6.3.- Consider Hotelling\'s model of product differentiation. Consumers are even

Question

6.3.- Consider Hotelling's model of product differentiation. Consumers are evenly distributed along the segment [0,1]. They pay a cost of transportation of $2 per unit. Two firms first choose their product characteristics (locations) and then, simultaneously and after observing the location choice of the rival, choose their prices. (Suppose the first firm cannot locate to the right of 0.25 and the second cannot locate to the left of 0.75.) Obtain the product positioning of the two firms in equilibrium.

Explanation / Answer

Stage 1: Firms A ad B Choose location along a Spectrum

Payoff for A(B): line segment covered

If both firms located at the end….

then firms have an incentive to move inwards.

A and B are back-to-back, but not in centre:

Incentive for A to jump in front of B…..

A and B are back-to-back in centre:

Neither firm has an incentive to move location, given the location of the other

But in this case 0.25 and 0.75 is nash equilibrium for the players because there is constraint to go beyond these points.

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