7. Suppose there are two bidders with valuations uniformly and independently drawn from [0, 1]. In addition, bidders are risk neutral, so that u(v,b) = vb if winning the object and u(v, b) = 0 otherwise. (a) Find the equilibrium bidding strategy in a first price sealed bid auction. (b) Find the equilibrium bidding strategy in a second price sealed bid auction. (c) Compare the expected revenues generated by the two auctions. Suppose now that bidders are risk averse, so that u(v, b) = v - b if winning the object and u(v, b) = 0 otherwise. (a) Find the equilibrium bidding strategy in a second price sealed bid auction. (b) Show that v(v) = (2/3)v is an equilibrium in the sealed bid first price auction. (c) Compare the expected revenues generated by the two auctions. Discuss your findings.