# Question on overlapping generations

My question is from over lapping generations

Question is as follows 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,$$k(t+1)=k(t)=k^*$$

## 1 Answer

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 $$A(t)$$.

• 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 – Brennan Jan 22 at 5:55
• 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. – Pekisch Jan 22 at 19:40