Measuring Land Use Benefits in Auction Markets Francisco Martínez University of Chile European Transport Conference Cambrigde 2001

Economic context The urban land market –Multiple consumers: residents and firms –Multiple location attributes –Location externalities –A variety of zone-building options –Auction market: imperfect competition –Market equilibrium analysis Measures of benefits of land use changes –Regulations –Transport projects

Modelling Consumers’ behaviour Indirect & conditional utility p: exogenous price for z yielding U Max value for z to achieve U Compensated demand Expenditure funtion

Auction markets: linear marginal utility of income Location prices are endogenous: highest bid Def. auction equilibrium : Thus for More... Theorem 1:

Proof: From Roy’s theorem and demand =1: In E : Variation in U: Variation in z:

Interpretation Since: in the auction market prices are always the WP for the final consumer for two identical consumers in (I,  ), these endogenous prices are different at different sites, but utility is the same Then, such prices HAVE to comply with theorem 1; other prices do not. Theorem 1:

Consumers’ WP function doubly linear Theorem 2: within E, WP is doubly linear, in I and U Follows from comsumption of one unit and Roy’s Theorem under Theorem 1 then

Measuring consumers’ surplus The classical measures: for (p,z,U) at equilibrium p=WP Notice U 1

Measuring total benefits Total Benefit = Consumers’ + Producers’ surplus Change in WP caused by changes in built environment Obs.: 1) extenal conditions 2) location externalities, agents interacction For a given location:

Summary Urban market characteristics: One location WP linear in I + Auction market....WP linear in U WP is doubly linear Income variation EV=CV=CS Total benefits measurable from WP values

Some implications Total benefits are change in WP valued at constant U, or change in U plus change in rents, or change in consumers value of built environment. They are NOT equal to change in rents

Application: building & land supply consumers clusters Logit auction model (short term) Auction best bid rule All agents are allocated z vi bhbh

Land use benefits Consumers’ surplus Producers’ surplus