The average annual growth rate of GDP is 4.6 %. The average annual growth rate o

Question

The average annual growth rate of GDP is 4.6%. The average annual growth rate of GDP per capita is 4.02%. Suppose that the production function is Y=zK0.4L0.6. The Sowlow residual in 2010 is 5.5664. _______% of GDP growth in Portugal can be explained by increases in TFP.

(I know the answer is 40.19% but I don't know how to get get the answer)

Year 1960 2010 GDP (billions 2005 US$) 23.109 218.569 Population (millions) 8.107 10.676 Labor (millions) 3.393 4.909 Capital (billions 2005 US$) 55.221 888.273

Explanation / Answer

We have the growth accounting equation where

growth rate of GDP = share of capital x growth rate of capital + share of labor x growth rate of labor + growth rate of TFP

4.596% = 0.4 x ((888.273/55.221)^(1/50) - 1) + 0.6 x ((4.909/3.393)^(1/50) - 1) + growth rate of TFP

4.596% = 2.2852% + 0.4449% + growth rate of TFP

growth rate of TFP = 1.8661%

Contribution of GDP growth in Portugal explained by increases in TFP = 1.8661%/4.596% = 40.6%

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