Consider a consumer who consumes housing (x) and a composite good (y), which consists of all other goods except housing and is measured in $ terms. The consumer receives a monthly income of $ 1000 and housing costs $2.5/square feet per month.

a.) Derive the consumer's budget constraint as an equation and plot it in a diagram with housing in square feet per month on the x-axis.

b.) Suppose the consumer's indifference curves have the slope -y/x (MRS=y/x). Calculate the optimal consumption bundle for the consumer and indicate it on your graph.

c.) Suppose the price of housing rises to $ 4 per square foot. Compute and identify the new consumption bundle in your graph. How much income would we need to transfer to this consumer so that she could afford as much housing as before the price increase?

d.) Let's assume that there is an income transfer from the government to this consumer so that she can afford her original housing unit. Identify her new choice with the income transfer. Would she be better off, as well off or worse off with the price rise and income transfer than before prices rose? Explain.