GDP to employed people ration - solow swan model - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2022-01-27T22:54:09Z https://economics.stackexchange.com/feeds/question/9115 https://creativecommons.org/licenses/by-sa/4.0/rdf https://economics.stackexchange.com/q/9115 0 GDP to employed people ration - solow swan model mkropkowski https://economics.stackexchange.com/users/5486 2015-11-11T16:46:21Z 2015-11-11T17:44:25Z <p>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&gt;s_B\$. a) What is the GDP to number of people employed ratio in those countries?</p> <p>Question is about Solow - swan model. How to apply this model in this particular case, because i am completely lost.</p> https://economics.stackexchange.com/questions/9115/-/9119#9119 1 Answer by Kelly for GDP to employed people ration - solow swan model Kelly https://economics.stackexchange.com/users/5367 2015-11-11T17:32:45Z 2015-11-11T17:44:25Z <p>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). </p> <p>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.</p> <p>1) \$\$ Y = A K^{1/3} N^{2/3} \$\$</p> <p>2) Divide by N</p> <p>3) \$\$ Y/N = A K^{1/3} N^{2/3-1} \$\$</p> <p>4) \$\$ Y/N = A K^{1/3} N^{-1/3} \$\$</p> <p>5) \$\$ Y/N = A (K/N)^{1/3} \$\$</p> <p>6) \$\$ y = A (k)^{1/3} \$\$</p>