Suppose that there are three bidders with values that are drawn independently from U[1,4] in an auction with one item. (a) Find an equilibrium of the first-price auction. (b) Find an equilibrium of the all-pay auction. (c) Find an equilibrium of the sealed-bid auction in which the winner pays the average of the first and second highest bids. (Hint: You can assume that the equilibrium bidding function is (v) = a v + b.)