The Harod Domer 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.