A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. Suppose that an auctioneer faces two bidders in an oral auction, each with a value of either $30 or $70, with both values equally probable.Assume the bidders know the reserve price when bidding. Calculate the expected revenue from auctioning the item with and without a reserve price, and identify the optimal reserve-pricing strategy.

Now suppose that the auctioneer has decided to run a sealed-bid second-price "Vickrey" auction and there are two types of bidders with values of either $55 or $70.Calculate the expected revenue from auctioning the item with and without a reserve, assuming the auctioneer chooses the optimal reserve level.