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Two countries A and B have identical production function $Y=AK^{1/3}N^{2/3}$, they are identical when it comes to all other factors with the exception that savings rate is $s_A>s_B$. a) What is the GDP to number of people employed ratio in those countries?
Question is about Solow - swan model. How to apply this model in this particular case, because i am completely lost.
GDP per worker is the ratio of GDP (Y) to the number of people employed (N), it is Y divided by N. Some books denote it as little Y (y). Divide both sides of the production function by N (remember to use the rules of dividing exponents for N on the left hand side i.e. subtract the exponents, for N it will be 2/3-1 = 1/3).
Simplify the equation, so on the left hand side you should have (K/N) raised to the power of 1/3. You can replace this fraction with little k (k), raised to the power of 1/3. The little k represents capital per worker then.
1) $$ Y = A K^{1/3} N^{2/3} $$
2) Divide by N
3) $$ Y/N = A K^{1/3} N^{2/3-1} $$
4) $$ Y/N = A K^{1/3} N^{-1/3} $$
5) $$ Y/N = A (K/N)^{1/3} $$
6) $$ y = A (k)^{1/3} $$
