424 THE AMERICAN ECONOMIC REVIEW costs but there is a pertinent observation about the relationship between a given area and the cost of externalities that seems s Tt i that thes costs will rise r in proportio t I shall argu now that a much natural premise rise more rapidly-perhaps roughly as the square of the number of inhabitants.For exam ple.consider the amount of dirt that falls into the house of a typical urban resident as a result of air pollution,and suppose that this is equal to n where is the number of residents in the area.Since the number of homes in the area, an,is also roughly proportionate to population size,total domestic soot- fall will be e soot per home times number of homes=kat akn2.Similarly if dela cro ded ad a 01 0, the nun of vehicles tra versing it,the to al nun an hour lost thereby will increase roughly as n,since the numbe r of passengers also grows roughly as the number of cars.The logic of the argument is simple and perhaps rather general:if each inhabitant in an area imposes external costs on every other,and if the magnitude of the costs borne by each individual is roughly proportionate to population size (density then since these costs are borne by each of the n persons involved,the total e rnal costs will var not in wvith a but with O eI do no ntain t such a re iversal or that it is ever satisfied more than approximately. am sugge that,typically,increases in population size may plausibly be expected to produce disproportionate increases in external costs-thus pressures on the municipality to do something about these costs may then grow cor- respondingly. 7.Cumulative Decay and Dynamic Pareto Optimalily Economic theory indicates yet another source of mounting urban problem are the of cu e urban set in motion ind ce ma ters t 0 rom Ito wo se.Sinc I have cussed these elsewhere can illustrate the central proposition rather briefly.Public transportation is an important example.In many urban areas with declining utilization,frequency of service has been sharply reduced and fares have been increased.But these price rises have only served to produce a further decline in traffic,leading in turn to yet an- other deterioration in schedules and another fare increase and so on,ap. ntly ad.More important.perhaps.is the logic of the con sons who a would ish to Apparently remain in the city ar drive deter rising c ng nu neighborhoods,etc.Once agai the e individu Is're community's problems and each feeds upon the other.Those who leave opyright 2001 All Rights Reserved