# Improve my solution: Question on solow model

There is a question about Solow growth and Ramsey model,

compared to solow model, the Ramsey model is better to explain growth patterns across countries because it predicts a slower convergence rate.

Can we evaluate this statement?

Firstly consider the production function as

$$f(k)=k^{\alpha}$$

For Ramsey model utility function is as:

where rho is discount rate. And it’s lagrangian function can be set up as;

After some calculations, speed of convergence is calculated as

where g is technological growth and n is labor growth.

And for solow model speed of convergence is $$μ_2= (1-\alpha)(\delta + n+ g$$

delta is depreciation rate. Again I obtain this formula after some calculations, it I don’t want to show in detail here.

Now assume that we set α=1/3 ρ=4%, n=2% g=1% θ=1 β=2%

Then we get

$μ_1=5.4$ and $μ_2=2%$ for delta is zero.

Thus adjustment is quite rapid in this caseof Ramsey model; for comparison, the Solow model with the same values of α, n, and g (and as here, no depreciation) implies an adjustment speed of 2 percent per year. The reason for the difference is that in this example, the saving rate is greater than $s∗$ when k is less than $k∗$ and less than s∗ when k is greater than $k∗$. In the Solow model, in contrast, s is constant by assumption.

For the evaluation of this statement, I consider such and explanation. But I wonder what you add this explanation? How can I explain more perfectly? Please share your ideas with me. Thanks.