Determining Urban Land Rent and Land Use Patterns

1. Chapter 6 Urban Land Rent

2. Purpose • We study how land is allocated among the different possible uses. • We explore the market forces that determine land use pattern.

3. Land Uses • Competing land uses: • Agriculture • residential • Manufacturing • Office • For each of these uses, there is a maximum willingness to pay (WTP) in return for using the land

4. How is land rent determined? • WTP for each use is determined by how much money can be earned by using the land. • Land will go to the highest bidding use or sector. • Due to competition, WTP for land drives profit to zero.

5. Definitions • Land rent: periodic payment from user to owner • Market value: amount paid to take ownership • In our discussion, we use the term “price of land” to refer to land rent, which is a periodic payment

6. Bid Rent • Bid rent is the amount that buyers are willing to offer land owners as rent for a unit of land. • Due to competition between buyers bid rent adjusts so as to drive profit to zero. • To calculate bid rent we use the left over principle . We need information about revenue and costs. • David Ricardo (1881) the price of land is determined by its fertility

7. Example: Agricultural land • Consider two types of one acre land: high fertility and low fertility. The price of corn is $10 Variation in land fertility generates variation in bid rent The bid rent equals the willingness to pay for land since competition between farmers drive profit to zero.

8. Bid-Rent for Manufacturing • Desirability of urban land for manufacturing is based on its accessibility. • Land closer to highways more desirable • Maximum WTP for a lot large enough for production facility = Total revenue - non-land costs • Bid rent per hectare = WTP / lot size

9. Manufacturing Bid Rent The firm’s freight cost is $20/ mile Variation in freight cost generates variation in bid rent

10. Manufacturing Bid Rent Curve The difference in land rent drives profit to zero and makes firms indifferent between all locations The Bid rent curve shows willingness to pay for land as a function of distance from highway.

11. Information Sector • For the City’s Office Sector: • firms gather, process, and distribute information • Face time required in information exchange • High opportunity cost of office workers • Travel for Information Exchange

12. Central Business District A B C D E F G

13. Travel Distance for Information Firms Travel distance increases at an increasing rate The median location minimizes the travel distance

14. Office Bid Rent • We can calculate the bid rent using the left over principle.

15. The bid rent curve is concave because travel cost increases at an increasing rate The bid rent curve is downward sloping because as we move away from the center the cost of travel for information increases Since travel cost increases at an increasing rate, to maintain profit at zero bid rent has to decrease at an increasing rate

16. Bid-Rent with Factor Substitution • Since the price of land increases near the center, people will economize on the use of land • They use less land space and build tall buildings and thus expanding upwards • Tall buildings requires capital to hold the units on top of one another • Thus people can substitute between land and capital.

17. Bid-Rent with Factor Substitution • Given land rent and capital price, people choose the building height that minimizes cost • Example: 4 units of office space

21. Bid-Rent with Factor Substitution • Substituting between land and capital saves on building cost. • This leaves firms with positive profit. • However, competition and free entry imply that profits will be driven back to zero • This takes place as bid rent increases.

22. Capital cost increases to 250, but you only need 0.04 hectares Convex Bid-Rent Assume that at x=5, the medium building is optimal The savings in cost raise profit. The higher profit in turn will raise the bid rent to …….. At x=1, land rent is high so the tall building is most efficient, i.e. costs less.

23. Housing Market • Model focuses on commuting as key location factor: • Monetary (not time) cost of commuting • One member of household commutes to an employment area (CBD or manufacturing area) • Non commuting travel insignificant • Identical public services, taxes, and amenities

24. Housing Price Curve A household has a fixed amount to spend on housing and commuting. Houses are available in standard dwellings of 1000 sq ft. The cost of commuting is $50/mile per month How much ? The house price is defined as price per sq ft

25. The slope of the housing price curve • Can you derive the slope analytically?

26. Housing price with substitution With factor substitution the housing bid rent curve will be convex as shown before Since land price is more expensive near the city center, the household consumes less housing

27. Land Use Patterns • We can use the bid rent curves of different land users to determine a city’s equilibrium land use pattern. • Three sectors compete for land: manufacturers, office firms and residents.

28. Land Use Patterns • Features of urban transportation system: • Manufacturers use trucks to transport output through highways • A highway goes through the center of the metropolitan area and a belt way • Residents work at the office sector and the manufacturing firm travel by automobile.

29. Bid Rent for the office sector

30. Bid Rent for Manufacturing Sector

31. Bid Rent for Employers

32. Land Use Patterns