Question

If Y = AK1/3L2/3 and A grows at a rate of 1 percent per year, K grows at a rate of negative 3 percent per year and L grows at a rate of 3 percent per year, then the growth rate of Y is

0 percent.

1 percent.

2 percent.

3 percent.

Answer 1

The correct answer is (c) 2 percent

Formulas :

(i) Growth rate of (A*B) = Growth rate of A + Growth rate of B

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

Here : Y = AK^1/3L^2/3

=> Growth rate of Y = Growth rate of (AK^1/3L^2/3)

Hence, using above formulas we get

Growth rate of Y = Growth rate of (AK^1/3L^2/3) = Growth rate of A + (1/3)*Growth rate of K + (2/3)*Growth rate of L

It is given that A grows at a rate of 1 percent per year, K grows at a rate of negative 3 percent per year and L grows at a rate of 3 percent per year.

Hence, Growth rate of Y = Growth rate of (AK^1/3L^2/3) = 1 + (1/3)*(-3) + (2/3)*3 = 2%

Hence, Growth rate of Y = 2$.

Hence, the correct answer is (c) 2 percent