Question

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.

Answer 1

(a)

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

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

(b)

$k=K(1-\delta)+SAf(K)$

$Af(K)=y$

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

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

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

(c)