Week 5_Technology (Print)

Week 5_Technology (Print) - Week 5 Technology Technologies...

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Unformatted text preview: Week 5 Technology Technologies • A technology is a process by which inputs are converted to an output. • E.g. labor, a computer, a projector, electricity, and software are being combined to produce this lecture. Technologies • Usually several technologies will produce the same product -- a blackboard and chalk can be used instead of a computer and a projector. • Which technology is “best”? • How do we compare technologies? Input Bundles • x i denotes the amount used of input i; i.e. the level of input i. • An input bundle is a vector of the input levels; (x 1 , x 2 , … , x n ). • E.g. (x 1 , x 2 , x 3 ) = (6, 0, 9 ⋅ 3). Production Functions • y denotes the output level. • The technology’s production function states the maximum amount of output possible from an input bundle. y f x x n = ( , , ) 1 Production Functions y = f(x) is the production function. x’ x Input Level Output Level y’ y’ = f(x’) is the maximal output level obtainable from x’ input units. One input, one output Technology Sets • A production plan is an input bundle and an output level; (x 1 , … , x n , y). • A production plan is feasible if • The collection of all feasible production plans is the technology set . y f x x n ≤ ( , , ) 1 Technology Sets y = f(x) is the production function. x’ x Input Level Output Level y’ y” y’ = f(x’) is the maximal output level obtainable from x’ input units. One input, one output y” = f(x’) is an output level that is feasible from x’ input units. Technology Sets The technology set is T x x y y f x x and x x n n n = ≤ ≥ ≥ {( , , , ) | ( , , ) , , }. 1 1 1 Technology Sets x’ x Input Level Output Level y’ One input, one output y” The technology set Technology Sets x’ x Input Level Output Level y’ One input, one output y” The technology set Technically inefficient plans Technically efficient plans Technologies with Multiple Inputs • What does a technology look like when there is more than one input? • The two input case: Input levels are x 1 and x 2 . Output level is y. • Suppose the production function is y f x x x x = = ( , ) . 1 2 1 1/3 2 1/3 2 Technologies with Multiple Inputs • E.g. the maximal output level possible from the input bundle (x 1 , x 2 ) = (1, 8) is • And the maximal output level possible from (x 1 ,x 2 ) = (8,8) is y x x = = × × = × × = 2 2 1 8 2 1 2 4 1 1/3 2 1/3 1/3 1/3 . y x x = = × × = × × = 2 2 8 8 2 2 2 8 1 1/3 2 1/3 1/3 1/3 . Technologies with Multiple Inputs Output, y x 1 x 2 (8,1) (8,8) Technologies with Multiple Inputs • The y output unit isoquant is the set of all input bundles that yield at most the same output level y. Isoquants with Two Variable Inputs y ≡ 8 y ≡ 4 x 1 x 2 Isoquants with Two Variable Inputs • Isoquants can be graphed by adding an output level axis and displaying each isoquant at the height of the isoquant’s output level. Isoquants with Two Variable Inputs Output, y x 1 x 2 y ≡ 8 y ≡ 4 Isoquants with Two Variable Inputs • More isoquants tell us more about the technology. Isoquants with Two Variable Inputs y ≡ 8 y ≡ 4 x 1 x 2 y ≡ 6 y ≡ 2 Isoquants with Two Variable Inputs Output, y x 1 x 2 y ≡ 8 y ≡ 4 y ≡ 6 y ≡ 2 Technologies with Multiple...
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This note was uploaded on 01/07/2011 for the course ECON 2101 taught by Professor Fransis during the Spring '10 term at HKU.

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Week 5_Technology (Print) - Week 5 Technology Technologies...

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