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PS10(09) - ECN 712 Fall 2009 Professor Schlee Problem Set X...

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ECN 712 Fall 2009 Professor Schlee Problem Set X, Due 17 November 1. Price discrimination (of the third degree) . A monopolist produces a single good under constant returns to scale. It sells the good in two markets, 1 and 2, and the demands are independent (for i 6 = j , the price it charges in market i does not affect the demand in market j , implying that it can charge different prices in the markets). (a) Let ε i ( p i ) denote the price elasticity of demand in market i as a function of the price in market i . Show that, at any interior solution p 1 > p 2 if and only if ε 1 ( p 1 ) > ε 2 ( p 2 ): at any solution the market with the higher price has a more inelastic demand. (b) Suppose now that the inverse demand in each market is a straight-line (as long as price is positive). The demand in market 1 is more price elastic than the demand for market 2 when the demand curves are evaluated at the same quantity . Evaluate : “The firm will charge a higher price in market 2.” How do you reconcile your answer with part (a)?
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