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Questions › GATE › GATE 2023 › Q64
2 marksEconomics of Growth and Development › Endogenous growth and technical progress › Technical progress and growth accountingModerateabout 2 min

GATE 2023 Question 64: Endogenous growth and technical progress

A labour-augmenting production function is Y=K0.33(AL)0.67Y = K^{0.33}(AL)^{0.67}Y=K0.33(AL)0.67 where Y=Y=Y= output, K=K=K= capital, L=L=L= labour, and A=A=A= technology.

Assume that the growth rate of LLL is 1.2 percent per annum, the growth rate of KKK is 3 percent per annum, and the growth rate of AAA is 1.5 percent per annum.

Using the growth-accounting approach, the growth rate of YYY in percent per annum is ______ (round off to two decimal places).

Answer and worked solution

Answer: 2.70 to 2.90

Taking logs of Y=K0.33(AL)0.67Y=K^{0.33}(AL)^{0.67}Y=K0.33(AL)0.67 and differentiating with respect to time gives the growth-accounting decomposition:

gY=0.33 gK+0.67 (gA+gL)g_Y = 0.33\,g_K + 0.67\,(g_A+g_L)gY​=0.33gK​+0.67(gA​+gL​)

where gA+gLg_A+g_LgA​+gL​ combines because AAA and LLL enter the production function jointly as the single composite term (AL)(AL)(AL), so their growth rates add before being weighted by the 0.67 exponent.

Substituting the given growth rates (gK=3%g_K=3\%gK​=3%, gA=1.5%g_A=1.5\%gA​=1.5%, gL=1.2%g_L=1.2\%gL​=1.2%):

gY=0.33(3)+0.67(1.5+1.2)=0.99+0.67(2.7)=0.99+1.809=2.799g_Y = 0.33(3) + 0.67(1.5+1.2) = 0.99 + 0.67(2.7) = 0.99+1.809 = 2.799gY​=0.33(3)+0.67(1.5+1.2)=0.99+0.67(2.7)=0.99+1.809=2.799

Therefore the growth rate of YYY is approximately 2.80% per annum, within the key's accepted range of 2.70 to 2.90.

The trap: 5.36

Students sometimes treat AAA and LLL as separate terms each carrying their own independent 0.67 weight (i.e., computing 0.33gK+0.67gA+0.67gL0.33g_K+0.67g_A+0.67g_L0.33gK​+0.67gA​+0.67gL​ — which actually gives the same correct result here since they're added inside the same exponent) OR mistakenly apply separate DIFFERENT exponents to A and L as if the function were K0.33A0.67L0.67K^{0.33}A^{0.67}L^{0.67}K0.33A0.67L0.67 with an implicit extra exponent, over-weighting the labour/technology contribution and inflating the growth rate.

Plain-text version

A labour-augmenting production function is Y = K⁰·³³(AL)⁰·⁶⁷ where Y= output, K= capital, L= labour, and A= technology. Assume that the growth rate of L is 1.2 percent per annum, the growth rate of K is 3 percent per annum, and the growth rate of A is 1.5 percent per annum. Using the growth-accounting approach, the growth rate of Y in percent per annum is (round off to two decimal places).

Also written as: A labour-augmenting production function is Y = K^(0.33)(AL)^(0.67) where Y= output, K= capital, L= labour, and A= technology. Assume that the growth rate of L is 1.2 percent per annum, the growth rate of K is 3 percent per annum, and the growth rate of A is 1.5 percent per annum. Using the growth-accounting approach, the growth rate of Y in percent per annum is (round off to two decimal places).

Endogenous growth and technical progress has come up 25 times in 6 exams since 2016.

What this question tests

This question is on Technical progress and growth accounting, part of Endogenous growth and technical progress in Economics of Growth and Development.

Splitting growth into inputs and technology, and the types of technical change.

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Question from the GATE 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.