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FinalReview

# FinalReview - Econ 100A Non-Comprehensive Review of...

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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 π 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, we’ll take the derivative of profit and set it equal to zero. d dq i π 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 firm’s 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

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(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? Answer: We know that the minimum level of AV C occurs where AV C = MC . 20 + q = 20 + 2 q (11) q = 2 q (12) This is satisfied when q = 0. The minimum level of AV C is the level of AV C when q = 0. AV C (0) = 20, thus the minimum level of AV C is 20.
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FinalReview - Econ 100A Non-Comprehensive Review of...

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