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Unformatted text preview: 1 Technology Professor John W. Diamond ECON 370: Microeconomic Theory Lecture 11 2 Technology: Introduction Technology Process by which inputs are converted to outputs Inputs also called “factors of production” Input: Labor (L) (skilled, unskilled) Input: Physical capital (K) (equipment, structures, inventories, land, intangibles) Many potential technologies could produce output Main issue: Which technology is best? 3 Input Bundles: Introduction x i the amount used (level) of input i Input bundle vector inputs (x 1 , x 2 , … , x n ) y output level Production function describes technology maximum output possible from input bundle implies “technical efficiency” achieved y f x x n ( , , ) 1 4 Production Functions: One input, one output y = f(x) is production function x’ Input Output y’ y‟ = f(x‟) is max output level obtainable from x‟ input units 5 Technology set  collection of all feasible production plans with x 1 ,...,x n > Technology Sets: Introduction Production plan – an input bundle and an output level (x 1 , … , x n , y) A production plan is feasible if y f x x n ( , , ) 1 6 Technology Sets: Graph x’ y’ y” y” = f(x‟) is output level that is feasible from x‟ input units Input Output 7 Technology Sets: Graph x’ Input Output y’ y” The technology set 8 Technology Sets: Technical Efficiency x’ y’ y” Technically inefficient plans Technically efficient plans Input Output 9 Technologies with Multiple Inputs The two input, one output case Input levels are x 1 and x 2 Output level is y y=f(x 1 , x 2 ) 10 Max output from inputs (x 1 ,x 2 ) = (8,8) is Technologies: Multiple Inputs Max output from inputs (x 1 , x 2 ) = (1, 8) is 4 2 1 2 8 1 2 2 3 / 1 3 / 1 3 / 1 2 3 / 1 1 x x y 8 2 2 2 8 8 2 2 3 / 1 3 / 1 3 / 1 2 3 / 1 1 x x y Suppose production function is CobbDouglas 3 / 1 2 3 / 1 1 2 1 2 ) , ( x x x x f y 11 Technologies with Multiple Inputs Output, y x 1 x 2 (8,1) (8,8) 12 Technologies with Multiple Inputs Isoquant Set of all input bundles yielding output level y Analogous to indifference curve Typically implies substitution across inputs possible (Although can have fixed proportions production function) 13 Isoquants with Two Variable Inputs y y=4 x 1 x 2 y=4 y=8 14 Isoquants in 3D Output, y x 1 x 2 y y Add third axis for output level y=f(x 1 , x 2 ) 15 Isoquants with Two Variable Inputs y y x 1 x 2 y y 2 More isoquants describe technology better 16 Isoquants with Two Variable Inputs Output, y x 1 x 2 y y y y 2 17 Technologies with Multiple Inputs Isoquant map complete isoquant collection is equivalent to production function Can be represented in 2D or 3D For example, if 3 / 1 2 3 / 1 1 2 1 2 ) , ( x x x x f y 18 Technologies with Multiple Inputs x 1 x 2 y 19 Technologies with Multiple Inputs x 1 x 2 y 20 Technologies with Multiple Inputs x 1 x 2 y 21 Technologies with Multiple Inputs x 1 x 2 y 22 Technologies with Multiple Inputs x 1 x 2 y 23 Technologies with Multiple Inputs x 1 x 2 y 24 Technologies with Multiple Inputs x 1 y 25 Technologies with Multiple Inputs x 1 y 26 Technologies with Multiple Inputs x 1 y 27 Technologies with Multiple Inputs x 1 y 28 Technologies with Multiple Inputs x 1 y 29 Technologies with Multiple Inputs x 1 y 30 Technologies with Multiple Inputs x 1 y 31 Technologies with Multiple Inputs x 1 y 32 Technologies with Multiple Inputs x 1 y 33 Technologies with Multiple Inputs x 1 y 34...
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 Spring '08
 DIAMOND
 Economics, Microeconomics, X1, Multiple Inputs

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