Question 3 In the city of Urbanville, land is divided between supermarkets and houses (for residents). There is a train station at :C : 0. 0 Urbanville residents all work from home. Their utility of living in the city is U = 2 R, where R is the rent they pay. These residents also have the option of moving out of the city and living far away from Urbanville. Doing so gives them a utility of U0 : 0. 0 Supermarkets receive goods from the central train station. Their prots are 71' 2 Pg 2d R. In the prot equation, d stands for the distance to the train station. 0 The price of groceries is Pg : 10. (a) Draw the bid rent curves for supermarkets and houses (b5. and 6,1,). (b) Find 33*, such that land from 0 to x\" is used for supermarkets and land farther away than 1* is used for houses. Transportation costs fall, such that supermarket prots are now given by TI" : Pg d R. (c) On the same diagram as before, draw the new bidrent curve for supermarkets (HS) and nd 331, the new boundary between supermarkets and houses. Question 4 We will model the same fall in transportation costs as Question 3, but now will will account for changes to the equilibrium in the market for groceries. Use the same prot and utility functions as Question 3. Supply of groceries is perfectly inelastic, with quantity supplied equal to the land area taken up by super- markets. For example, if all land from a: : 0 to a: : 5 is used for supermarkets, then supply is perfectly inelastic at 5 units. . . . D Demand for groceries 1s glven by P9 : 12 %. (a) Suppose that land use the same as in Q3b and that transportation costs have not yet fallen. Draw a supply and demand diagram to describe equilbrium in the groceries market. Label this diagram with: 0 The equilibrium quantity of groceries (as a number) a The equilibrium price of groceries Pg (as a number) The market now experiences the fall in transportation costs. This time, the land market is affected, but so is the groceries market. (b) Solve for: 0 3:2, the new boundary between houses and supermarkets. (You should get a different answer from Q30) 0 The new price of groceries Pg\