Consider the market for used cars. Assume that the quality of cars is uniformly distributed from 0 to 10,000 and that each quality unit corresponds to $1 of value. Assume buyers and sellers have the following utility functions: UB = X n j=1 j + 400 US = 1 2 X n j=1 j + 400 At a market price of P=4,000... a.) What is the change in utility that a seller will experience if he sells car 1 (X1)? That is, solve for: US=US(After Sale)-US(Before Sale) b.) Based on your answer to part (a), what condition must be satisfied in order for the seller to place his car on the market? c.) Display your answer to part (b) in a frequency graph with quality along the x-axis. d.) What is the change in expected utility that a buyer will experience if he purchases a car on the market? That is, solve for: E[UB]=E[UB(After Purchase)-UB(Before Purchase)] e.) Based on your answer to part (d), what condition must be satisfied in order for a buyer to be willing to purchase an available car? f.) In the market described above, will any used cars be exchanged? g.) Suppose sellers change so that they like cars slightly more. This causes sellers' utility to change to: US = 2 3 X n j=1 j + 400 Buyers' utility does not change. Under this regime, will any used cars be exchanged? h.) Suppose sellers' valuation of cars does not change (coefficient goes back to ), but the government introduces a price ceiling such that the market price for a used car cannot exceed $1,000. Under this regime, will any used cars be exchanged? i.) Suppose there is no price ceiling (price back to 4,000) and buyers' valuation of cars does not change (coefficient still ), but the government imposes a minimum car quality guaranteed such that cars worth less than $2,000 cannot be placed on the market. Under this regime, will any used cars be exchanged?