All the jobs in the city are located at its center (x = 0), and monthly wage is equal to w. Living at distance x from the city center imposes monthly (monetary) cost x on commuting. The city is open to anyone, and the monthly utility that can be achieved outside of the city is equal to u. Individuals consume consumption good (priced at 1) and housing. Jobs at the city

center also create pollution. Consumer preferences are given by the utility function: u(h, z, x) = (1 + x)[z + ln h] where h is consumption of housing, and z is consumption of the composite good, and x is the distance to the city center (because of the pollution utility is higher further away from the jobs). Assuming that the wage is high enough for consumption of both goods to be positive, derive the housing prices in this city as a function of distance to the city center. At which distance to the city center are the housing prices at their highest?