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Volume 1,     Number 1,     Winter 1993

 

PERTURBATION SOLUTIONS FOR THE
SECOND-BEST LAND USE PROBLEM
FREDERIC Y. M. WAN

Abstract. A perturbation solution is obtained for the second-best land use problem in residential land economics for cities with a fixed boundary and with an absentee landlord. When the transportation cost increases linearly with traffic density and is a relatively small fraction of the total household income, the perturbation solution shows that the cost-benefit criterion based on market land price allocates more land for roads throughout the city than the second-best allocation and results in a lower (common) utility for the households. The perturbation method also allows us to make other explicit comparisons between the two types of urban land allocation. A spline-collocation solution for the same boundary value problems validates the accuracy of the perturbation solution for a small transportation cost and provides numerical results to a prescribed accuracy for other cases. The perturbation and numerical methods used in this paper apply also to the public ownership case and for a city with a free boundary determined by a prescribed agricultural rent.

 

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© 2005, Canadian Applied Mathematics Quarterly (CAMQ)