16Part1MarketForcesin theDevelopmentof CitiesTABLE2-2 SpecializationandGainsfromTradeNorthSouthBreadShirtsBreadShirts-2+6+2-2Change in productionfrom specialization+2-4-2+4Exchange 4 shirtsfor2 loaves00+2+2Gain from tradeswitching two hours from shirt to bread production.Thefirst row shows the changesinproduction:-2loavesand+6shirtsforNorth;+2loavesand-2shirtsforSouth.As shown in the second and third rows,if the households exchange two loaves andfour shirts, each has a gain from trade of two shirts. After specialization and ex-change,each household has just as much bread as before and two additional shirts.What abouttransactioncosts?Thetransactioncost is theopportunitycostof thetime required to exchange products and is equal to the amount of output that couldbe produced during that time. For example,a North household can produce six shirtsper hour,so the opportunity cost for a 10-minute (1/6hour)transaction is one shirt.In this case,the net gain from trade is the gross gain of2 shirts minus the transactioncost of I shirt, or a net gain of one shirt. As long as the transaction time is less than1/3hour(twoshirts),tradeisbeneficial foraNorthhousehold.TheSouthhouseholdwithlowerproductivityandthus aloweropportunitycost,hasalowertransactioncost.Forexample,iftheopportunitycostis1/6hour,thetransactioncostis1/6loafofbread,andthenetgainis2shirtsminus1/6 shirt,or11/6loaves.ForaSouthhousehold, the threshold transaction time is 2 hours (2 loaves of bread).ScaleEconomiesinExchangeThe presence of specialization and trade will not necessarily cause a cityto develop.The second assumption of the backyard-production model is that there are constantreturns to scale in exchange.Under this assumption, an individual household is justas efficient in executing trades as a trading firm,so there is no reason to pay afirmto execute an exchange.Therefore,each North household will link up with a Southhousehold to exchange shirts andbread directly,without intermediariesTrading firms will emergeif there are economies of scale associated with ex-change and trade.Recall thefourth axiomofurban economics:Productionis subjecttoeconomies of scaleA trading firm could use indivisible inputs such as a large truck to transport outputbetween North and South.Similarly,workers who specialize in transportation taskswill be more efficient in transporting goods than workers who spend most of theirtimeproducingbreadorshirts,Ingeneral,becausetradingfirmshavelowertransac-tion costs, individual households will pay trading firms to handle exchanges.The emergence of trading firms will cause the development of a trading city.Tofully exploit scale economies,trading firms will locate at places that can efficientlycollect and distribute large volumes of output.The concentration of trade workerswill bid upthepriceof landnear crossroads,river junctions,andports.The increase
Chapter2WhyDo Cities Exist?17in thepriceof land will cause peopleto economize on land by occupying smallerresidential lots.Theresult is a place with a relativelyhigh populationdensityacityTRADINGCITIESINURBANHISTORYOur simple model of the trading city suggests that trading cities develop when com-parative advantage is combined with scale cconomies in transport and exchange.This observation provides some important insights into the history of cities beforethe Industrial Revolution of the 180Os. Most of the workers in these trading citiesdidn't produce goods,but instead collected and distributed goods produced else-where,such as agricultural productsfrom thehinterlands and handcrafted goodsfrom various locations.Trade was a risky business, and firms in the trading cityprovidedinsurance,credit,investmentopportunities,banking,andlegal services.TradingCities inWorldHistoryTrading cities have a long history. In the third millennium B.C., Phoenicians usedfast sailing ships to serve as traders for the entire Mediterranean basin,trading dye,raw materials,foodstuffs,textiles, and jewelry.They established trading cities alongthe Mediterranean coast in present-day Lebanon.Around 500 B.C.,Athens was athriving siteforregional trade,exchanging household crafts and oliveproducts forfood and rawmaterials from the countryside.During the1lthand 12th centuries,Italian city-states forged agreementswiththeByzantineand Islamicrulers fortradewith North Africa and the East.The Europeans traded wood, iron,grain,wine, andwool cloth formedicines,dyes,linen,cotton,leather,andprecious metals.Thistrade was the major force behind the growth of Venice, Genoa, and Pisa.Some cities were built on coercive transfer payments rather than voluntarytrade.TheAthenianempiredevelopedintheaftermathof thesuccessful waragainstPersia inthefifth centuryB.C.AftertheGreek city-statesrepelledthePersianinva-sion,theyformedtheDelian Leaguefor jointdefense and laterto carrythe war intoAsia Minor.By the end of the successful campaign,Athens controlled the leagueand transformed the voluntary contributions ofmember city-states into payments oftributetoAthens.The system of homageand tribute led tothePeloponnesianWarbetween theAthenian Empire and Sparta(431to 404B.c.).The war ended whenAthens renounced control over its empire and demolished its defensive walls.Bythethird centuryA.D.,RomehadapopulationexceedingImillion.TheRo-mans establishedcolonial citiesthroughoutEurope and focused on collecting theagricultural surplus while they neglected urban production activity (Hohenberg andLees, 1985).Instead of exchanging urban goods for agricultural products, Romeused conquest and tribute to feed its population.In thefourth andfifth centuries,at-tacksfromGermanictribesdisruptedtheRomancollectionsystem.Itappearsthatthere was little interest outsideof Romeinrestoring the“trade"routes,sothe lossesfromsuccessiveattackswerecumulative.IfRomehadreliedtoagreaterextentonvoluntary exchange, the colonies would have had a greater stake in maintainingtheexchange network and the Western empire might haverecovered from the Ger-manic raids.What are the lessons from the rise andfallofAthens and Rome? Early in its his-tory,Athensthrivedundera systemofvoluntarytradewithotherareas,exchangingurbangoodsforfood fromthe countryside.TheAthenians eventually switchedtoa
18Part 1Market Forces in the Development of Citiessystem ofconquest and tribute,resulting in war and thedecline of the city.Mumford(1961)suggests that the city of Rome should have been called"Parasitopolis"toindicate its dependenceon the labors ofoutsiders.The decline of Rome was causedin part by the disruption of its collection system by the Germanic raids.Perhaps thelessonisthatcitiesbased on coercivetransferpaymentsarenotsustainable.Trading Cities inAmericanHistoryThe historyof urban America illustrates therole of transport costs and comparativeadvantage in trading cities (Bartlett,1998).In the 1700s, most cities served largelyas trading posts for ocean trade.On the eastern seaboard, cities collected agricultural products from their hinterlands to the west and shipped them overseas.Thevolume oftrade was limited by the dirt roads servingthe interior:Travel was alwaysslow and, in times of rain and melting snow, slippery.The Pennsylvania Turnpike,built with stone and gravel in 1792, increased travel speeds to a steady two milesper hour,increasing the market area and trading volume of the city of Philadelphia.Farther to the north,New York State took more drastic steps, completing the360-mile Erie Canal in 1825.The canal linked New York City,with its naturalharbor, to vast agricultural areas to the north and west, and it cut freight costsfrom about 20 cents per tonmile to1.5 cents.An additional canal connecting LakeChamplain to the Hudson River extended the market area of New York City tonorthern New England.Thevast transportation network increased the volume oftradethroughNewYork City,increasing its size.By185o,thecityhad apopulationofhalfa million,about 20 times its size at theendoftheAmerican Revolution.Othercities, including competitors to the south (Baltimore and Philadelphia), respondedbybuilding canalsto connecthinterlands andports,and by1845there wereover3,300milesofartificial waterways intheUnited StatesComparative advantage also plays a role in urban history.Eli Whitney's cottongin (1794)providedameans of removingthe sticky seeds ofgreen-seedcotton,which could be grown throughout the south.Thetotal output ofcotton increased byafactorof 50overa15-year period,withmost of the output comingfrom inlandareas far from the east coast ports.American cotton was transported along riversto New Orleans for shipment to textile firms in New England and Europe.Theincrease in cotton trade caused the rapid growth of New Orleans at themouth ofthe Mississippi,and the development of upriver commercial cities such as Mobile,Alabama,andNatchez,MississippiLater innovations in transportation reduced transport costs and contributed tothe developmentof trading cities.Beforethe introduction of the steamboat in 1807,traffic was strictly downstream: After cargo was unloaded at the terminal point,wooden boats were broken up for lumber.The steamboat allowed two-way trafficand cut river freight costs, increasing the volume of trade and the size of river cit-ies. Later, the steam engine was used to power locomotives, and railroad freightreplaced river shipping as the principal means of transporting goods.Between1850and 1890,theratioofrailroad freightto riverfreightwentfrom0.10to2.0,and thevolume of railroad freight increased by a factor of 240.The shift from river to rail-road caused the decline of commercial cities along rivers and the rise of cities alongthevast railroad network.AFACTORYCITYThe third assumption of the backyard-production model is constant returns to scale
Chapter 2 Why Do Cities Exist?19in production.We'llmaintain this assumption forbread production,but apply thefourthaxiomofurbaneconomicstoshirtproduction:Production is subject to economies of scaleAshirtfactorywill useindivisibleinputs(machines)andallowworkerstospecializeinnarrowlydefinedtasks,leadingtoahigheroutputper workerand loweraver-age cost.Suppose a houschold can produce either a loaf of bread or one shirt perhour.A worker in a shirt factory is six times as productive as a home worker, so thefactoryworkerproducessixshirtsperhour.DeterminingWages andPricesWe assume that workers are perfectly mobile, so the utility level of a city workermustbethesameastheutilitylevel fora rural worker.Recall the firstaxiom ofurbaneconomics:Prices adjust to ensure locational equilibriumAfactorymustpay its workers enoughtomakethem indifferentbetweenwork-ing in the factory city and in the rural area. Arural worker earns one loaf of breadper hour, so city workers must earn one loaf per hour plus an amount high enoughtooffset the higher costof living in the factory city,such ashigher land prices.Forexample,if the cost of urban living is 50 percenthigher,locational indifferencerequires an hourly wage of 3/2loaves ofbread.Acityworker will pay1/2loaf forland,leaving oneloaf perhouroffactorywork,thesamethatshecouldearnproducing bread in a rural area.What's the price of factory shirts? The price must be high enough to coverthe costs of laborand the indivisible inputs used to produce shirts.In Table 2-3thelaborcostperhouristhewage(3/2loaves)andthehourlycostofindivisibleinputsis1/2loaf.Addingthesetogether,thehourlycostofproducingshirts istwoloaves of bread.To translate this into a costper shirt,recall that afactoryworkerproduces six shirts per hour, so the cost per shirt is one-sixth of thecost perhouror2/6=1/3loaf.Therefore,forzeroeconomicprofit,thepricepershirtmustbe1/3loafofbread.Suppose there is a single shirt factory in the region.The factory competes withhomemade shirts,and will sell shirtsto anyhouseholdforwhichthe netpriceoffactory shirts is less than the cost of a homemade shirt.The cost of ahomemadeshirt is the one loaf of bread that is sacrificed to produce a shirt.The netprice of afactory shirt equals the price charged by the factory (1/3 loaf)plus the opportunitycostoftraveltoandfromthefactorytobuytheshirtTheMarketAreaof aFactoryCityFigure 2-1 (page 20)shows the net price offactory shirts and the market area of theTABLE2-3CostofFactoryShirt3/2loavesLaborcostperhourCost of indivisible inputs per hourV2loaf2loavesTotal costperhou13loafCost per shirt with 6 shirts produced per hour
20Part1Market Forces in the Developmentof Citiesshirt factory.As shown by pointfthe netpricefor a consumer located justacrossthe roadfrom thefactory (distance=O)is the factoryprice,cqual toV3=4/12loaf of bread.Other consumers bear atravel cost when theybuyfactory shirts,sothe net price is higher. Suppose the travel time is 1/12 hour per round-trip mile: Ittakes 1/12 hour to complete a round-trip of one mile in each direction.In an hour,a rural household can produce one loaf of bread, so in /12 of an hour of travel, itsacrifices 1/12 loaf.For example, at pointg (twomiles from thefactory),thenetprice of a factory shirt is 6/12 loaves,equal to 4/12paid at thefactoryplus 2/12 intravel cost (forgone bread production at home).The market area of the factory is the area over which it underprices the homeproduction of shirts. In Figure 2-1,the horizontal line shows the opportunity costof homemade shirts,which isoneloaf of bread.The net price of factory shirtsis 4/12 at the factory and inereases by 1/12 per mile, reaching one loaf at a dis-tance of eight miles(4/12+8/12).In other words,the factory underpriceshomeproduction up to eight miles away,so households within eight miles of the factorybuy shirts rather than producing them at home. Beyond this point, households areself-sufficient,producingtheirownbreadand shirts.Afactorycitywill developaroundtheshirtfactory.Workerswilleconomizeontravel costsbylivingclosetothefactory,and competitionforland will bidup its price.The higher price of land will cause workers to economize on land,leading to a higher population density.The result is a place of relatively highpopulation density, a factory city. Note that we have already incorporated thehigher land price into the factory wage and the factory price:Workers receive anhourlywage of 3/2loaves to covertheopportunity cost oftheirtime(1 loaf)andlandrent(1/2loaf).FIGURE2-1MarketArea ofFactoryNetpriceoffactoryshirtCost of homemade shirteain6/124/12180182Distance to factory (miles)Market area of factoryThe net price of a factory shirt is the factory price (1/3 = 4/12 loaf of bread) plustransport cost (1/12 loaf per round-trip mile).The market area of the factory is the areaover which the net price ofa factory shint is less than the cost of a homemadeshirt(one loaf)