On procurement auctions with fixed budgets

We consider an organisation which has been allotted a fixed budget 'A' by higher authorities, for procuring certain specified items. It seeks price quotations from firms. The firm quoting the lowest price secures the contract to sell the item to the organisation. In this context we compare first price and second price auctions and derive the following results. (i) The expected price in the first price auction is lower than the expected price in the second price auction. (ii) The expected quantity sold is the same across the two auctions. (iii) With a rise in the number of firms the expected price goes down and the expected quantity sold goes up in both FPA and SPA. (iv) The expected profit to any firm in equilibrium is also the same across the two auctions. (v) We analyse the effect of reserve prices and discuss optimal reserve price. (vi) We also discuss quantity auctions and show that they are equivalent to standard benchmark auctions.