FinalReview - Econ 100A December 10, 2008 Non-Comprehensive...

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Unformatted text preview: Econ 100A December 10, 2008 Non-Comprehensive Review of Competition Michael Schihl Note the caveat utilitor . 1 Characteristics of a Perfectly Competitive Market According to the textbook, the model of a perfectly competitive market rests on three assumptions. 1. Price taking 2. Product homogeneity 3. Free entry and exit 2 Profit Maximization All firms, by assumption, maximize profits. One can express profit as i ( q i ) = TR i ( q i )- TC i ( q i ) (1) = p ( Q- i ,q i ) q i- TC i ( q i ) (2) Q- i represents the output of all firms except firm i . When we optimize, i.e., find the extrema of, a function, we typically set the first derivative equal to zero. For a firm maximizing profit, well take the derivative of profit and set it equal to zero. d dq i i ( q i ) = 0 (3) d dq i [ p ( Q- i ,q i ) q i- TC i ( q i )] = 0 (4) dp ( Q- i ,q i ) dq i q i + p ( Q- i ,q i ) | {z } MR i ( q i )- MC i ( q i ) = 0 (5) MR i ( q i )- MC i ( q i ) = 0 (6) MR i ( q i ) = MC i ( q i ) (7) This gives us the familiar result that marginal revenue equals marginal cost. Note that, for a perfectly competitive firm, p ( Q- i ,q i ) is a constant determined by the market equilibrium, thus its derivative is zero. So marginal revenue for a firm in a perfectly competitive market is simply price. MR i ( q i ) = dp ( Q- i ,q i ) dq i q i + p ( Q- i ,q i ) (8) = 0 q i + p ( Q- i ,q i ) since dp ( Q- i ,q i ) dq i = 0 for a firm in a perfectly competitive market (9) = p since p ( Q- i ,q i ) is a constant in a perfectly competitive market (10) This gives us the result that is specific to a firm in a perfectly competitive market: the firm produces q such that p = MC ( q ). This is the perfectly competitive firms profit-maximizing condition (i.e., it is the condition that characterizes the output choice when the firm solves its profit-maximization problem). 3 Simple Example Suppose that a firm has a total cost curve given by TC ( q ) = 100 + 20 q + q 2 , where the total fixed cost is 100 and the total variable cost is V C ( q ) = 20 q + q 2 . The corresponding marginal cost function is MC ( q ) = 20 + 2 q . 1 (a) What is the equation for average variable cost ( AV C ( q ))? Answer: AV C ( q ) = V C ( q ) q = 20 + q . (b) What is the minimum level of average variable cost?...
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This note was uploaded on 11/13/2009 for the course ECON 181 taught by Professor Kasa during the Spring '07 term at University of California, Berkeley.

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FinalReview - Econ 100A December 10, 2008 Non-Comprehensive...

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