I am confused about this question and the concepts that follow.
Countries $X$ and produces output per capita according to $y=Ak^a$. Country $X$’s savings rate is $s_X = 5\%$. Country $Z$ saves $s_Z = 25\%$. Each country has the same level of technology $A$ and capital depreciates at the same rate, $d$, as well.
a) Calculate the ratio of steady state outputs per capital when the share of income accruing to capital is $\frac{1}{3}$. b) Suppose the share of capital rises to $\frac{1}{2}$. Recalculate the ratio and explain the difference.
Assuming $n$, $d$, and $A$ are the same for each country, I did both calculations and got that the ratio of output per capita (Country $X$:Country $Z$) when capital share is $\frac{1}{3}$ is $0.447$:$1$. When capital share is $\frac{1}{2}$, I get $0.2$:$1$.
Why would the ratio be decreasing? Normally with the Solow model, it seems like the richer countries experience diminishing returns to scale and thus grow slower than poorer countries which justifies Solow's idea of conditional convergence. Can someone explain?
