# Golden Rule Of Accumulation

__Introduction__

Edmund Phelps while describing the golden age growth lays down the golden rule of accumulation. As per Golden Rule of Accumulation, per capital consumption is optimised in a golden age when the thrift rate parities the profit rate. If the thrift rate is lower than the profit rate, the per capital consumption is lower than the achievable maximum.

Alternatively, if the thrift rate is higher than the profit rate, per capita consumption will turn down. Therefore, it is a specific objective rate of thrift that optimises per capita consumption in a golden age. This is known as the golden rule saving rate or maximum thrift rate.

If the unchanged sum of consumption is given to members of every existing and prospect cohort, the maximum sum per capita consumption is called the golden rule consumption rate.

The golden rule is described where golden age per capita consumption, (C/L)* is brought on the vertical axis and the thrift rate s on the horizontal axis. While we shift along the CS curve per capita consumption enhances at low levels of saving and diminishes at high levels of thrift. It is at the Golden rule of thrift rate or saving rate s*g that per capita consumption is optimised at c*g level of per capita consumption. This is the greatest point H on the CS curve.

__Golden Age and Golden Rule of Accumulation__

There are various understandings of Phelps golden rule of accumulation. But, we shall follow the Solow's undemanding description. In a golden age, consumption, productivity, capital stock and every thing else is growing at the same rate. This growth rate is g and that is the symmetry growth rate. This rate is at liberty of the proportion of capital accumulation to productivity. Relating to this investment ratio or productivity ratio, there subsists at least one capital productivity ratio which will be upheld.

The subsistence of a symmetry growth or natural growth means that capital and labour are surrogatable in such a manner that the capital productivity ratio can regulate to any value of s. Under situations of symmetry growth the capital productivity ratio is

__K*__ = __s__ or
g = s __Q*__

Q* g K*

Where ‘*’ refers to symmetry value of K which is capital and Q which is productivity or output, s is thrift or saving rate and g is the golden age growth rate.

The growth rate g is not a function is s however it is s that ascertains K*/Q*. If we have two golden age paths with same growth rates, the one with the upper thrift or saving rate will have the higher capital productivity ratio and with optimist marginal products the higher level of productivity.

Therefore the thrift rate influences the level at which the fiscal system improves but it des not influence its improvement or growth rate. This situation is demonstrated in the below diagram where logarithmically parallel two golden age paths Q*A and Q*B pass a given check point say time nil.

They are similar in all manners. But the thrift rate on path Q*B is greater. This entails that path Q*B has a huger capital productive ratio and a greater level of productivity than path Q*A.

In judging which growth path is the best a generation will look only at the sum of consumption which each paths offers. Given an invariable s, each golden age path is linked with a per capital consumption path (C/L)* on which consumption grows exponentially at the unchanged rate as productivity. Under situations of symmetry growth, per capital consumption along these parallel trails (C/L)1*, (C/L)2* and (C/L)3* in the below diagram is at the similar rate g.

Thus there subsists some uniformly uppermost feasible per capita consumption path, such as (C/L)3* than any other consumption trail. All generations will obviously prefer this with its respective thrift rate to any lower per capita consumption path, such as (C/L)3* or (C/L)1*.

Therefore, the golden rule ascertains the symmetry growth path that optimises per capita consumption for all time once the fiscal system reaches that trail. The larger the thrift rate the larger the level of productivity. But the level of larger depends on the marginal product of capital, r. Having a few more capital, ΔK, at this phase would capitulate r ΔK more in productivity. Actually, r ΔK is the additional productivity of capital. But all this is not accessible for consumption.

Having a few more capital now perform the financial system to some supplementary in the existing and in prospect to keep the somewhat fewer well-built capital inventory developing at a fixed rate, g. In particular a little extra capital, ΔK, now means that the productivity of g ΔK of capital goods is required simply to keep the new little extra capital growing at rate g.

If r ΔK > g ΔK or r > g, keeping a few more capital at present will capitulate some additional consumption at present and for all phase. Or otherwise, if r < g keeping a few more capital at present would in fact, draw off sufficient efficient capacity to the investment segment to diminish consumption.

Consumption is at a maximum when r = g (when the marginal product of capital parities the growth rate). The rate of profit is incorporated in the value of the marginal product of capital. Therefore, the maximum amount of capital under the golden rule is that which parities the profit rate to the growth rate.

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**Other topics under Growth Models and Macro Economics in an Open Economy:**

- Adjustment Mechanisms of Balance of Payments
- Applications of Fixed Conversion (o) Exchange Rates
- Balance of Payments Meaning and Components
- Causes of variations in the Conversion Rate
- Capital Account
- Crucial Appraisal
- Double Entry Book Keeping
- Domar Models
- Disequilibrium in the Balance of Payments
- Endogenous Growth Theory
- Flexibility of Saving Ratio
- Foreign Exchange Rate
- Foreign Exchange Rate Policy
- Harrod Models
- Mechanical Price Regulation under Supple Convertible Rates
- Pictorial Representation of the Golden Rule
- Romer's Model of Hi-tech Variation
- Solow Swan Model of Growth
- Steady State Growth