My question is from over lapping generations

Question is as follows

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I found that

$$k(t+1)= \frac{\beta(1-\alpha)}{(1+\beta)(1+n)}A(t)k(t)^{\alpha}$$

How can I deal with A(t) to find the steady state $k^*$? By the way, at steady state,$ k(t+1)=k(t)=k^*$


Is that derivation for $k(t+1)$ correct? Technically, you never reach the steady state, but only asimptotically as $t\rightarrow\infty$, but at infinity the $A(t)$ will also be infinite because it grows exponentially with time. I suspect that $k(t+1)$ should depend on $(1+g)$ instead of $A(t)$.

Usually these models are expressed in units of effective labor, that is, dividing the capital stock $K(t)$ and the labor $L(t)$ (and hence, the production and consumption) by $N(t)$ and $A(t)$.

  • $\begingroup$ This is much better posed as a comment, you don't answer the problem. Also as you can see this is not one of those problems in which we impose Harrod-neutral technological progress. While your point is valid, that is not what is being used for this specific problem $\endgroup$
    – Brennan
    Jan 22 at 5:55
  • $\begingroup$ SE does not allow me to write comments. My point is that the capital stock, as is expressed in the formula written by OP does not have a steady state, because $A(t)$ grows exponentially. Maybe OP can share how he arrived at that law of motion for capital. $\endgroup$
    – Pekisch
    Jan 22 at 19:40

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