DSE 2016 Question 38: Endogenous growth and technical progress
Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each household is endowed with 1 acre of land and 1 unit of labour. They differ in initial capital: K0R (richer, 2<K0R<4) and K0P (poorer, 0<K0P<1). Two technologies exist: Technology A: Yt=(NtLt)1/2(Kt)2; Technology B: Yt=(NtLt)1/2(Kt)1/2, with Nt land, Lt labour, Kt capital. Each household picks the technology giving higher output. Each period they consume half of total income and save the rest, which becomes next period's capital; land and labour are constant; existing capital depreciates fully upon production.
In the short run, the average capital stock Kˉ evolves according to the dynamic path:
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Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each household is endowed with 1 acre of land and 1 unit of labour. They differ in initial capital: K₀^R (richer, 2<K₀^R<4) and K₀^P (poorer, 0<K₀^P<1). Two technologies exist: Technology A: Yₜ=(NₜLₜ)^(1/2)(Kₜ)²; Technology B: Yₜ=(NₜLₜ)^(1/2)(Kₜ)^(1/2), with Nₜ land, Lₜ labour, Kₜ capital. Each household picks the technology giving higher output. Each period they consume half of total income and save the rest, which becomes next period's capital; land and labour are constant; existing capital depreciates fully upon production. In the short run, the average capital stock K̄ evolves according to the dynamic path: (A) dK̄/dt=1/4[(Kₜ^R)^(1/2)+(Kₜ^P)²-2(Kₜ^R+Kₜ^P)] (B) dK̄/dt=1/4[(Kₜ^R)²+(Kₜ^P)²-2(Kₜ^R+Kₜ^P)] (C) dK̄/dt=1/4[(Kₜ^R)^(1/2)+(Kₜ^P)^(1/2)-2(Kₜ^R+Kₜ^P)] (D) dK̄/dt=1/4[(Kₜ^R)²+(Kₜ^P)^(1/2)-2(Kₜ^R+Kₜ^P)]
Also written as: Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each household is endowed with 1 acre of land and 1 unit of labour. They differ in initial capital: K_0^R (richer, 2<K_0^R<4) and K_0^P (poorer, 0<K_0^P<1). Two technologies exist: Technology A: Y_t=(N_tL_t)^(1/2)(K_t)^2; Technology B: Y_t=(N_tL_t)^(1/2)(K_t)^(1/2), with N_t land, L_t labour, K_t capital. Each household picks the technology giving higher output. Each period they consume half of total income and save the rest, which becomes next period's capital; land and labour are constant; existing capital depreciates fully upon production. In the short run, the average capital stock K_bar evolves according to the dynamic path:
Endogenous growth and technical progress has come up 25 times in 6 exams since 2016.
What this question tests
This question is on Technology choice and long-run income paths, part of Endogenous growth and technical progress in Economics of Growth and Development.
How the choice of technique and initial endowments shape long-run income.
TestStop has 4 past-paper questions on this subtopic.
