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ajaz_eco204_2009_chapter_5.3

# ajaz_eco204_2009_chapter_5.3 - University of Toronto...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Chapter 5.3: Firms with Market Power: Opportunity Cost and Uncertainty Analysis Please help improve the course by sending me an e mail about typos or suggestions for improvements 1. Opportunity Cost Analysis In chapter 5.2, we modeled the optimal output and price of a business with market power, i.e. a business with a downward sloping demand curve (output impacts price): Price Output Firm’s Demand q P This firm could be a monopoly; or, the firm could be in an oligopoly with the caveat that there is no strategic interaction between firms (i.e. rival firms don’t react or respond to this firm’s decisions – we will relax this assumption in oligopoly). Recall from chapter 5.2 that a business with unlimited capacity chooses the profit maximizing output as follows: m Πൌܴ ሻെܥሺ ݀Π ݀ݍ ax ሺݍ ݍሻ ܴ݀ሺݍሻ ݀ݍ ݀ܥሺݍሻ ݀ݍ ൌ 0 1 ECO 204 (Draft) Chapter 5.3

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ݀ܥሺݍሻ ܴ݀ሺݍሻ ݀ ݀ݍ ݍ 2 ܯܴ ൌ ܯܥ We saw that ܯܴ ൌ ܯܥ can be re arranged to give the optimal pricing rule: ܲൌ ൬ ܧ 1൅ܧ ൰ ܯܥ Next, recall from chapter 5.2 that a business with limited capacity chooses the profit maximizing output as follows: max ൌܴሺݍሻെ ܥ ݍ s.t.ݍ൑ܳ max L ൌܴሺݍሻെܥሺݍሻെ ߣሾݍെܳ Π ሺ ሻ The FOC and Kuhn Tucker conditions are: ݀ L ݀ ݀ܥሺݍሻ ܴ݀ሺݍሻ ݍ ݀ݍ ݀ݍ ߣ൒0 ,ݍ൑ܳ ,ߣሾݍെܳ ሿൌ 0 ߣൌ 0 Observe that the FOC can be re arranged : to yield ܴ݀ሺݍሻ ݀ݍ ݀ܥሺݍሻ ݀ݍ ൅ ߣ Or: ܯܴ ൌ ܯܥ ൅ ߣ This too can be re expressed as the optimal pricin rule: g ܧ ൰ ሾܯܥ ൅ ߣሿ Now, compare the ample capacity problem with the limited capacity problem: Ample Capacity Limited Capacity max Π ܴ ݍ ܥሺݍሻ ൌ ሺ ሻെ ܯܴ ൌ ܯܥ ܧ ൰ ܯܥ max Πൌ ሺ ሻ . ܴሺݍሻെ ܥ ݍ s t.ݍ൑ܳ ܯܴ ܯܥ ൅ ߣ ܧ ൰ ሾ ܯܥ ൅ ߣ ECO 204 (Draft) Chapter 5.3
University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain Notice that when a firm has limited capacity, the “marginal cost” is equal to ܯܥ ൅ ߣ : the actual marginal cost of production plus the opportunity cost ߣ . From chapter 5.2, recall that ߣ is an opportunity cost because ‐‐‐ from the envelope theorem ‐‐ ߣ is the marginal value of expanding capacity. Thus, when a firm with limited capacity produces another good, it incurs the actual cost of production and the opportunity cost of (profits foregone from) not allocating resources to expanding capacity.

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ajaz_eco204_2009_chapter_5.3 - University of Toronto...

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