We consider the Hotelling model of a linear city of size 1 ( N consumers
uniformly distributed on the segment). However, unlike what we've seen in
class, there is only one fresh food retailer located at xₛ = 0, that is, the left
endpoint of the city segment. Its unit cost of production c is normalized to be
0 . In this variant, the transportation costs are quadratic, and for a consumer
located at x ϵ [0,1] on the segment, they are equal to C(x) = k(xₛ - x)² where
k>0 is a parameter. The consumer who consumes 1 unit at most of fresh food
product derives a surplus S >0 from consumption. As per the duopoly model,
some consumer may decide not to purchase from the retailer if their surplus
from doing so is negative and their consumer surplus is then 0 (in this case,
they only consume inferior dehydrated food products). The timing of the game
is as follows:
The retailer decides its price p at date 0 .
Each consumer decides whether to buy or not.
Questions: Solve for the model by deriving the equilibrium price chosen by
the monopolist retailer, its demand, and its equilibrium profit. In particular,
discuss the equilibrium as a function of the parameter k. Is there a food desert
in this city?