_Lecture_15

_Lecture_15 - Lecture 15 1-minute review productive...

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Unformatted text preview: Lecture 15 1-minute review productive efficiency not possible to produce more total output with same inputs not possible to produce same total outputs with less inputs Edgeworth Box RTS = RTS 1 Example Two firms q 1 = x 1 / 2 + y 1 / 2 q 2 = x 1 / 2 y 1 / 2 Total inputs ( k, ` ) = (1 , 2). RTS 1 = RTS 2 (1 / 2) x- (1 / 2) 1 (1 / 2) y- (1 / 2) 1 = (1 / 2) x- (1 / 2) 2 y 1 / 2 2 (1 / 2) x (1 / 2) 2 y- (1 / 2) 2 Simplifying gives y 1 / 2 1 x 1 / 2 1 = 1- y y 1- x 1 Square both sides, multiply out and solve to obtain y 1 = x 1 y 2 = x 2 Prices If both firms maximize profits with respect to the same profits for inputs/outputs then we obtain productive efficiency. RTS = RTS algebraic proof Say firm 1s profit-maximizing plan uses inputs ( k 1 , ` 1 ) produces output q 1 (of good x ) and firm 2s profit-maximizing plan uses inputs ( k 2 , ` 2 ) and produces output q 2 (of good y ). If these are NOT productively efficient then there are alternative plans ( k * 1 , `...
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_Lecture_15 - Lecture 15 1-minute review productive...

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