small K = k = K/L
rate of growth of k= rate of growth of K - rate of growth of L
ok?
rate of growth of k = (dK/dt)/K - (dL/dt)/L
Now , since in the long run , economy reaches steady state and at steady state rate of growth of k is equal to zero ( capital per person doesn't grow).
this gives ,
(dK/dt)/K = (dL/dt)/L
Now i can replace dK/dt by amount of investment done = savings rate x total output(income)= s * Q,
where Q is the total income ( output).
Next ,substitute this into the equation;
we get Investment/ total capital = rate of growth of labour
(s*Q)/K= 2%
s/capital-output ratio= 2%
we have s = 20%
=> capital-output ratio = 10.
"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."