auctions were and are applied for trade in diverse contexts. These contexts are antiques, paintings, rare collectibles, expensive wines, commodities, livestock, radio spectrum, used cars, even emission trading and many more.