THE HARROD MODEL:
The Harrod-Domar

For more than half -a century, have applied the Harrod-Domar model to calculate short-run investment requirements for a target growth rate in the economy. If there is a gap" between the required investment and available resources, this gap presents an obstacle to economic growth and has to be financed through borrowing or external aid. In simple terms, the Harrod model is used to explain the relationship between income Yt, Savings, St, and Investment It in the econmoy: There are two main equations in the model and an equilbrium condition.

Eq.1 St=sYt, where s is marginal propensity to save : MPS,

Eq.2 It=a(Yt-Yt-1), in this equation a is a consatant and is assumed to be equal to both marginal and average capital-output ratios. The equilibrium equation is:

Eq.3 a(Yt-Yt-1)= sYt or (a-s)Yt=ayt-1. Divide both side by (a-s), and we have a typical first -order difference equation Yt= [a/(a-s)]Yt-1. The solution to this equation is:

Yt= (Y0-0)(a(/(a-s))^t +0= (a/(a-s)^t *Y0

The stability of the time path for this equation dependends on the ratio a/(1-s).. since (s) is greater than 0, but less than one, the ratio a/(a-s) will be larger than 0. If it is greater than one, Yt will continue to increase without osillation. For investment and savings to remain in long-run equilibrium, the ecoomy has to grow at a rate which is equal to :

eq. 4 s/(a-s) which should produce a coefficient with a value of less than one. This value is known as the warannted rate of growth. See the following example:

> Yt:=(2.12/(2.12-0.12))^t*Y0;

The warranted rate of growth is :

> GW:=0.12/(2.12-0.12);

Note that the warranted rate of growth is just 6 percent above the 1.06^t coefficient. Now assume Y0 =50 and t=10, find YT.

> Yt:=(1.06^10)*50;

> St:= 0.12*89.54238485;

> Yt:=(1.06^9)*50;

> It:=2.12*(89.54238485-84.47394795);