Income Distribution and Product Quality
Namrata Gulati (Indian Statistical Institute, Delhi)
Tridip Ray (Indian Statistical Institute)
Abstract: How is the location of an educational institute or health
facility and quality of their services decided? Is the private
provision of these facilities socially optimal? These questions are
vital given the externalities involved in these sectors. In this paper
we aim to address these issues by considering a circular city model
where the households are distributed uniformly over the circumference
of the city and the firms, the providers of these facilities, decide
their location and the price and quality of their services given the
income distribution of the households.
In the benchmark model where households in the same city have the same
income, we compare between cities and find that (a) in richer cities,
firms produce higher quality products, charge a higher price for them,
but are served by fewer firms, (b) in cities with better
infrastructure also, quality is higher and number of firms are lower,
whereas (c) more densely populated cities are served by more firms
with no effect on quality or price.
We next consider that households with different incomes reside in the
same city. We distinguish between two cases: (a) the overlapping
income groups, where rich and poor live side by side, and (b) the
segregated income groups, where they live in separate regions. With
the overlapping income groups, the nature of the equilibrium depends
on two income thresholds of the poor. In one extreme, when the income
of poor is lower than the lower threshold, the firms completely ignore
their presence and choose the price and quality as if there were only
rich individuals residing in the city. Product quality then is the
highest and equal to the quality in the benchmark model of a city with
only rich households. On the other hand, if the income of the poor is
above the upper threshold, each firm has to compete with its adjacent
firms for both poor and rich customers, and product quality is
determined by the weighted average of poor and rich incomes.
Understandably, the quality is lower than the above case. Quality is
the lowest in the intermediate case when the poor income is in between
the two threshold levels. Even in this intermediate case, there are
pockets where the poor households are left out of the market. Of
course all the poor are left out of the market if the poor income is
below the lower threshold.
Finally, with segregated income groups, we address the issue of
regional inequality in income distribution in the sense that there are
different stretches of the city circumference with households on one
stretch having the same income, whereas households on different
stretches have different incomes. We characterize the location
equilibrium and find that the area of operation of terminal firms in
the poorer regions encroaches into the neighbouring richer region.
Interestingly, in equilibrium, there are quality and price ladders
where households residing in the interior of the richest region are
offered the highest quality and are charged with the highest price.