# Pictorial Representation Of The Golden Rule

The golden rule of accumulation is explained in Diagram. As the golden rule associates to the maximisation of per capita consumption we plot productivity or output (Q), saving or Thrift (s), investment (I) and capital stock (K) as ratios to the quantity of labour (L) i.e.

* *

__I__ = s __[Q]__ since
I = K ….Equation (1)

L [L]

Or, * *

__I__ = g __[K]__ ….Equation
(2)

L [L]

Where * over the variables refers golden age enormity. Equation (2) depicts that in a golden age per capita investment or saving should parity the symmetry growth rate times per capita capital stock.

Thus, per capita investment is in a straight rational to capital labour ratio. Consequently, per capita investment is straight line from origin.

Now, by substituting and equating Equations (1) and (2), we obtain

* *

__I__ = __s__ or
g = __Q__

*

L g K

*

Equation (3) demonstrates the golden age growth rate which is the slope of the
I/L curve.

Next, the manufacturing function;

1-a

Q = A(t)
(K*, L )

Where A(t) is some invariable , by keeping t = 0 and dividing L on both sides, we obtain the following;

__Q__ = A{__K__}*

L {L}

By switching variables in the above equation in association to the golden age, we obtain
the following;

* *

__Q__ = A{__K__}* ;

L {L}

*

which is drawn in the diagram as the Q/L curve. By inequitable demarcation, we get
the incline of the *

Q/L
curve as follows:

* *

d__(Q/L)__ = a__(Q)__

* *

k(K/L) (K)

* * *

Therefore, a (Q/K) is the incline of the Q/L curve that parities the marginal product
of capital.

*

The incline of the I/L curve is equal to the golden age growth rate, g and the slope
of the

*

Q/L curve parities the marginal product of capital, r is the rate of interest. As per
the golden rule of accumulation, the growth rate should equal the rate of interest,
g = r, in a maximum golden age.

* * *

This is described in the above diagram, where Q/L, S/L and I/L are shown on the vertical
side and

*

K/L on the horizontal axis; the maximum golden age according to the golden rule of
accumulation is at symmetry capital – labour ratio

*

(__K__)*

(L)

* *

where the vertical remoteness amid the curves Q/L and I/L is the largest;

It is AB in the diagram. Therefore, the golden rule of accumulation is fulfilled. When
the vertical deviation among the two curves;

* *

Q/L and I/L are at the optimum.

It is here that the per capita consumption is optimised.

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