Firm S plans to sell an office building via an English auction. The firm expects two buyers to bid, each with a value uniformly distributed between $300,000 and $360,000. In addition, firm S knows it can sell the building to a third outside buyer for $300,000 if the auction does not produce a better price.
a. Suppose firm S sets the auction reserve price at Pmin = $300,000. Show that the expected price in the English auction is $320,000.
b. Suppose instead that firm S sets Pmin = $330,000. What is the chance that neither buyer will meet this price? What is the chance that exactly one buyer will meet this price? What is the chance that both buyer values exceed this price? Conditional on both values being above $330,000, what will be the expected price in the English auction?
c. Averaging over the three possibilities in part (b) by the appropriate probabilities, compute the seller’s expected revenue. Confirm that it is to the seller’s advantage to set the higher reserve price.