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homework1 2009_final version

# homework1 2009_final version - wage is L t L t A t K F t w...

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ECN/APEC 6000/7230 Fall 2009 Homework 1 Due 9/8/09 1) Show the following properties of the growth rates of positive variables (i.e dt t dX t X ) ( ) ( 1 for a variable X ( t ). a) The growth rate of the product of two positive variables is the sum of their products: . ) ( ) ( 1 ) ( ) ( 1 )) ( ) ( ( ) ( ) ( 1 dt t dY t Y dt t dX t X dt t Y t X d t Y t X + = b) The growth rate of the ratio of two positive variables is the difference in their growth rates: . ) ( ) ( 1 ) ( ) ( 1 ) ( ) ( ) ( ) ( dt t dY t Y dt t dX t X t Y t X dt d t X t Y - = c) The growth rate of a positive variable raised to the α power is α times the growth rate: . ) ( ) ( 1 )) ( ( ) ( 1 dt t dX t X dt t X d t X α α α = 2) Suppose that labor and capital are both paid their marginal products, so the real

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Unformatted text preview: wage is L t L t A t K F t w ∂ ∂ = )) ( ) ( ), ( ( ) ( and the rate of return on capital is . )) ( ) ( ), ( ( ) ( δ-∂ ∂ = K t L t A t K F t r a) Show that if F exhibits constant returns to scale then ECN/APEC 6000/7230 Fall 2009 ))]. ( ( ' ) ( )) ( ( )[ ( ) ( t k f t k t k f t A t w-= b) Show that if F exhibits constant returns to scale then ), ( ) ( ) ) ( ( ) ( ) ( t Y t K t r t L t w = + + δ so the sum of factor payments equals net output....
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homework1 2009_final version - wage is L t L t A t K F t w...

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