1. Jim is selling his house in Toronto with the assistance of a real estate agent. The agent informs Jim that. there are k 2 2 buyers registered to submit. offers to purchase. The I: identical prospective buyers will submit their bids, bl. b3, . . . ,bk independently, and the GDP of each offer is denoted by F with support [0, b]. Jim plans to accept the highest bid, Yk =max{b1,b2,...,bk}. (1) We will therefore refer to the random variable Y}.- as the purchase price. (i) Let G denote the CDF of the purchase price. Derive an expression for the function G. (ii) Let 9 denote the PDF of the purchase price. Derive an expression for the function 9. (iii) Compare the GDP of the purchase price, 6', with the CDF of each bid1 F. in terms of rst order stochastic dominance. (iv) Derive an expression for the expected purchase price, ]E[Y,.]. Show that it is increasing in the number of bidders. Ir. (v) Let. H and h denote the GDP and PDF of the second highest bid. Derive an expression for the function h