PLEASE ANSWER (b)

Question 4 [14 points] Consider a rst price auction with two buyers 1,2. Their valuations v], v: are independent and each follows the triangle distribution in the interval [0, 2], as shown below. Diagram 1 vi 0 x 2 (a) [3 points] For any 1: between 0 and 2, determine the expression of the density function f (x) of the triangle distribution given above. (b) [3 points] For any it between i] and 2, determine the expression of the distribution inction x) of the triangle distribution given above. (e) [4 points] The bid functions of buyers 1,2 are in = low, if); = kzvz where In, t: are positive numbers. Showing all steps of your work, show that the expected net income of buyer l is vi 2 _ EMU 1'1) {d} [4 points] Using the arithmetic mean-geometric mean (AMdGM) inequality, determine the choice of it] that maximizes the expected net income of buyer 1