For c to be constant across locations, the price per square foot of housing must vary with x in a way that allows the consumer to afford a fixed amount of bread after paying his rent and his commuting cost. Let c denote this constant level of bread consumption for each urban resident. For the moment, c is taken as given. We'll see below, however, that c* must take on just the right value or else the city will not be in equilibrium. a. Substituting c in place of c in the budget constraint c + 1200 p = 32 - 0.03 x, solve for p in terms of c* and x. The solution tells what the price per square foot must be at a given location in order for the household to be able to afford exactly c* worth of bread. How does p vary with location? (You don't need to calculate and exact number for this last part, but explain intuitively the relationship. For example, the relationship is positive or negative because....) Recall that the zoning law says that each developed block must contain 24,000 square feet of floor space. Suppose that annualized cost of the building materials needed to construct this much housing is 120 (that is, $120,000). b. Profit per square block for the housing developer is equal to 24,000p - 120 - r, where r is land rent per square block. In equilibrium, land rent adjusts so that this profit is zero. Set profit equal to zero, and solve for land rent in terms of p. Then substitute your solution to p from (a) in the resulting equation. The result gives land rent r as a function of x and c+. How does land rent vary with location? Since each square block contains 24,000 square feet of housing and each apartment has 2,400 square feet, each square block of the city has 20 households living on it. As a result, a city with a radius of x blocks can accommodate 20 TX households ( TX - is the area of the city in square blocks). c. Suppose the city has a population of 350,000 households. How big must its radius x be in order to fit this " population? Use a calculator and round to the nearest block