The Harrod-Domar Growth Model
Every economy must save a certain proportion of its national income, if only to replace worn-out or impaired capital goods (buildings, equipment, and materials).
However, in order to grow, new investments representing net additions to the capital stock are necessary. If we assume that there is some direct economic relationship between the size of the total capital stock, K, and total GNP, Y—for example, if
$3 of capital is always necessary to produce a $1 stream of GNP—it follows that any net additions to the capital stock in the form of new investment will bring about corresponding increases in the flow of national output, GNP.
Suppose that this relationship, known in economics as the capital-output ratio, is roughly 3 to 1. If we define the capital-output ratio as k and assume further that the national savings ratio, s, is a fixed proportion of national output (e.g., 6%) and that total new investment is determined by the level of total savings, we can construct the following simple model of economic growth:
1. Saving (S) is some proportion, s, of national income (Y) such that we have the simple equation
S
sY (4.1)
2. Net investment (I) is defined as the change in the capital stock, K, and can be represented by K such that
I
K (4.2)
But because the total capital stock, K, bearsa direct relationship to total national income or output, Y, as expressed by the capital-output ratio, k, it followsthat or K
Y

k
K
Y

k
114 Principles and Concepts or, finally,
K
kY (4.3)
3. Finally, because net national savings, S, must equal net investment, I, we can write this equality as
S
I (4.4)
But from Equation 4.1 we know that S
sY and from Equations 4.2 and 4.3 we know that
I
K
kY
It therefore follows that we can write the “identity” of saving equaling investment shown by Equation 4.4 as
S
sY
kY
K
I