2. Sales taxes in frictional product markets. Consider the product market model of Burdett and Judd {1983). The buyers' utility from consuming a unit of the good is 4 > 0 and the disutility from paying p dollars for the good is p. The sellers can produce the good at the unit cost e, where 2 (). Each buyer meets one seller with probability o > 0 and two sellers with probability s = (). The government taxes consumption of the good at the rate = ({0, 1). a. Write down and solve the problem of a buyer who meets a seller charging the price p. Remember to take into account that the buyer has to pay the sales tax tp. b. Write down and solve the problem of a buyer who meets a seller charging the price p; and a seller charging the price pa. c. Write down the profits of a firm that charges the price p. d. What is the highest price on the equilibrinm price distribution F7 e. Compute the maximized profits of a seller IT* f. Compute the equilibrinm price distribution F. g. Does the price distribution increase or decrease if the tax rate increases? Provide an intuition for your findings