# Domar Model

__Increase in productive Capacity__

Domar describes the supply side as the annual rate of investment is I and the annual productive capacity per dollar of newly created capital is equal on the average to s and this represents the ratio of increase in actual earnings or productivity to an enhancement in capital or the reciprocal of the accelerator or the marginal capital productivity ratio. Therefore the productive capacity of I dollar invested will be I.s dollar a year.

But some new investment will be at the expense of the old. It will thus, compete with the latter for labour markets and other aspects of production. Consequently the productivity of old plants will be curtailed and the enhancement in the annual productivity of the fiscal system will be rather less than I.s.

This can be depicted as I σ, where σ is the sigma which represents the net latent social average output of investment (= Δ Y / I). Hence I σ is less than I.s. I σ is the aggregate net potential enhancement in productivity which the fiscal system and is termed as the sigma effect.

__Required Enhancement in Total Demand__

The demand side is described by the Keynesian multiplier. Let us assume the annual enhancement is denoted by Δ Y and the enhancement in investment by Δ I and the propensity to save by α – alpha (= Δ S / Δ Y). Then the enhancement in earnings will be equal to the multiplier (1 / α) times the enhancement in investment.

It is given by: Δ Y = Δ I
* __1__

α

__Symmetry__

To maintain full employment symmetry level of earnings, total demand must be equal to total supply. Thus we accomplish at the fundamental equation of the model:

ΔI
*__1 __ = I α

Α

Solving this equation by dividing both sides by I and multiplying by α we obtain the following:

__ΔI__ = α σ

I

This equation depicts that to uphold full employment the growth rate of net independent investment ΔI / I should be equal to α σ (the MPS times the output of capital). This is the rate at which investment must grow to assure the use of potential capacity in order to uphold a steady growth rate of the fiscal system at full employment.

A numerical illustration could explain us better the Domar Model.

__Illustration 60__

Assume σ be 20% per annum, α be 10% and Earnings Y be $ 300 billions per annum.

- Compute to achieve full employment what would be amount of investment to be made.
- Also ascertain the productive capacity of investment and
- The comparative hike in earnings with the given values

__Solution__

- The amount to invested to accomplish full employment is

Y * α / 100

**300 * 10 / 100 = $30
billions**

**Hence, in order to achieve full employment, the investment to be made is $ 30
billion dollars.**

- To know the productivity of capital investment,

Y * (α / 100) * (σ / 100)

300 * (10 / 100) * (20 / 100)

**$ 6 billion dollars**

**Therefore, the capital investment productivity would increase by 6 billion dollars.**

- The comparative hike in income is,

Y * __(α / 100) * (σ / 100)__

Y

300 * __(10 / 100) * (20 / 100)__

300

**6 / 300 % = 2%**

**Hence the comparative increase in income would be 2%.**

__The Harrod Model__

The Harrod model depends on three discrete rates of growth. Primarily, there is the actual growth rate symbolized by G which is ascertained by the saving ratio and the capital-productivity ratio. It depicts short run cyclical changes in the rate of growth. Next to it, there is the warranted growth rate represented by Gw which is the full capacity growth rate of earnings of a fiscal system. Lastly, there is a original growth rate depicted by Gn which is considered as “the welfare optimum” by Harrod. It is termed as capable or full employment rate of growth.

__The Actual Growth Rate__

In the Harrodian model the first fundamental equation is:

GC = s

Where, G is the rate of growth of productivity in a given period of time and can be expressed as Δ Y / Y; C is the net adding up to capital and is denoted as the ratio of investment to the enhancement in earnings, i.e. I / Δ Y and s is the average inclination to save, i.e. SlY. By substituting these ratios in the above equation we obtain:

(Δ Y / Y) * (I / Δ Y) = S / Y or I / Y = S / Y or I = S

The equation is merely a summary of the axiom that original savings parities original investment.

__The Warranted Rate of Growth__

The warranted rate of growth is as per to Harrod, the rate at which producers will be content with what they are performing. It is the industrial symmetry, it is the line of sophistication which if accomplished will content profit takers that they have done the correct obsession. Therefore this growth rate is primarily associated to the behaviour of businessmen. At the warranted rate of growth, demand is huge enough for business men to sell what they have manufactured and they will carry on manufacturing the same percentage of 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
- Disequilibrium in the Balance of Payments
- Endogenous Growth Theory
- Flexibility of Saving Ratio
- Foreign Exchange Rate
- Foreign Exchange Rate Policy
- Golden Rule of Accumulation
- 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