Let us look at a graphical interpretation:
Now, the initial equilibrium of education lies at the point S1 where the cost of education comes to $3000. Now, for this example we will suppose that the subsidy that will be provided, assuming that it is portable which would ensure that the sorting of schools in the city would not remain an endogenous variable in this matrix, will move the budget line from MN to M'N'. Therefore, with the voucher system the increase in education from S1 to S2 will cost around $200, an amount which will be covered by the subsidy that is provided by the government via this voucher system as the new equilibrium is now at S2. Due to the portability factor of the voucher i.e. the voucher can be used anywhere in the city, the link between the quality of the education that is provided to children and the location of the public school ceases to exist as families do not have to relocate to the urban city centers now in order to ascertain better levels of education for their children. Therefore, the role of urban housing markets takes greater importance in the decline of cities with the implementation of this policy as the decision to move to an urban housing area does not remain dependent on the level of education provided by the schools in the suburbs.
We will now look at an economic model which will shed some light on the role urban housing markets play in the decline for cities:
As we can see from the graph, the supply curve of housing is defined from the equilibrium point determined at quantity Q1. This price is the minimum price level that can lead to housing construction which implies that if prices were to fall below the premium then no new housing would be built. Therefore, urban housing markets provide the greater supply in relation to the increased demand for housing due to which the equilibrium shifts to D1. This leads to the greater decline of cities as people move towards the suburban areas created by these urban housing markets.
Moving on to the practical side of this discussion i.e. the expected impact of the voucher system on the decline of cities it is clearly evident from the fact that the quality of education plays a significant role in determining where people choose to reside and the voucher system provides an incentive to people which basically eliminates education as a line of argumentation in their decision of choosing their area of housing. In addition, as the proposed vouchers are portable, these can be used in any public educational institution due which there will not be much difference of quality between city schools and suburban schools, therefore, people will not be essentially hard pushed to level the city, due to which we can say that the voucher system will have a positive effect on the proposition of resuscitating central