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In the long run Solow steady state, the growth rate of output in a country is g + n. If there is some other country with exactly the same properties of the first country and the same initial conditions, will the combined output of both the countries also grow at g + n?

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Yes, for any A and B $$ \text{A}\cdot(g+n) + \text{B}\cdot(g+n) = \text{(A+B)}\cdot(g+n) $$ does indeed hold.

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