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Questions › IIT JAM › IIT JAM 2022 › Q14
2 marks, −0.667Economics of Growth and Development › Harrod–Domar and Solow growth models › The Solow model and its steady stateModerateabout 2 min

IIT JAM 2022 Question 14: Harrod–Domar and Solow growth models

An economy follows the Solow model with production function y=ky = \sqrt{k}y=k​, where yyy is output per worker and kkk is capital per worker. The steady-state output per worker is yss=A1/(1−α)(γδ)α/(1−α)y^{ss} = A^{1/(1-\alpha)}\left(\dfrac{\gamma}{\delta}\right)^{\alpha/(1-\alpha)}yss=A1/(1−α)(δγ​)α/(1−α), where AAA, γ\gammaγ, δ\deltaδ and α\alphaα are productivity, the investment share (in percent), the depreciation rate (in percent) and capital's income share (a fraction). Suppose A=1A=1A=1, k=400k=400k=400, γ=50%\gamma=50\%γ=50%, δ=5%\delta=5\%δ=5% and α=1/2\alpha=1/2α=1/2. Then current output is

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Answer and worked solution

Answer: (A)

With α=1/2\alpha = 1/2α=1/2, 11−α=2\dfrac{1}{1-\alpha} = 21−α1​=2 and α1−α=1\dfrac{\alpha}{1-\alpha} = 11−αα​=1, so yss=12(γδ)1=505=10y^{ss} = 1^{2}\left(\dfrac{\gamma}{\delta}\right)^{1} = \dfrac{50}{5} = 10yss=12(δγ​)1=550​=10.

Current output is y=k=400=20y = \sqrt{k} = \sqrt{400} = 20y=k​=400​=20. Since 20>1020 > 1020>10, current output is above the steady-state level, option (A). Capital per worker will fall over time towards the steady state.

The trap: (B) at the steady-state level of output per worker.

Plugging k=400k=400k=400 into the steady-state formula instead of into y=ky=\sqrt{k}y=k​ confuses the current position with the steady state; the two are computed from different expressions.

Plain-text version

An economy follows the Solow model with production function y = √k, where y is output per worker and k is capital per worker. The steady-state output per worker is y^(ss) = A^(1/(1-α))(γ/δ)^(α/(1-α)), where A, γ, δ and α are productivity, the investment share (in percent), the depreciation rate (in percent) and capital's income share (a fraction). Suppose A=1, k=400, γ=50%, δ=5% and α=1/2. Then current output is (A) above the steady-state level of output per worker. (B) at the steady-state level of output per worker. (C) below the steady-state level of output per worker. (D) at the Golden Rule level.

Also written as: An economy follows the Solow model with production function y = sqrt(k), where y is output per worker and k is capital per worker. The steady-state output per worker is y^(ss) = A^(1/(1-alpha))(gamma/delta)^(alpha/(1-alpha)), where A, gamma, delta and alpha are productivity, the investment share (in percent), the depreciation rate (in percent) and capital's income share (a fraction). Suppose A=1, k=400, gamma=50%, delta=5% and alpha=1/2. Then current output is

Harrod–Domar and Solow growth models has come up 113 times in 7 exams since 2006.

What this question tests

This question is on The Solow model and its steady state, part of Harrod–Domar and Solow growth models in Economics of Growth and Development.

Growth with substitutable factors: capital per worker settles where saving covers depreciation and dilution.

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