Unformatted text preview: Econ 4621–1/22/04 Moncentric Model of the City • Explicit model of the internal structure of a city • Developed in 1960s by Alonzo and Mills • Monocentric structure is at odds with current structure of cities. But... • Can use the model to understand what changed • Model remains useful abstraction for understanding the interplay of important forces • Can use the model as a vehicle for understanding qualitative impacts of policy changes (e.g. urban growth boundaries ) • The building blocks of the model are very much alive in cutting edge research (e.g. Lucas and RossiHansberg, Econometrica, 2002) Model (corresponds to residential model in text, p. 177) • Land is line, CBD is at zero. • H is number of individuals. All are identical • All individuals work in the CBD • u a location, a distance u from CBD. • w is wage • t is commuting cost per unit distance, dollars per mile (so not in time units) • U (x, L) is utility function –x is widgets, nonland consumption –L is land consumption –Assume utility function has usual properties (e.g. quasiconcave....) • R is agricultural land value (in dollars) • p is price of a widget in dollars (exogenous) Equilibrium (rough, more detail later) • R(u): price of land at distance u from CBD • D(u): population density at u • Supply equal demand for land Consumer Problem • Consumer takes as given R(u) and p • Chooses u, x, and L to maximize utility
(u,x,L) max U (x, L) : such that px + R(u)L + tu = w • Two steps. (i) pick u (ii) given u, pick x and L • Goal of derivation. We get the following equation: R (u) = − or R (u) ∗ L(u) = −t MB = MC t L(u) Budget Constraint • px + R(u)L = w − tu • Graph • Result: marginal rate of substitution condition (MRS) p Ux = UL R • U ∗(u) Maximized utility given location u U ∗(u) = U (x∗(u), L∗(u)) • In equilibrum, U ∗(u) must be constant in u. (Individuals must be indiﬀerent where to live.) dU ∗(u) dx∗ dL∗ = Ux + UL =0 du du du • Using MRS condition, dx∗ dL∗ p +R = 0. du du • Next take the budget constraint px + R(u)L + tu = w and diﬀerentiate with respect to u dL∗ dx∗ + R (u)L + R +t=0 p du du yields R (u)L + t = 0 or t R (u) = − . L which is what we wanted to show. ...
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This note was uploaded on 02/17/2011 for the course ECON 4621 taught by Professor None during the Spring '11 term at Algoma University.
 Spring '11
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