Question

A labour-augmenting production function is \(Y = K^{0.33}(AL)^{0.67}\). Given growth rates: \(g_L=1.2%\), \(g_K=3%\), \(g_A=1.5%\). Using growth accounting, the growth rate of \(Y\) per annum is ____________ (round off to two decimal places).

Hint:

With labour-augmenting technical change, combine \(g_A\) and \(g_L\) first, then weight by the labour share \((1-\alpha)\).

Answer 1

Correct Answer: 2.7

Step 1: Growth-accounting formula for Cobb–Douglas.
For \(Y = K^{\alpha}(AL)^{1-\alpha}\),
\(g_Y = \alpha g_K + (1-\alpha)(g_A + g_L)\). Here, \(\alpha=0.33\).
Step 2: Plug in numbers.
\(g_Y = 0.33(3) + 0.67(1.5 + 1.2)%\ = 0.99 + 0.67(2.7)%\).
\(0.67 \times 2.7 = 1.809%\).
Step 3: Add the components.
\(g_Y = 0.99 + 1.809 = 2.799% \approx \boxed{2.80%}\).