Question

1. Suppose Peter has $500,000 to spend on a house and” other goods”(denominated in dollars). The price of 1 square foot of housing is $200, and Peter chooses to purchase optimally sized house at 1,250 square feet. Assume throughout that Peter spends money on housing solely for its consumption value (and not as part of his investment strategy).

Suppose Peter’s tastes for ”square feet of housing” (x) and ”other goods” (y) can be represented by the utility function: u(x,y) = x1/2y1/2. Then, MUx = (1/2)x−1/2y1/2 and MUy = (1/2)x1/2y−1/2.

(e) Calculate Peter’s optimal housing consumption as a function of the price of housing (px) and their exogenous income M (assuming that py is by definition equal to 1).

(f) Will he indeed purchase a 1,250-square-foot house when his income is $500,000 and the price per square foot is $200?

(g) Now suppose the price of housing falls to $156.25 per square foot and he chooses to sell his 1,250-square-foot house. How big house would he now buy?

(h) Calculate his utility at his initial 1,250-square-foot house and his new utility after he bought his new house. Did the price decline make him better off?

(i) How would your answers to (g) and (h) change if, instead of falling, the price of housing had increased to $250 per square foot?

Answer 1