Economics 312: Urban Land Economics University of Victoria Midterm Examination #2 VERSION 1 SOLUTIONS

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1 Spring 2017 Instructor: Martin Farnham Midterm Exam #2, Page 1 Economics 312: Urban Land Economics University of Victoria Midterm Examination #2 VERSION 1 SOLUTIONS Section 1: Multiple Choice (2 points each) Select the most appropriate answer, and carefully bubble in the letter of the answer on your bubble form. Unless otherwise stated, assume markets are competitive and that the Leftover Principle holds. For purposes of calculating present discounted values, assume payments are received at the end of each year. Questions 1-7 refer to the diagram below, which illustrates a competitive farmer s non-land cost curves (marginal and average costs) and price (=$50) for different fertility grades of land: MC Grade&A& Grade&B& $ MC $ $ ATC ATC ,000 Bushels 8,000 Bushels 5,000 1) What are the total revenues associated with producing the optimal quantity of corn on a Grade A piece of land? A) $40,000 B) $50,000 C) $400,000 D) $500,000 E) None of the above. Grade&C& MC ATC Bushels 1

2 2) What are the total non-land costs associated with producing the optimal quantity of corn on a Grade A piece of land? A) $40,000 B) $50,000 C) $400,000 D) $500,000 E) None of the above. 3) If a farmer makes the optimal production choice on a Grade C piece of land, how many bushels of corn will she produce? A) 0 B) 60 C) 5000 D) 50,000 E) 300,000 4) Assuming farmers are all equally productive, what will be total profits in equilibrium on a Grade A piece of land? A) $0 B) $60 C) $5000 D) $10,000 E) $100,000 5) Suppose that the price of corn rises in world markets. Which of the following will occur? I. The farmer s optimal quantity will increase on the Grade B piece of land. II. The farmer s pre-rent profits will increase on the Grade A piece of land. III. The farmer s overall profits will increase on the Grade A piece of land. A) I only. B) II only. C) III only. D) I and II only. E) I, II, and III only. 2

3 6) Questions 1-5 assumed that the farmer had the same productivity as all other potential farmers. Now suppose the next most productive competitor to the farmer above can earn pre-rent profits that are $10,000 less than those of the farmer above (in other words, the farmer above is the most productive farmer around) on each piece of land. What will be the total profits of the farmer above, in equilibrium, on a Grade B piece of land? A) $0 B) $60 C) $5000 D) $10,000 E) $100,000 7) Keep the same assumption as in Question 6 (that this farmer s next most productive competitor earns $10,000 less in pre-rent profits on each piece of land). Assume price and the interest rate will remain fixed forever. What should a piece of Grade A land sell for in equilibrium, assuming an interest rate of 5%? A) $80,000 B) $100,000 C) $1,800,000 D) $2,000,000 E) None of the above. Questions 8 and 9 share the following setup: Suppose the city of Victoria taxes each renter $300 at the end of each year and burns the revenues in a large bonfire (assume no one gets any benefit from the bonfire and that this policy is expected to continue forever). The annual interest rate is fixed at 5%. Assume all properties in Victoria have one residential rental unit in them and that the supply of housing is fixed. 8) What would you expect would happen to annual rents in Victoria in equilibrium? Assume people can choose to live elsewhere. A) They would fall by $300. B) They would rise by $300. C) They would remain the same D) They would fall to $0. E) None of the above. 3

4 9) How much should property values in Victoria change as a result of this policy? A) They would rise by $9000. B) They would fall by $9000. C) They would rise by $6000. D) They would fall by $6000. E) None of the above. 10) In a monocentric city, the office bid-rent slopes down due to I. travel costs by workers that are paid for by the firm. II. commuting costs by workers that are paid for by the workers. III. factor substitution A) I only. B) II only. C) III only. D) I and III only. E) I, II and III. 11) Suppose that the only thing influencing the shape of the residential bid-rent is commuting costs and that there is no consumer substitution and no factor substitution in the housing market. The residential bid-rent will be I. Downward sloping and linear. II. Downward sloping and concave (decreasing at an increasing rate). III. Downward sloping and convex (decreasing at a decreasing rate). A) I only. B) II only. C) III only. D) I or II only. E) I or III only. 4

5 12) Causes of suburbanization in North America after World War II include I. The rise of cars and highways. II. Changes in technology of transport and production in manufacturing. III. Changes in communications technology in the office sector. A) I only. B) II only. C) III only. D) I and II only. E) I, II, and III. 13) Policies that could help to reduce sprawl include I. Lowering gas taxes. II. Restricting development at the periphery, and encouraging development at the core (for example, Smart Growth ). III. subsidies. A) I only. B) II only. C) III only. D) II and III only. E) I, II and III. End Section 1. Section 2: Short Answers Use well-labeled diagrams in your answers below 5

6 1) 12 points total Consider a monocentric city whose land use is denoted in the diagram below. Bid-Rent ($) City edge Distance from center a) (6 points) On the diagram above, clearly mark the land-use pattern in this city along the x-axis. Denote which area of the region will be rented by business, which area will be rented by residential users, and which will be occupied by farmers. Clearly denote the urban fringe (the edge of the city). Note that explanations were not required to get full credit. These explanations are included to clarify my drawings. The solid brackets denote the original,, and zones. Note that the agricultural zone does not end it extends infinitely out from the edge of the city (where residential land turns into farmland). 6

7 b) (6 points) On the diagram above, illustrate the effect of a gasoline tax implemented in the local area, which is redistributed lump sum (everyone in the area receives an equal share of the revenue, regardless of how much they drive). Assume the gas tax only affects the residential bid-rent. Also, assume that all three types of land users are present in the city in the new equilibrium. Clearly denote,, and zones of the city after the gas tax is introduced. The dashed residential bid-rent curve denotes the bid-rent after the gas tax and lumpsum redistribution are implemented. The dashed brackets denote the new,, and zones. The tax raises the price of gas which raises the per km cost of commuting (thus steepening the residential bid-rent). The redistribution gives everyone some extra income (more than enough to compensate for the gas tax for locations near the city center; less than enough to compensate for the gas tax for locations far from the city center). 2) 6 points total Consider a monocentric city whose land use is denoted in the diagram below. 7

8 Bid-Rent ($) Distance from center Now consider the introduction of Uber (a taxi service with self-employed drivers) to a city. Assume that residents don t use Uber to commute to work, but that businesses (assume these are office firms) use Uber to get their employees from meeting to meeting. Assume that Uber lowers travel costs of these office firms. Also, assume that all three types of land users are present in the city in the new equilibrium. Illustrate the effect of the introduction of Uber using the above diagram. Clearly denote the Office,, and zones before and after Uber is introduced. Note that Uber lowers costs of firms getting workers to meetings. Firms do business all through the business district (and possibly throughout the city), so the lower travel costs will raise firms pre-rent profits at all locations (including right at the center). Note the flattening of the curve, which results from the lower travel costs. This is because locating further from the center lowers pre-rent profits less when travel costs per km are lower. 8

9 3) 6 points total Consider a monocentric city whose land use is denoted in the diagram below. Bid-Rent ($) Halfway point of original residential zone Distance from center On the diagram above, illustrate the effect of a road widening project that works in the following way: Highways that take commuters from the edge of the city (and that extend well out into farmland) are widened. The widening allows traffic to move more quickly over the widened parts of the highways, which lowers the time cost of commuting. But the highway widening only extends from the east side of the diagram halfway into the current residential zone. From that halfway point inward (toward downtown), roads remain at their current capacity (width). Traffic continues to move toward downtown on the old narrower roads at the same pace as before. Assume the road widening only affects the residential bid-rent. Also, assume that all three types of land users are present in the city in the new equilibrium. Clearly denote,, and zones of the city before and after the road is widened. 9

10 The widening lowers commuting costs (due to decreased congestion) from where the road widening begins, all the way out into the agricultural zone. This is represented by the flatter residential bid-rent curve after the halfway point of the original residential zone. This has no effect on the business district, but it widens the residential district and causes the city edge to move outward, as residential use encroaches on what was originally agricultural land. End Section 2 End of Exam 10