This is urban economics!

4. (25 pts) This question illustrates residential distribution with segregated equilibrium (where the high-income and the low-income live in different neighborhoods) and integrated equilib rium (where the high-income and the low-income live in the same neighborhood). Suppose the high-income households have a wage of $20 per unit of time, the low-income households have a wage of $10 per unit of time. Suppose both the low-income and the high-income go to work by bus. It takes the bus one unit of time to cover 1 mile. Suppose the low-income households have a marginal benefit curve MBL = 20 -d, where d is the distance between where they live and where they work (downtown). The high-income households have larger demand for housing, their marginal benefit curve is MBH = 60 - 2d. (a) (10 pts) What is the distance between where the low-income households live and the downtown? What is the distance between where the high-income households live and the downtown? Is it a segregated equilibrium or an integrated equilibrium? (b) (5 pts) Now suppose that the demand for housing for the low-income households in- creases, the marginal benefit for the low-income households becomes MBL = 30 - d. Re-calculate the residential location for the low-income households. (c) (5 pts) Now suppose that the high-income households drive to work. Car is twice as 3 fast as bus. What is the new marginal cost for the high-income households? What is the new residential location for the high-income households? (d) (5 pts) Now suppose that the wage of high-income households increases. Suppose their demand for housing does not change. Without solving for the new residential location for the high-income households numerically, answer how does it affect the marginal cost curve for the high-income households? Will they choose to live closer or farther away from the downtown