Let a monopolist has 8 stores in a city. Using Hotelling linear city model,a)calculate the Total Social Surplus (TSS) and profit of the monopolist.b) Can we say that TSS is at its maximum when the number of firms is four?c) Can we say that profit is maximised when the number of firms is seven? Justify your answers clearly.(Note: Use ALL of the assumptions below and also following values for the parameters: R = $10; c = $2; N = 1000; t = $2; and F = $40 in your analysis).Assumptions :prices and quantities for the two stores given any fixed locations for the two.how the two stores would compete in terms of locations if they could move back and forth along the length of land l at zero costs.the socially efficient location of stores for any number of stores.Main Street is of length l = 1 mile; so the street begins at l = 0 and ends at l = 1. There are N identical consumers each with the same utility function equally spaced along Main Street; that is, there is a uniform density of identical consumers.The reservation price R is the highest price a consumer will pay for a unit of the good and this reservation price includes transportation costs.The marginal cost of production is c (Recall that Hotelling set c = 0).The transportation cost t is the cost of travelling one round-trip unit of distance along l to and from a store, or alternatively, t can be thought of as a measure of the disutility associated with the consumer not receiving his ideal product.p is the price of the good.d represents the consumer’s distance from the store.The consumer’s total price for a unit of the good is thus p + td which includes the seller’s price plus the consumer’s transportation costs.The fixed costs of setting up an additional store are F.

Monopolist - A person who produce items in cheapest price.

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

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Let a monopolist has 8 stores in a city. Using Hotelling linear city model,

a)calculate the Total Social Surplus (TSS) and profit of the monopolist.

b) Can we say that TSS is at its maximum when the number of firms is four?

c) Can we say that profit is maximised when the number of firms is seven? Justify your answers clearly.

(Note: Use ALL of the assumptions below and also following values for the parameters: R = $10; c = $2; N = 1000; t = $2; and F = $40 in your analysis).

Assumptions :

prices and quantities for the two stores given any fixed locations for the two.
how the two stores would compete in terms of locations if they could move back and forth along the length of land l at zero costs.
the socially efficient location of stores for any number of stores.
Main Street is of length l = 1 mile; so the street begins at l = 0 and ends at l = 1.
There are N identical consumers each with the same utility function equally spaced along Main Street; that is, there is a uniform density of identical consumers.
The reservation price R is the highest price a consumer will pay for a unit of the good and this reservation price includes transportation costs.
The marginal cost of production is c (Recall that Hotelling set c = 0).
The transportation cost t is the cost of travelling one round-trip unit of distance along l to and from a store, or alternatively, t can be thought of as a measure of the disutility associated with the consumer not receiving his ideal product.
p is the price of the good.
d represents the consumer’s distance from the store.
The consumer’s total price for a unit of the good is thus p + td which includes the seller’s price plus the consumer’s transportation costs.
The fixed costs of setting up an additional store are F.

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