1. Suppose a seller (i.e. the principal) wants to sell his good to a buyer (i.e. the agent) by pricing it optimally. Suppose the seller's utility function is given by t-q and the buyer's utility function is given by 0q/3-t whenever q 0 is the amount of good sold to the buyer in exchange of t 0 amount of transfer made to the seller. Suppose the seller does not observe the buyer's taste parameter 0, but it is common knowledge that this parameter can be either 3 with probability v = 1/4 or 0 = 1 with probability 3/4. Suppose that the seller offers a menu of contracts (i.e. quantity-transfer pairs) after the buyer observes her type. 1 = (a) Write down the seller's optimization problem by clearly stating the objective function and the constraints. (b) Simplify this problem by identifying binding and non-binding constraints, and making necessary substitutions. (c) Solve the simplified problem; that is, find an optimal contract as a quantity-transfer pair offered for each type of the buyer. (d) Calculate the expected utility of the seller. Find each type of buyer's information rent. (e) Find the minimum value of such that the shutdown policy becomes optimal given all other parameters.