# Using the Solow model in this scenario, why does the ratio of output per capita not increase?

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 $$0.2$$:$$1$$.
• Can you add how you calculated the ratios? The ratios should contain the constants $A,g, \delta, n$. Mar 8 at 2:59