4 THE Monocemmc CITY Moon [20 PDINTS] Consider the following linear city. I Employnrent takes place at a single location 1' = l}, the Central Business District {CED}. I Each resident commutes to the CED everyday and gets an exogenous wage of w = 150. I Preferences are represented by a utility function U{cfl}.l where c is the consumption of nonland goods and l is the consumption of land. This function is assumed to be CobbDouglas: Ufc, l} = c'5l'5 I Assume that the cost of oommuting is strictly monetary and increases linearly 1with distanoe to the CED, so that a resident living at distance a: from the CED incurs a commuting cost of TI. Assume that 'r = E. I Land covered by the city is endogenously determined in the model and is represented by the positive segment on the line between [(1,173]. I Residents are assumed to be identical, with an exogenous daily utility level I? deter mined outside the model {this is an open city}. Assume that {l = ll}. a} Let P[3:} be the rental price of one unit of land at a distance I from the CED. Write down the representative consumer's budget constraint as a function 3:. [2} b} Residents must choose their location of residence and allocate their disposable income optimally between land and nonland consumption goods. The price of land, and thus the budget constraint they face, varies with their location choice. 1Write down. but do not solve. the consumer's optimization problem. [2] Now assume that land consumption is xed and equal to 1 for every resident. The only difference between land plots is the distance to the CED. Assume that there is competing land use {agriculture} with rent equal to 1'3 = 14. c) Solve for the equilibrium residential bidrent function. What is the slope of the bidrent function? Explain why the bidrent has this slope. [4] d} Solve for the equilibrium extent of the city, 5. [4] e} Graph the resulting residential bidrent function. Indicate on your graph the residential bidrent at location II} and the distance to the edge of the city. [2} f} Suppose the commuting cost declines to T = 3. Show how this changes your graph in part e}. What happens to population of the city as a result? [3] 5} Go back to the environment in part c}. Now suppose that agricultural rent goes up to 2|] because the price of wheat increases. Show how this changes your graph in part e}. 1What happens to population of the cit].r as a result? [3]