Suppose the Potter family has $400,000 to spend on a house and "other goods" (denominated in dollars). The price of 1 square foot of housing is $100, and the family chooses to purchase their optimally sized house at 2,000 square feet. Assume throughout that they spend money on housing solely for its consumption value (and not as part of your investment strat- egy). (a) On a graph with "square feet of housing" on the horizontal axis and "other goods" on the vertical, illustrate the Potters budget constraint and your optimal bundle A. (b) After they bought the house, the price of housing falls to $75 per square foot. Given that they can sell their house from bundle A if they want to, are thery better or worse off? (c) Assuming they can easily buy and sell houses, will they now buy a different house? If so, is their new house smaller or larger than their initial house? (d) How does your answer to (c) change if the price of housing went up to $150 per square foot rather than down to $75. Suppose the Potter's tastes for "square feet of housing" (x) and "other goods" (y) can be represented by the utility function: U(x,y) = xy1. Then, MUx = x1y1 and MUy = xy. (e) Calculate Potters 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) For what value of will they indeed purchase a 2,000-square-foot house when their income is $400,000 and the price per square foot is $100? Use the value of from previous part in the remaining calculations. (g) Now suppose the price of housing falls to $75 per square foot and they choose to sell their 2,000-square-foot house. How big a house would they now buy? (h) Calculate your utility (as measured by your utility function) at their initial 2,000-square-foot house and their new utility after they bought your new house. Did the price decline make them better off? (i) How would your answers to (g) and (h) change if, instead of falling, the price of housing had increased to $150 per square foot?