# Flexibility Of Saving Ratio

The assumptions are that the fiscal system comprises of only two classes the remuneration earners and the profit earners. Their savings are a function of their earnings.

But the inclination to save of profit earners (sp) is more than that of remuneration earners or wage earners (sw). Consequently, the overall saving ratio of the community is based on the distribution of earnings.

1. Flexible Saving Ratio (s) and Flexible Capital Productivity Ratio (v)

Steady state growth can be depicted by considering both saving earnings ratio and capital productivity ratio as variables. With the classical saving function specified by sp.π/Y the warranted growth rate s/v can be written as follows:

Gw      =          s/v        =          sp.π/Y  =          sp.π/K

Hence,

S          =          sp.π/Y              ;           v          =          K/Y

Where π/K is the rate of profit on capital which can be specified by r. Therefore, the warranted rate becomes spr. For steady state growth spr = n+m, whilst sp = 1symmetry among the two is lowered to r = n+m.

Steady state growth with a variable saving ratio and a variable capital productivity ratio is presented in the diagram below. OP is the manufacturing function whose incline measures the marginal efficiency of capital r at any capital productivity ratio on a point on OP.

Symmetry takes place where the tangent WT cuts the OP curve at point A. The tangent WT initiates from W and not from O for the reason that savings taking place out of non-remuneration earnings WY. Point A shows the rate of proceeds respective to the marginal output of capital.

In other terminology, at point A labour and capital receive the rewards equal to their marginal efficiencies. OW is the remuneration rate and WY is the profit. Therefore, the steady state symmetry subsists at A.

1. Technical Progress

In this model, we consider labour increasing technical development which enhances the effective labour force L* in the form of a rate of progression in labour efficiency.

Presume that the labour force L is progressing at an invariable rate of n in year t, such that,
nt
Lt        =          Lo e             …Eq (i)

With labour increasing technical progress, the effective labour force L* is mounting at the invariable rate of λ in the year t such that,
(n+ λ)t
L*t      =          L*o e              …Eq (ii)

Where L*o depicts the aggregate total productive labour force in the base period t = o ; exemplifying all technical development up to the point in phase:

n is the natural growth rate of productive labour in the base phase.
λ is an invariable percentage growth rate of productive labour materialised in the base phase.

Hence the manufacturing function for productivity per labourer is

q          =          Q         =          Q         =          f   [ Q ]            =            (k)      …Eq (iii)
L*                    Le ^(λt)                   [Le ^(λt)]

*                                                                       *
Where k           =          K / L* and the growth rate of k – the capital productive

*
labour ratio parities to the disparity among growth rate of capital stock {K}and the growth rate of productive labour

*
{L}, i.e.

*                      *    *
k          =          K – L               …Eq (iv)

(n+ λ)t
As, L* =          L*o e

the growth rate of productive labour L* is exogenously given as (n + λ) as the equation (iv) is represented as follows:
*
k          =         Q – (n + λ)
K

=          q - (n + λ)
k

[q/k      =          (Q /L) / (K/L)  =          Q/K]

=          f(k) - (n + λ)

Since, q = f(k) in equation (iii).                                                           …Eq (v)

*
By fixing k      =          O, we obtain the following,

f (k)     =          (n + λ)             k                                  …Eq (vi)

which is the symmetry condition for steady state growth with technical progression and this has been illustrated pictorially below.

The capital per productive worker k is considered horizontally and productivity per effectual worker q is considered on the vertical axis.

The incline of the ray (n + λ) k from the base point E on the manufacturing function f (k) ascertains the stable symmetry values k’ and q’ for k and q correspondingly at point E and the capital utilised per unit of productive labour increases at the rate λ with technical progress.

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