San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
USA

 Theoretical Models of Economic Growth

## The Harrod-Domar Growth Model

The Harrod-Domar growth model gives some insights into the dynamics of growth. We want a method of determining an equilibrium growth rate g for the economy. Let Y be GDP and S be savings. The level of savings is a function of the level of GDP, say S = sY. The level of capital K needed to produce an output Y is given by the equation K = σY where σ is called the capital-output ratio. Investment is a very important variable for the economy because Investment has a dual role.

Investment I represents an important component of the demand for the output of an economy as well as the increase in capital stock. Thus ΔK = σΔY. For equilibrium there must be a balance between supply and demand for a nation's output. In simple case this equilibrium condition reduces to I = S. Thus,

#### I = ΔK = σΔY and I = S so σΔY = sY.

Therefore the equilibrium rate of growth g is given by

#### g = ΔY/Y = s/σ

In words, the equilibrium growth rate of output is equal to the ratio of the the marginal propensity to save and the capital-output ratio. This is a very significant result. It tells us how the economy can grow such that the growth in the capacity of the economy to produce is matched by the demand for the economy's output.

Consider this numerical illustration. Suppose the economy is currently operating at a capacity production level of 1000 per year and has a capital-output ratio of 3. This means the capital stock is 3000. Assume the marginal propensity to consume out of GDP is 0.7 so the marginal propensity to save is 0.3. This includes business and public saving as well as household saving. The Harrod-Domar growth model tells that the equilibrium growth rate is g = 0.3/3 = 0.1; i.e., the economy can grow at 10 percent per year. We can now check this result. At the current GDP of 1000 the level of saving is 0.3*1000=300. The growth in GDP is 0.1*1000 = 100 and with a capital-output ratio of 3 the additional capital required to produce the additional output is 3*100=300. This is the investment required in order to increase capacity by the right amount and, sure enough, this happens to be equal to the amount of saving available in the economy.

But we must made sure there is adequate aggregate demand next year to absorb the production of 1100. At that level of income the consumer demand is 0.7*1100 = 770. The level of investment the next year under the assumed equilibrium growth conditions is derived as above. The ten percent growth on production of 1100 is 110 which with a capital-output ratio of 3 requires an increase in capital stock of 330. Thus next year's investment will be 330. This, added to the consumer demand of 770 gives an aggregate demand of 1100. Thus everything balances.

For contrast, let us consider what would happen if the level of current level of investment were to be higher, say 350. This, combined with consumption demand of 700 generates more demand than the capacity of the economy to produce. That excess of investment of 50 induces a demand for an additional 3*50 = 150 units of capital which the economy cannot achieve. There is an irresolvable excess of demand in the economy.

On the other hand, suppose the investment demand fell short of 300, say 250. Now the aggregate demand is only 950, less than the capacity of the economy. If production falls to 950 there is an excess of capital and no need for any investment. Thus aggregate demand fall as investment dropped to zero and consumer demand would drop along with. There would be an irresolvable deficiency of demand.

The equilibrium of the Harrod-Domar model is a razor-edge equilibrium. If the economy deviates from it in either direction there will be an economy calamity.

(To be continued.)