Suppose that an economy grows by 6 percent, total factor productivity grows by 4 percent, and the capital stock increases by 2 percent.....

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Suppose that an economy grows by 6 percent, total factor productivity grows by 4 percent, and the capital stock increases by 2 percent.....

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Suppose that an economy grows by 6 percent, total factor productivity grows by 4 percent, and the capital stock increases by 2 percent. If labor and capital are the only inputs used in production and capital contributes 25 percent to GDP, then the labor force has risen by _____. Question 10 options: 1) 1.5 % 2) 2% 3) 4% 4) 6% 5) 8%
I might be able to help if you tell me the relationships between economy, factor productivity and capital stock Is economy (E) a function of stock (S) and productivity (P)? Something like $$ E=\alpha S + \beta P +\delta SP~? $$ Where \(\alpha, \beta~\&~\delta\) are constants
My book shows this @ybarrap

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Ok, so $$ \%\Delta Y=\%\Delta\text{TFP}+0.7(\%\Delta L)+0.3(\%\Delta K) $$ Givens: $$ \%\Delta Y=6\\ \%\Delta\text{TFP}=4\\ \%\Delta K=2 $$ We need to find \(\%\Delta L\), percent change in the labor force. Using the first equation: $$ \%\Delta Y=\%\Delta\text{TFP}+0.7(\%\Delta L)+0.3(\%\Delta K)\\ 6=4+0.7(\%\Delta L)+0.3\times 2\\ \implies \%\Delta L=\cfrac{6-4-0.3\times 2}{0.7}\\ $$ Does this make sense?
Um yes? But I completed this question 3 hours ago. I took a guess and got it right.

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