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(Solved): 2. Consider a consumer located at point x with the utility function of Ux={pAxa ...




2. Consider a consumer located at point \( x \) with the utility function of
\[
U_{x}=\left\{\begin{array}{ll}
-p_{A}-\tau|x-
2. Consider a consumer located at point with the utility function of where (resp. ) is the price paid for purchasing from firm A (resp. B), denotes the location of each consumer, is the length of a linear street, is transportation cost per unit of distance when a consumer has to pay for shopping at a (resp. b) where A (resp. B) store is located, given that the total number of consumers in the economy is . (a) Find the demand functions faced by firm A and firm B, respectively. (b) Find the Bertrand-Nash equilibrium prices and firm profits. (c) Comments on your results.


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a) The demand functions faced by firm A and firm B can be found by taking the derivative of the utility function with respect to the price. For firm A
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