Midterm+1+Review

Midterm+1+Review - Midterm I - Review Growth Accounting...

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Unformatted text preview: Midterm I - Review Growth Accounting Solow in Short Friday, January 29, 2010 Deriving Output Growth The output in the economy: Y=f(K,AL) In general - an increase in Y is: Where: Thus: Δ Y = ∂ Y ∂ K Δ K + ∂ Y ∂ AL ( ) Δ ( AL ) Δ ( AL ) = L Δ A + A Δ L Δ Y = f K ⋅ K ( ) Δ K K + f AL ⋅ AL ( ) Δ A A L L + A A Δ L L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = f K ⋅ K ( ) Δ K K + f AL ⋅ AL ( ) Δ A A + Δ L L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Friday, January 29, 2010 Deriving Output Growth In competitive market, factors earn their marginal product: and Thus: Notice: rK is the total payments to owners of capital wAL is the total payments to labor r = f K Δ Y = r ⋅ K ( ) Δ K K + ω ⋅ AL ( ) Δ A A L L + A A Δ L L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = r ⋅ K ( ) Δ K K + ω ⋅ AL ( ) Δ A A + Δ L L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ω = f AL Friday, January 29, 2010 And Last Step... Output growth: or: Note: is the share of capital in total output is the share of labor in total output Δ Y Y = r ⋅ K ( ) Y Δ K K + ω ⋅ AL ( ) Y Δ A A + Δ L L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ S K = r ⋅ K ( ) Y S AL = r ⋅ K ( ) Y ˆ Y = r ⋅ K ( ) Y ˆ K + ω ⋅ AL ( ) Y ˆ A + ˆ L ( ) = S K ⋅ ˆ K + S AL ⋅ ( n + g ) Friday, January 29, 2010 Cobb-Douglas Production Assume that the production function is Cobb-Douglas: Y=K α (AL) 1- α Here, S K = α is the share of the capital in the total output and S AL =1- α is the share of the labor in total output....
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This note was uploaded on 03/11/2010 for the course ECN ECN111b taught by Professor Meissner during the Winter '10 term at UC Davis.

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Midterm+1+Review - Midterm I - Review Growth Accounting...

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