Question 2 In this question, we will consider a version of the hold-up problem. As usual, there is a (S)eller and a (B)uyer. S chooses investment e at cost -e . B chooses investment E at cost $ 12 S has a widget. B needs this widget to produce a final good. (No asset is involved.) The quality of the widget, and thus of the final good, increases with the players' investments. Specifically, Up = 2E +e and Us =0, pout = 0 and DS = 0, where Up is the value that B gets if he receives the widget and produces the final good; Up and Us are the outside-option values that B and S get if S keeps the widget. Instead of Nash Bargaining, one player makes an offer to the other. We will start by assuming that S makes an offer to B. The game proceeds as follows: 1. S chooses e, and B chooses E. 2. S offers to sell the widget to B at a price p. B then decides whether to accept or reject. 3. B and S receive their payoffs (or their outside-option payoffs if the offer is rejected). We'll work this out step-by-step: a) Given the optimal price p' chosen by S in step 2, what will B's payoff be? What will S's payoff be? Your answers should be in terms of E and e, and should not include p. (Hint 1: think about how the principal chooses the fixed payment a when making an offer to the agent in our principal-agent models. Hint 2: you don't have to explicitly calculate p* to answer this question.) b) Calculate the equilibrium investments e" and E". c) Suppose that in step 2, instead of S making B an offer, the price is determined through Nash bar- gaining. Calculate the equilibrium investments e" and E* in this case. d) Explain, in words, why the the seller invests more when he makes B an offer, but the buyer invests more under Nash bargaining. e) As the social planner who seeks to maximize the sum of buyer and seller payoffs, would you prefer to (i) implement Nash bargaining or (ii) have the seller make the buyer an offer in step 2? Explain why, in words. Is there an alternative protocol for step 2 that would further increase total payoffs