Exercise 3. Consider a homogeneous product market with two types of buyers and two types of sellers in which each seller can sell one unit and each buyer has unit demand. Buyer H has valuation vy for the product and buyer L has valuation v; with vy > vy. Seller H has opportunity cost cy and seller L has ; with y > ;. There is a unit mass of each buyer and each seller type. Consider the parameter restriction vy > cyg > vp > cp. Suppose that buyers and sellers are randomly matched once. Suppose furthermore that buyers and sellers bargain efficiently and that joint surplus from a match is split equally. If the joint surplus is negative within a buyer-seller pair no trade occurs between the two. 1. Determine the expected allocation and the expected surplus for each buyer and seller. Write one or two sentences describing the outcome. 2. Is the allocation first-best efficient? Explain. 3. An intermediary enters the market and offers to trade on its trad- ing platform. The intermediary charges a fee P > 0 to the seller whenever a transaction occurs. If at least one seller and at least one buyer join the intermediary, they are randomly matched. Buy- ers and sellers decide whether to remain in the non-intermediated matching market or to move to the intermediated market. A ran- domly matched pair splits the net surplus from trade evenly. Do there exist transaction fees P > 0 such that trade on the interme- diated platform occurs and thus the intermediary makes strictly positive profits? Can trade of one unit via the intermediary be sup- ported in equilibrium? Is the non-intermediated matching market active in equilibrium (i.e., does trade take place both on the inter- mediary's platform and outside)? 4. In the model with an intermediary from above, what can you say about the efficiency properties of the equilibria characterized in part 3 of the exercise