# What happens to aggregate C, K, and Y when TFP increases permanently?

I was wondering what would happen to aggregate capital, consumption and output (i.e. K, C, Y) in the Solow model with constant population growth (i.e. n > 0) and no technological growth (i.e. a = 0) if TFP suddenly increases permanently at time $t_{0}$ (i.e. $A_{0}$ --> $A_{1}$). I am assuming that all three K, C, and Y will increase and converge to the new steady state level. But I wanted to know how it would adjust(i.e. would it be an instant increase or gradual increase from previous to new steady state level).

Take a look at the dynamics of the capital: $k_{t+1}=sA_ty_t+(1-\delta-n)k_t$. A sudden positive shock to TFP in period $t$ increases the capital stock of the next period $k_{t+1}$. So, there is no contemporaneous effect on $k$, convergence to the new steady state will be gradual.
• @DavidKim If you suddenly become more productive today, what would happen to your wage, output and consumption today? Also, the answer to all your questions can be seen one single graph ($k_t$ in x-axis, and $f(k_t)$ in y-axis). I suggest you do attempt to get this graph. Sep 16, 2017 at 7:50