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technology.18b

technology.18b - Econ 100A Production Technology Part...

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Unformatted text preview: Econ 100A: Production: Technology, Part II (Chapter 18) Thomas G. Koch Fall 2008 Thomas G. Koch Production: Tech (18B) 1(46) Clickers • Turn on your clicker • Hit a button Thomas G. Koch Production: Tech (18B) 2(46) From last time • Talking about technology • How firms take inputs (labor, capital) • and make outputs Production Function y = f ( x 1 , x 2 , x 3 ,... ) Thomas G. Koch Production: Tech (18B) 3(46) Production Set with One Input Thomas G. Koch Production: Tech (18B) 4(46) In particular MP x 1 = Δ y Δ x 1 = f ( x 1 + Δ x 1 , x 2 ) Δ x 1 Thomas G. Koch Production: Tech (18B) 5(46) Thinking on the Margin • How many more iPods will another CS’er get me? • How many more apples will extra fertilizer get me? • Like marginal utility • But didn’t we need the ratios? MRS? Thomas G. Koch Production: Tech (18B) 6(46) Technical Rate of Substitution • Production with two inputs, ( x 1 , x 2 ) • How much more of the second input (Δ x 2 ) do we need • to keep output constant ( y ) • if we decrease amount of first input (Δ x 1 ) Thomas G. Koch Production: Tech (18B) 7(46) In Math MP 1 ( x 1 , x 2 )Δ x 1 + MP 2 ( x 1 , x 2 )Δ x 2 = Δ y = 0 Rearrange! TRS ( x 1 , x 2 ) = Δ x 2 Δ x 1 =- MP 1 ( x 1 , x 2 ) MP 2 ( x 1 , x 2 ) Thomas G. Koch Production: Tech (18B) 8(46) Our Three Favorite Examples • Perfect Substitutes • Cobb-Douglas • Fixed Proportions Thomas G. Koch Production: Tech (18B) 9(46) Perfect Substitutes Thomas G. Koch Production: Tech (18B) 10(46) Perfect Substitutes f ( x 1 , x 2 ) = A ( x 1 + x 2 ) Marginal Products MP 1 = MP 2 = A Thomas G. Koch Production: Tech (18B) 11(46) TRS for Perfect Substitutes TRS PS ( x 1 , x 2 ) =- A A =- 1 Intuition MPs are constant, so is TRS Thomas G. Koch Production: Tech (18B) 12(46) Cobb-Douglas...
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technology.18b - Econ 100A Production Technology Part...

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