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Consider a model of vertical differentiation. A consumer is characterized by a taste parameter A and would obtain utility U = r+As-p from purchasing a good of qually s at price p. There is a continuum of consumers, each with their taste parameter drawn from a uniform distribution on the interval [O; 2]. Normalize the total measure of consumers in the market to be 1. There are two firms producing goods of differing qualities with quality of firm 2 equal to 2 and quality of firm 1 equal to 1.5. The marginal cost of production for each firm is 1. Assume that the parameter r is large enough that all consumers prefer buying one of the two goods to the outside option. If the two firms compete by choosing prices simultaneously, what are the Nash equilibrium prices? (Please round to 2 decimal points e.g. 1.23) P1 $ P2 $ Consider a model of vertical differentiation. A consumer is characterized by a taste parameter A and would obtain utility U = r+As-p from purchasing a good of qually s at price p. There is a continuum of consumers, each with their taste parameter drawn from a uniform distribution on the interval [O; 2]. Normalize the total measure of consumers in the market to be 1. There are two firms producing goods of differing qualities with quality of firm 2 equal to 2 and quality of firm 1 equal to 1.5. The marginal cost of production for each firm is 1. Assume that the parameter r is large enough that all consumers prefer buying one of the two goods to the outside option. If the two firms compete by choosing prices simultaneously, what are the Nash equilibrium prices? (Please round to 2 decimal points e.g. 1.23) P1 $ P2 $

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