Personal emission permit trading scheme: urban spatial equilibrium and planning

Abstract

This paper studies the effect of personal emission permit trading scheme as a policy to limit greenhouse gas emissions from commuting and housing. First, urban spatial equilibrium is established under personal emission permit trading scheme which incorporates the interaction between residents’ location choice and emission permit market. For a given emission permit scheme, residents’ residential location choices and housing market structure in terms of housing rental price and space can be endogenously determined and the permit price is governed by the permit market equilibrium. On this basis, we prove its equivalence with the first-best planning model and propose the social welfare maximization planning model to determine the total amount of permits issued and the endogenous permit price. Model properties and income redistribution effect are numerically illustrated. Further, the pareto-improving scheme is numerically explored in terms of residents’ utility improvement and emission reduction. The study helps show the effectiveness and efficiency of the personal emission permit trading scheme and planning on the urban system in terms of emissions reduction, social welfare and residents’ utility.

Appendix Mathematical symbol description table

Variable and parameters	Description
$U$	Household utility
$g(x)$	Housing good consumption at location $x$
$z(x)$	Non-housing good consumption at location $x$
$c\left(x\right)$	One-way travel cost of a resident at location $x$
$T\left(x\right)$	Total travel time from the location $x$ to CBD
$\phi (x)$	Revenue or expenditure on emission permit trading at location $x$
$s(x)$	Emission permit consumption at location $x$
$p(x)$	Bid housing rental price per square meter at location $x$
$r(x)$	Land rent cost at location $x$
$h(x)$	Housing production at location $x$
$n(x)$	Population density at location $x$
$B$	City boundary
$G$	City-wide emission permit issued
$E$	Total emissions
${E}_{c}$	Total commuting emissions
${E}_{h}$	Total housing emissions
$\tau$	Permit price
$\lambda$	Marginal damage of the pollutant emissions
$\alpha ,\beta ,$	Coefficients of Cobb–Douglas function
$a$	Value of travel time
${c}_{f},{c}_{v}$	Fixed cost, and variable cost per unit of distance
$m$	Initial permit allocation to each resident
$e$	The amount of commuting emissions per kilometers
$\gamma$	The amount of housing emissions per square meters
$\upxi$	Annual work-home round trips
$Y$	Residents’ annual income
${\theta }_{1},{\theta }_{2}$	Parameters in the housing production function
$i$	Price of capital
$N$	Total population in the city
${r}_{a}$	Agriculture rent