# IntroPD - Industrial Organization EC460 Spring 2009...

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Industrial Organization: EC460 Spring 2009 Instructor: Thomas D. Jeitschko Introductory Notes on Pricing for Firms with Pricing Power Classic Analysis: Uniform Pricing Consider a firm with the following cost function, C ( Q ) = Q 2 + 100 so that marginal cost is given by MC = C 0 = 2 Q . Suppose that the demand for the firm’s product is given by P ( Q ) = 1200 - Q . The firm’s revenue is Rev ( Q ) = P ( Q ) × Q = (1200 - Q ) Q = 1200 Q - Q 2 . Therefore its marginal revenue is MR = Rev 0 = 1200 - 2 Q . The firm chooses an output level at which the marginal cost is equal to the marginal revenue, i.e., MC = MR 2 Q = 1200 - 2 Q. Hence the optimal amount to produce is Q m = 300. The price associated with this output is found on the demand curve, namely, P m = P ( Q m ) = 1200 - Q m = 900. Welfare Implications: Deadweight Loss DWL Notice that there is a discrepancy between the firm’s marginal cost and the price it charges when it produces the profit- maximizing level of output. In particular, MC ( Q m ) = 2 Q m = 600, whereas P m = 900. This says that the marginal consumer who is just not served by the firm has a value of the product at just under 900, whereas it would only cost the firm 600 to produce another unit. Hence, under uniform pricing there are potential gains from trade that are not realized. How much un-realized gains from trade are there? So long as marginal costs (the costs 1

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of producing additional units) is below the value of those units to consumers (as reflected in the price on the demand curve), additional gains from trade are to be had. Indeed, this ceases to be the case when the marginal cost is exactly equal to the price. We can find that level of output by setting marginal cost equal to the price from the demand curve. Specifically, MC = P 2 Q = 1200 - Q. From which it follows that there is no deadweight loss if the firm sells Q * = 400 units and sells these at a price of P * = P ( Q * ) = 1200 - Q * = 800. This nicely illustrates the
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