The production function used by the Australian Bureau of Statistics is written Y = AK L rY where Y is aggregate output, A is total-factor productivity, K is aggregate capital, L is the size of the labor force, I is aggregate intermediate input (e.g., energy, material), and the exponents are constants. Given this production function, which of the following expressions correctly represents the growth rate of per-capita income, 9Y? = gA + agK + BgL + Y9I = gA + agk + (1 – B) gL +ygı = 9A + agk + (B– 1) gL +Yg1 O None of the choices given is correct.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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The production function used by the Australian Bureau of Statistics is written as:

\[ Y = AK^\alpha L^\beta I^\gamma \]

where \( Y \) is aggregate output, \( A \) is total-factor productivity, \( K \) is aggregate capital, \( L \) is the size of the labor force, \( I \) is aggregate intermediate input (e.g., energy, material), and the exponents are constants. Given this production function, which of the following expressions correctly represents the growth rate of per-capita income, \(\frac{g_Y}{L}\)?

Options:
- \(\frac{g_Y}{L} = g_A + \alpha g_K + \beta g_L + \gamma g_I\)
- \(\frac{g_Y}{L} = g_A + \alpha g_K + (1 - \beta) g_L + \gamma g_I\)
- \(\frac{g_Y}{L} = g_A + \alpha g_K + (\beta - 1) g_L + \gamma g_I\)
- None of the choices given is correct.

[Diagrams/graphs explanation]
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Transcribed Image Text:The production function used by the Australian Bureau of Statistics is written as: \[ Y = AK^\alpha L^\beta I^\gamma \] where \( Y \) is aggregate output, \( A \) is total-factor productivity, \( K \) is aggregate capital, \( L \) is the size of the labor force, \( I \) is aggregate intermediate input (e.g., energy, material), and the exponents are constants. Given this production function, which of the following expressions correctly represents the growth rate of per-capita income, \(\frac{g_Y}{L}\)? Options: - \(\frac{g_Y}{L} = g_A + \alpha g_K + \beta g_L + \gamma g_I\) - \(\frac{g_Y}{L} = g_A + \alpha g_K + (1 - \beta) g_L + \gamma g_I\) - \(\frac{g_Y}{L} = g_A + \alpha g_K + (\beta - 1) g_L + \gamma g_I\) - None of the choices given is correct. [Diagrams/graphs explanation] There are no diagrams or graphs in the image.
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