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Suppose Peter have $500,000 to spend on a house and “othergoods” (denominated in dollars). The price of 1 square foot ofhousing is $200, and Peter chooses to purchase optimally sizedhouse at 1,250 square feet. Assume throughout that Peter spendsmoney on housing solely for its consumption value (and not as partof his investment strategy). a) On a graph with “square feet of housing” on the horizontalaxis and “other goods” on the vertical, illustrate Peter’s budgetconstraint and Peter’s optimal bundle A. b) After Peter bought the house, the price of housing falls to$156.25 per square foot. Given that Peter can sell his house frombundle A if he wants to, is Peter better or worse off? … / 4 Winter2018 Econ 301 Assignment 1 continued Page 4 of 5 c) Assuming Peter can easily buy and sell houses, will Peter nowbuy a different house? If so, is Peter’s new house smaller orlarger than his initial house? d) How does Peter’s answer to c) change if the price of housingwent up to $250 per square foot rather than down to $156.25?Suppose Peter’s tastes for “square feet of housing” (x) and “othergoods” (y) can be represented by the utility function: u(x, y) = x1/2 y 1/2. Then, MUx = (1/2)x -1/2 y 1/2 and MUy = (1/2)x 1/2 y-1/2. . . .