Now suppose that u and v are unknown. In particular, suppose that both u and v are uniform random variables on [0, 1]. Suppose the seller assumes the buyer will bid truthfully, and aims to maximize her expected payoff. Show that there is a linear offer function s(u) = a bu that is the best response for the seller, and find a and b. In other words, show that when the seller's value is u, it is optimal for her to make an offer of a bu, if she assumes the buyer will bid truthfully. (Note that if the seller uses the offer function s(), and the buyer bids truthfully, it is a (Bayesian) equilibrium: each is playing a best response to the other.)