Question #266468

A hypothetical economy is represented by the following parameters-

Labour force (L) = 40 million, Capital stock (K) = 700 million, saving rate (S) = 0.35, rate of depreciation (δ)


=0.05, rate of population growth (n) =0.015, partial (α) = 0.45 and total factor productivity (A) is constant.

Calculate effective output (y) and effective stock of actual capital (k) (3+3)

b) Find out steady-state stock of effective capital (k*) (3.5)

c) Show graphically the impact of a fall in the rate of depreciation using Solow’s diagram.


1
Expert's answer
2021-11-16T11:36:29-0500

(a)

K=(Sn+δ)2=(0.350.015+0.05)2=28.998K=(\frac{S}{n+\delta })^2=(\frac{0.35}{0.015+0.05})^2=28.998

y=(Sn+δ)=(0.350.015+0.05)=5.385y=(\frac{S}{n+\delta })=(\frac{0.35}{0.015+0.05})=5.385


(b)

k=K(1δ)+SAf(K)k=K(1-\delta)+SAf(K)

Af(K)=yAf(K)=y

y=(Sn+δ)α1αy=(\frac{S}{n+\delta})^{\frac{\alpha}{1-\alpha}}

y=(0.350.015+0.05)0.82=3.98y=(\frac{0.35}{0.015+0.05})^{0.82}=3.98

k=700,000,000(10.05)+(0.35×3.98)=665,000,001.393.\therefore k= 700,000,000(1-0.05)+(0.35\times3.98)=665,000,001.393.


(c)


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