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) $$ y = A (k)^{1/3} $$

  • $\begingroup$ Could you possibly try to type it? It would be much clearer for me, to type equations on this website you need to use latex to use it you need to: "LaTeX mathematics can be entered inline by enclosing the LaTeX code in \$ like this: \$a=b^x\$." $\endgroup$ Nov 11 '15 at 17:37
  • $\begingroup$ I had no idea about that, thanks! I edited the question $\endgroup$
    – Kelly
    Nov 11 '15 at 17:45

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