LECTURE NOTES: MATURITY AND STAGNATION 
J^^Sir Roy^ Harrods theory is a good starting point for an explanation 
of maturity. a i gebra 
In the following his XKMXjf is a tiny bit complicated by introducing 
the concepts of capacity and NKX utilisation. 
* . V 
We define: Y output volume (i.e. its value in constant prices) 
K capacity output ( as above) 
2 u= Y /K degree pf utilisation 
^ v= I/A K marginal capital coefficient ^<zZ-cofr&t* 
Writing each variable with a subscript t we make them all depend on time. 
We £btain 
+ K*Au t (-,) 
XK% 
k Kt = (1/U t (A u t /u t ) K| (£) 
I t = v^K| 
i t = f v / u t )^Xf " V (A u t/ u t^ K t 
I t = s t = sY^ 
T^jh propensity to save s and the capital coefficient v are assu med 
to be constants, dividing the last *wo equations we obtain 
(v/s u t )(A^t) = 1 + (v/s)^u t / u t ^ 
A Y t/ ^t =(f/ v ) u t + A V u t (4) 
It follows that if the actual growth rate (left side) 
is smaller than the warranted growth rate^s/v^u^. at a given rate of 
utilisation - say, at the normal or desired rate - than the rate of 
utilisation will hatre to decline. Harrod deals with the case where 
the rate of growth cannot surpass a certain level for lack of manpower 
-the so-called natural rate of growth - and where consequently 
and unemployment 
the system is driven into dBpression^because the low rate of 
utilisation will discourage private investment. 
This is a description of maturity even though this term 
is not used by Harrod .