Consider a price searcher selling at a single market where the demand is given by Q = P^−ε, where ε > 1. Suppose the firm has a constant marginal cost of c.
a. Calculate the demand elasticity, and write down the marginal revenue function as a
function of price.
b. Using your above calculation, find the price charged by the price searcher as a function
of ε.
c. What happens to the price searcher’s price when ε increases? Interpret your result.
d. What happens to the price searcher’s price as ε approaches 1? Explain.
e. What is the price searcher’s profit maximizing output?

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