2. Consider the following Solow Growth Model. An economy has the per-worker prod
ID: 1103134 • Letter: 2
Question
2. Consider the following Solow Growth Model. An economy has the per-worker production function yt here ye is output per worker in period t and k is capital per worker in period t. The depreciation rate is d = 0.2, the population growth rate is n = 0.1, and the saving rate is s = 0.2. the following tables kt yt Ct t=2 (b) In steady state, what are the equilibrium values of the capital per worker, output per worker, and consumption per worker? (c) Repeat Part (b) for a production function of yt = 94.5 due to technology improvement, how do the steady state values change? (d) Use the Contraction Mapping Theorem to show that in the Solow Model above, as t increases. , converges to its steady state value if initially > 4.Explanation / Answer
From Solow Growth Model we ave the following equations.
yt = 6kt0.5 -----------------------(i)
ct = (1-s)yt ---------------------(ii)
and For steady state kt+1= kt =k* -------------------(iii)
(Capital grows but at a declining rate
k* = {sA/(n+d)}1/(1-0.5) ------------------------(iv)
kt+1 = {(1-d)/(1+n)}kt + {sA/(1+n)}kt0.5 --------------(v)
In above equations of the present problem, s = 0.2; n= 0.1; A = 6; d = 0.2
Therefore, the the blanks of the table may be filled up as follows.
Answer (b)
In steady state, we use the formula as given in (iv)
Hence, k* = {sA/(n+d)}1/1-0.5
= {0.2x6/(0.1+0.2)}2
= 42
= 16
Answer (c)
Due to technological upgradation k* = {0.2x9/0.3}2
=36
kt yt ct t=1 9 18 14.4 t=2 3.93 11.894 9.51 t=3 2.448 9.387 7,51Related Questions
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