The US goverment helps low-income consumers to purchase housing. Suppose the consumer has regular preferences over housing and EOG. The consumer has a fixed income and must pay price ph for each "unit" (c.g., square foot). 16 pts. a. Use a budget line and an indifference map and derive the consumer's optimal consumption bundle graphically. Label the axis and denote the optimal housing consumption by ha. What is the slope of the budget line? b. Suppose the government wants to induce the poor to increase his housing consumption by giving him an income subsidy of S dollars in cash. Show the effect of this on housing consumption using the same graph. Denote the new housing consumption by he c. Now the government considers giving the poor a housing coupon (voucher) worth of S dollars that can be redeemed only for housing. Use the same graph and show the effect of this on housing consumption. Denote the new housing consumption by bg d. Explain the relationship among b4, be and h Can bexceed B? How about the opposite? Explain