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1. Long-run figures for the economy are reported in TABLE 1 TABLE 1 Long-run growth figures Capital-share of income 20% Population growth rate 1% Capital stock growth rate 7% Output growth rate 5%...

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1. Long-run figures for the economy are reported in TABLE 1 TABLE 1 Long-run growth figures Capital-share of income 20% Population growth rate 1% Capital stock growth rate 7% Output growth rate 5% Assume that the country’s production function is a constant-returns-to-scale Cobb-Douglas, Y = AKaLb, where Y is real national income, K is national capital stock and the total factor productivity is represented by A. Total population coincides with total workers and is denoted by L.
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1. Long-run figures for the economy are reported in TABLE 1 TABLE 1 Long-run growth figures Capital-share of income 20% Population growth rate 1% Capital stock growth rate 7% Output growth rate 5% Assume that the country’s production function is a constant-returns-to-scale a b Cobb-Douglas, Y = AK L , where Y is real national income, K is national capital stock and the total factor productivity is represented by A. Total population coincides with total workers and is denoted by L. (a) compute the Solow residual - state clearly/describe the formula you are using - compute the mathematical result Now consider some additional data provided reported in TABLE 2 TABLE 2 Ministry of Commerce Depreciation rate of capital 0.1 Marginal propensity of 0.75 consumption (b) Determine the steady state level of ‘consumption per human-capital- ~ augmented efficiency units of labour’ (c ) - state clearly/describe the formula you are using - compute the mathematical result(c) Derive the growth rate of consumption-per-worker in the steady state (?c c ) - state clearly/describe the formula you are using - compute the mathematical result (d) Sketch graphically the representation of the steady state and illustrate what happens to the steady state when there is an increase in the rate of population growth. Explain your answer by discussing whether or not that is in line with the empirical evidence. - state clearly/describe the graph you are using - describe clearly the changes that occur to the graph and compare the final result with the initial situation - give an economic intuition of the result, within the context of the model - talk about the empirical evidence illustrated in class in relation to the effects of the exogenous change on the endogenous variables.

Answered Same Day Dec 23, 2021

Solution

Robert answered on Dec 23 2021
118 Votes
Solow model:
We are given
Production function: Y = A K
a
L

Capital share of income (a) = 20% or 0.20
So, production function: Y = AK
0.20
L
0.80

Population growth rate (n) = 1%
Capital stock growth rate (ΔK/K) = 7%
Output growth rate (ΔY/Y) = 5%
(a)
Solow‟s Residual: the portion of actual growth in GDP which is not explained by the use of more
inputs. So Solow residual is a value that measures changes in productivity growth in a Solow
growth model.
Given that share of capital in income is 20%, so the share of labor would be 80% and hence
production function can be represented as;
Y = A K
0.20
L
0.80

Taking log both side and differentiating with respect to time „t‟, we get the production function
in growth form as:
(dlogY/dt) = (dlogA/dt) + 0.20*(dlogK/dt) + 0.80*(logL/dt) or
Where
(dlogY/dt) = growth rate of output = 5%
(dlogA/dt) = productivity growth = ?
(dlogK/dt) = growth rate of capital = 7%
(logL/dt) = population growth rate = 1%
This implies Solow residual: (dlogA/dt) = (dlogY/dt) - 0.20*(dlogK/dt) - 0.80*(logL/dt)
= 5 - 0.2*7-0.8*1 = 2.8%
We denote it by „g‟. So g = 2.8% or 0.028
(b)
Depreciation rate...
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