# Consider a Hotelling line of length 1. A grocery store is located at each endpoint. The...

###### Question:

Consider a Hotelling line of length 1. A grocery store is located at each endpoint. The grocery store at the west end point is owned and operated by Jack Donaghy and offers customers the use of a personal “grocery concierge”, free of charge, who assists the customer in shopping. The grocery store at the east endpoint is owned and operated by Milton Greene and does not offer its customers a grocery concierge. The utility of a consumer at location x who visits Jack’s store is given by u J x = vJ − tx − pJ and utility from visiting Milton’s store is given by u M x = vM − t(1 − x) − pM, where vJ > vM because of the grocery concierge and the p terms represent prices and t is the transportation cost per unit of distance. Assume for simplicity that the grocery stores have no marginal costs of production. (a) [20 points] Given some prices, pJ and pM, what is the location of the indifferent consumer? If those prices were the same, would the location of the indifferent consumer be to the left or right of 0.5, or exactly at 0.5? (b) [20 points] Solve for the equilibrium prices charged by each grocery store and call them p ∗ J and p ∗ M. Are they equal? (c) [10 points] Where is the location of the indifferent consumer in equilibrium?

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