Suppose Peter's tastes for "square feet of housing" (x) and "other goods" (y) can be = (1/2 )x1/2-1/2 represented by the utility function: u(x, y) = x / y . Then, MU. = (1/2)xy and MUy e) Calculate Peter's optimal housing consumption as a function of the price of housing (p.) and his exogenous income M (assuming that p, is by definition equal to 1). f) What information does a demand function from part e) impart? Is there anything unusual about this demand function? g) What is the equation of the inverse demand curve for housing? Draw this on a graph. If income were to increase, what would happen to the inverse demand curve for housing? Illustrate on graph. h) Using answer from part e), verify that Peter will purchase a 1,250-square-foot house when his income is 500,000 and the price per square foot is $200. i) Now suppose the price of housing falls to $156.25 per square foot and Peter chooses to sell his 1,250-square-foot house. How big a house would Peter now buy? j) Calculate Peter's utility (as measured by his utility function) at his initial 1,250- square-foot house and his new utility after he bought his new house. Did the price decline make Peter better off? k) How would answers to (i) and (j) change if, instead of falling, the price of housing had increased to $250 per square foot