Derivation of Harrod domar growth model ?

The Harrod-Domar growth model is a macroeconomic model that explains the relationship between savings, investment, and economic growth. It was developed independently by economists Roy Harrod and Evsey Domar in the 1930s and 1940s.

The model is derived from the Keynesian theory of income determination, which emphasizes the importance of aggregate demand in driving economic growth. Harrod and Domar extended this theory by focusing on the role of investment in determining the rate of economic growth.

The basic premise of the model is that economic growth is driven by investment, which in turn is determined by the level of savings in the economy. The model assumes that there is a stable relationship between the level of investment and the rate of economic growth, known as the capital-output ratio.

The Harrod-Domar growth model can be mathematically represented as follows:

Y = I + C
Y = GDP or national income
I = Investment
C = Consumption

The rate of economic growth (g) is equal to the ratio of investment (I) to the capital-output ratio (k):

g = I / k

The model also assumes that the economy is in a state of equilibrium when the rate of investment is equal to the rate of economic growth. If the rate of investment is higher than the rate of economic growth, the economy will experience inflation and excess capacity. If the rate of investment is lower than the rate of economic growth, the economy will experience deflation and unemployment.

Overall, the Harrod-Domar growth model provides a framework for understanding the relationship between savings, investment, and economic growth in an economy. It highlights the importance of maintaining a balance between investment and economic growth to achieve long-term sustainable development.