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Question 3: Suppose we are studying the market for good x1; there are 90 consumers in this market (all with income M ). 50 consumers have the following demand function: x!(pi, p2, M) = Mp3 - p1. The other 40 consumers have the following demand function : r!(P1, P2, M) = 2Mp2 - SP1. a) Derive the Market Demand Function. b) Derive the income elasticity of demand. c) At M =5, p2 = 1,and p1 = 3, is good x1 a normal or inferior good? If normal, is it a necessity or luxury?II. Consider the following ISL[M model: c = 200 + 0.251}, r = 150 + 0.251? 1,000: o = 250 T = 200 (sum-=1 = 2r 0,000: MI? = 1,500 a. Derive the [S relation. (Hint: You want an equation with Y on the left side and everything else on the right} b. Derive the [M relation. (Hint: It will be convenient for later use to rewrite this equation with 1' on the le side and everything else on the right.) c. Solve for equilibrium real output (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output) d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part (c) into either the IS or LM equations and solve for i- If your algebra is correct, you should get the same answer from both equations.) e. Solve for the equilibrium values of E' and I, and verity the value you obtained for Y by adding C, I, and 6. 1'. Now suppose that the money supply increases to MfP = 1.8411}. Solve for Y, E, C, and I, and describe in words the effects of an expansionary monetary policy. g. Set MfP equal to its initial value of 1,630. Now suppose that government spending increases to G = Summarize the effects of an expansionary scal policy on Y, i, and C. Auction Design Suppose we have a seller who owns an object and there are two people who are interested in buying it. Each of these two people, we'll call them A and B, are known to have values for the object, VA and VB that were independently and randomly chosen from the range [0,1]. Only A and B know what the true values are. Assume the seller values the object at 0. The seller decides they want to try the following mechanism. They offer the object at a \"take- it-orleaveit\" price of some amount a: E [0, 1]. If A or B, but not both, say they want the object at that price, that person gets it and pays 3:. If both accept the price then they ip a coin to decide who gets it and the winner pays 3:. If neither accept the at price then the object goes unsold. a. Assume that :c = .5 and that VA = .7. Should A be willing to accept the price of .5? b. Suppose that neither of the Bidders agrees to buy at the initial a: chosen by the seller and the seller decides to make a descending series of \"take-itorleaveit\" offers. How will this process compare with the auction mechanisms we have studied? Should the seller expect that the rst \"take-it-orleave-it\" offer they make will have an impact on their revenue? (positive, negative, no difference) 0. Now assume that the way the seller conducts the auction is through using a second price sealed bid mechanism but with one catch. The seller sets a reserve price, i", such that they refuse to sell below that price. If only one bidder submits a bid above *r then that bidder pays 1" instead of the second highest bid. If no bidder submits a bid above 1" the object goes unsold. Assume that the bidders are not informed of the level of the reserve price prior to submitting their bids but they do know that one has been chosen. Does this change the equilibrium bidding strategy from the standard second price sealed bid auction? d. Should a reserve price set in this manner be expected to increase the expected revenue over the case of a second price auction in which a reserve price is not used? Why or why not. Explain clearly. Numerical examples may help