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II.B. - Douglas example one can show that the growth rates...

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II.B. Production and Growth 1. Production Theory Production Function ) , ( L K AF Y = Example: Cobb-Douglas Production Function, α - = 1 L AK Y , where 1 0 < < Properties of the Production Function (i) Constant Returns to Scale (ii) Positive but diminishing marginal productivity Figure 3.5-3.6 Example : L K A MPL ) 1 ( - = , - - - = 1 1 ) 1 ( K L A MPK 2. Output per Worker Using property (i) we can write ( 29 ( 29 L Y L K AF L L L L K AF / , ) / 1 ( / , / = = Defining ( 29 ) 1 , / ( , / , / L K F k f L K k L Y y , lets us write ( 29 k Af y = Example : Ak y =
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3. Growth Accounting One can also put the production functions in “growth rate” form. When the production functions are multiplicative in the inputs, as in the Cobb-
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Unformatted text preview: Douglas example, one can show that the growth rates of the variables are related in additive form (approximately) ) / )( 1 ( ) / ( / / L L K K A A Y Y ∆-+ ∆ + ∆ = ∆ α ) / ( / / k k A A y y ∆ + ∆ = ∆ This allows us to begin “accounting” for the different “sources” of growth (technology, capital, and labor) Asian Tiger Growth Accounting / y y ∆ / k k ∆ / A A ∆ Hong Kong 7.3 3.0 4.3 Singapor e 8.7 5.6 3.1 South Korea 8.5 3.3 5.2 Taiwan 8.5 2.9 5.6...
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II.B. - Douglas example one can show that the growth rates...

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