Question

8. Consider the following production function Y = AK0.3(NH)0.7 where Y is GDP, A is total factor productivity, K is capital, N is employment and H is human capital. Denote by P the population of the country. Thus, Y/P is per-capita GDP and N/P is the fraction of the population employed. What is the contribution of the fraction of the population employed (N/P) to the growth rate of per-capita GDP (Y/P)? (a) Growth rate of N/P. (b) Growth rate of N/P multiplied by 0.3. (c) Growth rate of N/P multiplied by 0.7. (d) Growth rate of N.

Answer 1

Answer

Production function is given by :

Y = AK^0.3(NH)^0.7

Dividing both sides by P and also using P = P^0.7P^0.3 we get :

Y/P = A(K/P)^0.3(N/P)^0.7H^0.7

Formulas :

Growth rate of (AB) = Growth rate of A + Growth rate of B

Growth rate of (A^B) = B(Growth rate of A)

Using above formulas we have :

Growth rate of (Y/P) = Growth rate of A + 0.3(Growth rate of (K/P)) + 0.7(Growth rate of (N/P)) + 0.7(Growth rate of H)

Hence Contribution of N/P to growth rate of Y/P is 0.7(Growth rate of (N/P))

Hence, the correct answer is (c) Growth rate of N/P multiplied by 0.7.