Ec146_soln_hw_4

Ec146_soln_hw_4 - EC 146: Industrial Organization Solutions...

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Unformatted text preview: EC 146: Industrial Organization Solutions to Homework 4 Department of Economics Brown University December 3, 2007 1. Recall that the less [more] intense the price competition is, firms will tend to locate their products closer [further away] from each other (i.e., differentiate their product to a lesser [larger] extent.) When firms collude in prices, they agree to set the same price, presumably the monopoly price. In this context, price competition becomes irrelevant, such that the only dimension in which firms compete is location. Thus, firms would tend to locate their products as close to each other as possible (i.e., low degree of differentiation.) 2. (a) The firm would like to locate at i * = 1 / 2 because this point minimizes the average distance between the firm and all the consumers that are uniformly distributed along the [0 , 1] interval. In other words, this location would maximize the profit of the firm. More formally, the firm solves Min { i } Z i t ( i- x ) d x + Z 1 i t ( x- i ) d x = ti 2 + t 2- ti. The FOC is 2 ti- t = 0 . Thus, i * = 1 2 . (b) Assume that V ≥ t/ 2. In essence, we need to show that firms have an incentive to change their location all the time except when both locate at 1 / 2. We need to assume, furthermore, that the price is fixed (think of small firms that are price-takers), so the only dimension of...
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This note was uploaded on 07/06/2009 for the course ECON 146 taught by Professor Campos-ortiz during the Fall '07 term at Brown.

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Ec146_soln_hw_4 - EC 146: Industrial Organization Solutions...

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