LAND USE in the MONOCENTRIC CITY

2. LAND USE in the MONOCENTRIC CITY

3. Monocentriccity: Coredominatedcity • Thekeyfeature of themonocentriccity: Heavyconcentration of employment in thecentralcorearea. • Today’smostmediumsizedcitiesaremonocentric. • However, in thetypical modern city, employment is not concentrated in thecentralarea but insteaddistributedthroughoutthemetropolitanarea, withlargefraction of employment in thesuburbanareas.

4. Ourfocus: Land use in thecentralbusinessdistrict(CBD). Wewillconsider, factories, officesandhouseholds. Wewillworkwiththebid-rentfunctions: • Bidrent of factories (manufacturers) • Bidrent of offices • Bidrent of households

5. Bid-rent of manufacturers: • Fixedfactorproportions: Assumption:Manufacturersproducedoorsandthesefirmshavethefollowingproperties: • Eachfirmusesoneacre of landand $Cdworth of non-landinputs (Labor, capitalandmaterials). • Price of doors (Pd) is fixed. • Competitivemarkets. • Doorfreightcostsfromfactorytothecentral terminal node: $td.

6. Question: How much a door firm willing to pay for an acre of land? Firms prefer to locate near the railroad terminal to increase their potential profit. Hence, profit is a function of distance from the terminal (u). d (u)= Pd. D-Cd-td.D.u-Rd(u) Since door market is perfectly competitive, competition for land will drive up the price of land where economic profit =0.

7. This means, price of land is equal to: Pd. D-Cd-td.D.u After a firm uses its revenue to pay for its input suppliers, the landowner gets whatever is left. This is called the “left-over principle”. If a particular firm offers to pay a landowner less than the entire gap between total revenue and total non-land costs, the landowner could find another firm to outbid the first firm. Left-over principle results form this competition between potential land occupants. If we set d (u)= 0, and solve for rent, we get the bid-rent for land by the door industry. Rd(u)=Pd. D-Cd-td.D.u

8. Bid rent for fixed input proportions technology

9. E.g. Each firm produces 50 doors (D) using 1 acre of land and $1000 worth of non-land inputs. If price of doors is $60 per unit and unit freight cost (td) is $4 per unit, what is the bid rent for this firm? Rd(u)=(60)(50)-1000-(4)(50)(u) Bid rent depends on the distance from the terminal (u). Slope of the bid rent function: -td.D=-(4)(50)=-200. Under the assumption of fixed factor proportions, we obtain a linear bid-rent function. Bid rent with fixed factor substitution 2000 Distance from the central node

10. Is fixedfactorproportionsassumptionrealistic? No… Mostproductionprocessesareflexible, firms can substitutenonlandinputsforland. Withvariablefactorproportions, firms can adjusttheircosts. 2. Flexiblefactorproportions: Forsuch a firm, weshould define theprofitfunction as follows: d (u)= Pd. D-Cd(u)-td.D.u-Rd(u).Td(u) Td(u)= Amount of landused Bidrentforlandbecomes: Rd(u)=(Pd. D-Cd(u)-td.D.u)/Td(u) Factorsubstitutionincreasesprofitsandaccordingtotheleft-overprinciple, higherprofitstranslateintohigherbidrentsforland.

12. Flexible bid-rent function lies above the inflexible bid rent function for all locations except u=7. At that distance same factor proportions are used. Flexible bid-rent function is convex due to factor substitution. By factor substitution, the firms will generate savings in both transportation costs and production costs. As we approach to the export node, bid-rent curve becomes steeper. Who will occupy the land? Flexible or inflexible firms? Since flexibility translates into lower production costs, higher profits and a higher bid rent for land which, flexible firms will occupy the land. Flexibility also brings efficiency.

13. Bid-rent of officefirms: Office firmsprovide a variety of goodsandservices but theysharetwoimportantcharacteristics: • Theygatherandprocessinformation. • Office firmsrely on face-to-facecontact in thisprocess. E.g. Loanofficers of banksmeetwiththeirprospectiveborrowerstoappraisetheircreditwothiness. Investmentadvisors of firmsmeetwiththeirclientstoassesstheirattitudestowards risk andtheirinvestmentinclinations.

14. Supposethatofficefirms in thecityprovidefinancialservices. Theindustry has thefollowingcharacteristics: • Eachfirm is based in an office. Output : Financialconsultations, echfirmproduces F consultationspermonth. • Eachconsultationrequires 1 tripfromofficetocitycenter. • Pf (consultationprice)is fixed. • Nonlandproductioncost of theoffice = Cf(u). Itvarieswiththeprice of landand u (distancetothecitycenter). • Travelcost of a financefirm: Opportunitycost of workers’ travelbetweenofficeandclients in thecitycenter. tf.W.F.u= Travelcostfor a location u blocksawayfromthecitycenter. tf: Minutestowalk 1 round-tripblock, W: wage/minute

15. f (u)= Pf. F-Cf(u)-tf.W.F.u-Rf(u).Tf(u) Usingthezeroprofitcondition, bidrentforlandbecomes: Rf(u)=(Pf. F-Cf(u)-tf.W.F.u-Rf(u))/Tf(u) Onlydifferencefromthedoorcompany is aboutthetransportationtechnology. Transport costper mile of financefirmdepends on theopportunitycost of thefirm’sworkers (wage). Convexandnegativelyslopedbidrentfunction.

16. Residential Land Use Assumptions: • Onemember of eachhhcommutesto a job in the CBD. • Noncommutingtravel is insignificant. • Publicservicesandtaxesarethesame at alllocations. • Airquality is thesame at alllocations. • Allhouseholdshavethesameincomeandtastesforhousing. • There is a monetarycost of commuting but no time cost; theopportunitycost of commuting time is zero.

17. According to the left-over principle , the bid rent for residential land equals the excess of total revenue of housing producers over total cost. • Hence, we can first talk about the revenue side of the housing market. • Price of housing decreases as we move away from the city center. • We will consider two cases: No consumer substitution for housing and consumer substitution for housing. (i) No consumer substitution for housing: P(h)= Price per square foot of housing per month The housing price function indicates how much a hh is willing to pay per square foot for dwellings at different locations in the city.

18. Assume that this hh has a fixed budget of $300 per month to spend on housing and commuting. Monthly cost of commuting is $ 20 per mile per month. How much is the hh willing to pay for dwellings at different locations in the city? $ 0.30 Housing-price function Miles to city center 15 The linear housing-price function indicates that city’s dwellings are identical; everyone lives in a 1000 sq-foot house regardless of the price of the housing. Only distance form the center matters.

19. The equilibrium housing-price function makes residents indifferent among all locations because differences in commuting costs are exactly offset by differences in housing costs. A move of u miles toward the city center generates benefits and costs: • Benefits: Commuting costs decrease by the change in the distance times the commuting cost: -th. u • Costs: Housing costs increase by the change in the price of housing consumption: Ph. H • Household will be indifferent if: -th. u= Ph. H

20. (ii) Consumersubstitutionforhousing: Ifthehousingconsumptiondepends on price (morerealistic); hhswillconsumesmallerhouseswhenprice is higher. As consumermovestowardthecitycenter, it pays a higherpriceforhousingand it occupies a smallerdwelling. As relativeprice of housingincreases, hhssubstitutenonhousinggoodsforhousing (e.g. Entertainment, restaurantfood, etc.). Assumedconsumptionpattern:

21. Ph/sq mile Price function without consumer substitution Price function with consumer substitution 0.06 Miles to city center 12 Now, the trade off between commuting and housing costs becomes: -th. u= Ph. H(u) Slope of the housing function becomes:

22. Residentialbid-rent: Residentialbidrentindicateshowmuchhousingproducersarewillingto pay forland at differentlocations in thecity. Accordingtotheleft-overprinciple, housingproducerswill pay landrentequaltotheexcess of total revenueover total costs. Assumethathousing is producedwithfixedproportions. Eachfirmproduces Q sq. feet of housingusing 1 acre of landand $K worth of capital. Whenthebuilding is complete, it can be used as either a singledwellingordividedinto x units , witheachlivingspaceequalto Q/x.

23. h (u)= Ph(u).Q-K-Rh(u) Rh(u)= Ph(u).Q-K $ TR=Ph(u).Q Cost of non-land inputs (K) Bid rent function Miles to city center u* Since, price of housing declines as distance increases, TR is downward sloping.

24. What happens if we relax the fixed factor proportions assumption? • This means housing producers substitute K for land through building houses closer together or taller apartment complexes. E.g. Mavişehir, Güzelyalı. • This decreases production costs and allows housing firms to pay more for land. • Result: Bid rent function becomes more convex. • Population density becomes higher in the central city.

25. Land Use in the Central Business District

26. IncomeandLocation: Inmanydevelopedcountries, recently, thewealthytendtolocate in thesuburbsandthepoortendtolocatenearthecitycenter. Averagehouseholdincomeincreases as wemoveawayfromthecitycenter. However, themostexpensiveland is nearthecitycenter. Is thislocationpatternpuzzling? Whyshouldpooroccupythemostexpensiveland?

27. The answer lies in the “theory of income segregation” developed by Alonso (1964) and Muth (1969). • This theory suggests that: “Central locations provide the best trade-off for the poor, while suburban locations provide the best trade-off for the wealthy”. • E.g.

28. Housingprice Housing price function If a high income hh consumes 2000 square feet of housing, a move from city center to 1 mile out saves $ 240 (0.12 x 2000=240) MB of moving decreases as distance increases. Commuting cost of moving 1 mile from the center: $ 40. Optimum location: MB=MC: 6 miles from the city Distance from the city center

29. If low income hh consumes 200 sq feet of housing, MB=MC occurs 2 miles away from the city center. Why is this difference between the optimum location of wealthy and poor? If wealthy hh receives an income four times the poor and if the wealthy has a house consumption 10 times the poor ( 2000 sq feet and 200 sq feet); if commuting costs of wealthy is two times the poor (40 vs. 20)… These indicate that income elasticity for housing is greater than income elasticity of commuting cost. This means, the gap between the benefit curves is greater than the gap between the cost curves.

30. Wealthy hhs live farther from the city center. This is the traditional explanation for the pattern of income segregation. MBw MBp MCp MCw 6 2 Distance

31. IncomeandResidentialBidRentFunction Incomesegregation can also be explainedwiththehousingpricefunctionandtheresidentialbidrentfunction. Weknowthattheactivitywiththesteeperbidrentfunctionoccupiesthelandclosertothecitycenter. Slope of thehousingpricefunction in thesimplemonocentric model:

32. An increase in income increases both oppotunity cost of commuting (th) and housing consumption (H). Hence, increase in income has an ambiguous effect on the slope of housing-price function. If income elasticity of housing is greater than income elasticity of commuting cost, then rich will have a flatter houing price function and a flatter bid-rent function. Land rent Poor occupy the land less than u* miles away from the center. Bid rent function of the poor Bid rent function of the rich Distance from the city u*

33. An alternative explanation of income segregation suggests that the slope of the residential bid rent function is affected by other factors: Problems of the central city (pollution, crime, inferior education, etc.) decrease the slope of the bid rent function. If the income elasticities of demand for safety, clean air, eduction are relatively large, bid rent function of wealthy hhs will be flatter than the bid rent function of poor hhs. In other words, if wealthy are willing to pay much more than poor for safety, clean air, superior education, welathy will outbid poor hhs for land in such areas.

34. Policy implications for income segregation: • A housing policy that encourages renovation of the central city housing stock may cause some high-income hh to return to center. • Polices that decrease poverty decrease crime rate, reduce fiscal problems, etc. Which encourage high-income hh to live in central city. • Policies that control exclusionary zoning allow poor to move to suburbs.