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- 1. Geography/Planning 379 “Urban Growth & Development” Lecture 7: Urban Rent and Land Use Theory 1. von Thünen’s Agricultural Land Use Theory 2. The Concept of ‘Economic’ or ‘Bid’ Rent 3. Graphing Bid Rent Lines 4. The Negative Exponential Rent Gradient 5. Urban Land Uses and Bid Rents 6. Amenity versus Location Rent Reading: Required: Textbook, Ch. 6, pp. 147-148 Optional: Cadwallader PROJECT 1 DUE TUESDAY 12:30 “It makes all the difference whether one sees darkness through the light or brightness through the shadows.” – David Lindsay
- 2. von Thünen’s Agricultural Land Use Theory • Modern urban rent theory based on: agricultural rent theory as formulated by Johann Heinrich von Thünen • His 1826 book: The Isolated State • Basic idea: Agricultural uses conform to predictable patterns around cities, which are the markets for the farm goods • Those goods with greatest demand and having the highest transport costs should be produced closest to the city
- 3. von Thünen’s Agricultural Land Use Theory • Where does milk come from? Top three dairy states: 1. Wisconsin 2. California 3. New York • Why does milk have high transport costs? “Perishability”
- 4. Definition: economic rent or bid rent The monetary return a farmer can receive for growing a particular crop on a unit of land after all the costs of production (including transportation to the market) are taken into account.
- 5. The Concept of ‘Economic’ or ‘Bid’ Rent • Farmers responsible for hauling produce to market – so economic rent higher for land closer to the city – lower for land farther out • Economic rent: highest price farmer could pay for land and break even growing a particular crop: the maximum rent that could be paid to grow a crop • So it is sometimes called: bid rent • The land may or may not be put into the use depending on whether another use can bid more for the parcel of land. • Extensive agriculture (example photo: Wheat farming) • Intensive agriculture (example photo: Rice paddies)
- 6. Let’s graph some hypothetical bid rents! Corn: PC = Market Price = $100 (for amount grown on a unit of land – e.g., one acre) SC = “Spatially Invariant” Costs = $50 (for seed, fertilizer, labor, harvesting…) Graphing Bid Rent Lines 0 10 20 4030 50 60 70 80 90 100 X, Dist from Mkt (Miles) Ri(X) Bid Rent $0 $20 $40 $60 What’s the Bid Rent right next to the Market? Rc(x) = PC - SC = 100 - 50 = $50 Assume transporting corn costs 50 cents / mile What’s the Bid Rent 10 miles from Market? 100 - 50 – (10 x .50) = $45How far out will it be where Bid Rent is equal to zero? 100 - 50 - .50 Xmax = $0 50 = .50 Xmax Xmax = 100 miles We can now draw in the Bid Rent Line for Corn… Assume tomato transport costs $1 / mile Tomatoes: PT = Mkt Price = $150 ST = S.I. Costs = $75 Point of Intersection Tomatoes outbid Corn Corn outbids Tomatoes Tomato Land Corn Land
- 7. The Predicted Land Use Pattern and the Negative Exponential Rent Gradient • What would a land use map of our two-crop example look like? • But what if there are other competing land uses? Margin of Cultivation Market City Tomatoes Corn Dairy Grapes Grazing “Marlboro Country”
- 8. The Predicted Land Use Pattern and the Negative Exponential Rent Gradient • With more and more competing land uses, what does the actual overall rent gradient look like? • Rent gradient shows the declining value of land as you go away from the city; land being used for the “highest and best use” • It is the upper envelope of the bid rent lines for all competing land uses • The gradient takes on a negative exponential form: decreasing with increasing distance, but with a decreasing slope. • In 3-D: It looks kind of like a one-pole circus tent! Ri(X) X R*(X) = R0 e-bX
- 9. Urban Land Uses and Bid Rents • Urban translation of the definition: ‘Economic’ or ‘Bid’ Rent The monetary return a developer can receive for developing a particular land use (e.g., apartment buildings, office complex, shopping center, single-family homes) on a unit of land after all the costs of development are taken into account and including the willingness of renters/buyers to pay for the level of accessibility provided by the location Office Buildings Multi-family Residential (Apartments) Single-family Residential Agriculture Bid Rent X (Dist from CBD Center) Edge of the Urbanized Area
- 10. Urban Land Uses and Bid Rents • The basic von Thünen-style urban economics model describes a monocentric city, such as during the omnibus, horsecar, and streetcar suburbs eras • Urban areas now polycentric: distance to multiple centers matters • What would a polycentric bid-rent land use map look like?
- 11. Amenity versus Location Rent • How are rents actually determined in the ‘real world’? • Let’s take the case of y’all’s slumlords (or slumladies) • How do they go about figuring out how much they can gouge you for? Rent = ‘Location Rent’ + ‘Amenity Rent’ • Location Rent: Based on accessibility and supply and demand factors • How do supply and demand fit into the basic bid rent framework? • Amenity Rent: Amenities may be site-specific or externalities; externalities can be positive or negative
- 12. Practice Bid-Rent Problem These are the bid-rent functions for single-family residential land use, R S(x), and multi-family residential land use, RM(x), where x is the distance from the center of the CBD in kilometers: R S(x) = 20,000 – 2,000 x RM(x) = 160,000 – 30,000 x Where would we expect to find the boundary between multi- and single-family residential land use? (A) At x = 0 km (D) At x = 5.333 km (B) At x = 2 km (E) At x = 10 km (C) At x = 5 km Solution: Set R S(x) = RM(x) and solve for x… 20,000 – 2,000 x = 160,000 – 30,000 x 28,000 x = 140,000 x = 140,000 / 28,000 >>>> x = 5 km
- 13. These are bid-rent functions for single-family residential land use RS(x) and multi-family residential land use RM(x) where x is the distance from the center of the CBD in kilometers: RS(x) = 20,000 – 2,000 x RM(x) = 160,000 – 30,000 x Suppose Agricultural land use can pay $2000 per unit of land regardless of how far out it is from the center : R A(x) = 2,000 Find the distance xmax where we would expect to find the outer edge of the urbanized area. Show your work! POP QUIZ Name ____________________
- 14. QUIZ SOLUTION. These are bid-rent functions for single-family residential land use R S(x) and multi-family residential land use R M(x) where x is the distance from the center of the CBD in kilometers: R S(x) = 20,000 – 2,000 x RM(x) = 160,000 – 30,000 x Suppose Agricultural land use can pay $2000 per unit of land regardless of how far out it is from the center : R A(x) = 2,000 Find the distance xmax where we would expect to find the outer edge of the urbanized area. Show your work! 150,000 100,000 50,000 0 0 2 4 86 109 RS(x) = RA(x) 20,000 – 2,000 xmax = 2,000 18,000 = 2,000 xmax xmax = 18,000 / 2,000 = 9 km

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