Eco Presentation Copy

7/29/2019 Eco Presentation Copy

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Using the Hotelling Model, discuss in detail how firms can use

their location decisions as part of their strategic behaviour. Is

the resulting Nash equilibrium the socially optimal solution?

Hotelling Model --> Location

decisions of firms -->

Un-cooperative interaction --

> Identical location --->Nash

Equilibrium ---> Increased

overall travel costs for

consumers


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Hotellings Law

Principle of minimum differentiation

Rational for producers to make their products

as similar as possible.


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Location Models of

Product Differentiation

Differentiation between products modelled as

spatial location

Consumer preferences modelled by their

location within the product space

Models differ in how product space is

modelled/defined


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Linear City Model(Differentiation defined by location)

Product space is defined linearly, e.g. A

Street of length 1.

Equilibrium prices constant irrespectiveof distance (Products equal in quality &

Price)

Consumers located with uniform density

Consumers have a transportation cost

(subject to location) and each eats only

one ice cream.


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One shop?

Street of length 1

Firm locates anywhere, indifferent

All consumers go to this one shop regardless

of location on the street

Socially Optimal? Half-way.


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Two shops?

Two shops that are free to move at any time

To maximise market share, firms locate

centrally at the half-way point.

Each firm serves half the market

Socially optimal? No, 0.25 & 0.75 would be

(Lower aggregate travel cost for consumers)


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Quick Model Critique

Price of goods fixed

When this assumption isnt met, companies do

maximum differentiation to avoid the

toughness of price competition


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Hotelling Model (cont.)

Minimum Differentiation:

Model concludes that in the absence of pricecompetition, firms will follow the demand, and

end up locating next to one another.


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The street is a metaphor for product differentiation

An example.The election market.

Why are both candidates always similar?

They want the most voters so stay close to the middle of the political spectrum (street)

Assumption that people choose the least distant option (distance here is ideological, not

spatial)

Most votes to be had by being in the direct center.


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Game Theory

In our two-vendor linear city model, after firms

have made their location decisions to

strategically increase their market share, a nashequilibrium forms in the middle.

Nash Equilibrium - Neither firm can improve their

position by deviations from their current strategy.


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Socially Optimal?The Nash equilibrium isnt socially optimal.

Social Optimum - The outcome which best

serves consumers, e.g. lowest travel costs.

Firms locate at point 0.5 on the street(1), it

would be more socially optimal for them to

locate at 0.25 and 0.75 (No consumer travelsmore than 1/4)

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