The Aggregate Production Function
An implicit assumption of the Harrod-Domar model is that there are no diminishing returns to capital. The total product of capital curve (TPk) is a straight line from the origin this means that the marginal product of capital (MPk) is constant and equal to the average product of capital (APk). The reciprocal of the marginal product of capital is the incremental capital output ratio (ICOR).

The Savings Function
It was assumed that the proportion of income that was saved, the average propensity to save (APS) was constant. Thus, both the total product of capital (TPk) curve and the average propensity to save (APS) curve were straight lines beginning at the origin. In this diagram, the ratio (S1/Y1) is equal to the APS.

Per Worker Basis
These graphs can be put on a per worker basis by dividing the capital stock (K), GDP (Y) and Savings (S) by the number of workers (N). The shapes of the curves will not change if we assume that there are constant returns to scale.

Net Investment Per Worker
The blue line indicates the amount of new capital that goes to replace depreciated capital and the amount needed to equip new workers with the same amount of capital as the present workers (capital widening). The difference between that and total saving is net capital accumulation. The net addition to the capital stock can be used in the next period to increase the capital/labor ratio (capital deepening). In this model, per worker income grows at a constant rate indefinitely and the absolute increments to growth get bigger every year.

Calculating the Growth Rate of GDP
The growth rate of GDP can be calculated very simply. The ICOR is defined as the growth in the capital stock divided by the growth in GDP. Since Investment (I) is defined as the growth in the capital stock, the ICOR is equal to Investment divided by the growth of GDP. Investment will be equal to savings and Savings is equal to the APS times GDP. If we divide both sides by the ICOR and we divide both sides of the equation by GDP we have the result that the growth rate of GDP will equal the Average Propensity to Save (APS) by the Incremental Capital -Output Ratio (ICOR). Thus if the APS is 12% and the ICOR is 3 the growth rate of GDP, G(Y), would be 4%.

Calculating the Growth Rate of GDP Per Capita
The growth rate of GDP can be calculated very simply. The growth rate of any ratio is equal to the growth rate of the numerator minus the growth rate of the denominator. In this case we must subtract the growth rate of population, G(P) from the growth rate of GDP, G(Y). The growth rate of GDP, G(Y) is equal to the APS/ICOR. Therefore the growth rate of GDP Per Capita, G(Y/P) is equal to APS/ICOR – G(P).

The Effect of Savings Rates
An increase in the savings rate (APS) will increase the growth rate of per capita income. The size of the increase will be inversely proportional to the size of the incremental capital output ratio (ICOR). If the ICOR was 3, a 6% increase in the savings rate would be needed to increase the growth rate of per capita income by 2%, assuming that both the ICOR and the rate of population growth G(P) remained constant.

An Increase in the Incremental Capital-Output Ratio
The incremental capital-output ratio, or ICOR, is equal to 1 divided by the marginal product of capital. The higher the ICOR, the lower the productivity of capital. The ICOR can be thought of as a measure of the inefficiency with which capital is used. In most countries the ICOR is in the neighborhood of 3.

The Effect of an Increase in the Population Growth Rate
The Growth Rate of GDP will equal the average propensity to save (APS) divided by the incremental capital-output ratio, (ICOR). If the population growth rate is zero, that will also equal the growth rate of GDP per capita since the growth rate of GDP per capita is equal to the growth rate of GDP minus the growth rate of the population. Thus every 1% increase in the population growth rate translates into a 1% fall in the growth rate of per capita GDP.