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

Kelly
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