2010_lecture_2_ho

2010_lecture_2_ho - Economics 101—Lecture 2 Mathematics...

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Unformatted text preview: Economics 101—Lecture 2 Mathematics of Optimization George J. Mailath January 18, 2011 Odds and ends Office hours for recitation instructors: 1 Garth Baughman (McNeil 415): Mondays and Wednesdays, 12:30-1:30. 2 Lingwen Huang (McNeil 329): Wednesdays, 10-12. 3 Soojin Kim (McNeil 453): Tuesdays 12-2. Return to our competitive firm. The firm’s problem is to choose q to maximize profits, i.e., to maximize the function π ( q ) , where π ( q ) = pq − C ( q ) . Note that p is being treated as a parameter (as is everything in C , like w , other than q ). Suppose C and so π is differentiable. Why economists like derivatives An important property of differentiable functions is that for marginal (i.e., small) changes in q , Δ q , we have π ( q + Δ q ) ≈ π ( q ) + π ( q ) Δ ( q ) . Consider possible choice q 1 : If π ( q 1 ) > 0, a marginal increase in q ( Δ q > 0) increases profits: π ( q 1 + Δ q ) > π ( q 1 ) . If π ( q 1 ) < 0, a marginal decrease in q ( Δ q < 0) increases profits: π ( q 1 + Δ q ) > π ( q 1 ) ....
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2010_lecture_2_ho - Economics 101—Lecture 2 Mathematics...

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