Question

An economy has the production function The current capital stock is 100, the depreciation rate is 10 percent, and the population growth rate is 2 percent. For income per person to grow, the saving rate must exceed

1. 6 percent.
2. 8 percent.
3. 10 percent.
4. 12 percent.

Answer 1

Answer

The correct answer is (a) 6 percent

Production function or Income is given by: y = 20k^1/2.

We can see from above function, Output or Income will increase when k increases.

k will increase If Change in k >0 As, change in k = sy - (d + n)k

=> Change in k =  sy - (d + n)k > 0

where s = saving rate , d = depreciation rate = 10% = 0.10 , n = population growth rate = 2% = 0.02 and k = 100

Thus, sy - (d + n)k > 0

=> s(20k^1/2)- (0.1 + 0.02)k > 0

=> s(20k^1/2)- (0.1 + 0.02)k > 0

=> s(20*100^1/2)- (0.1 + 0.02)100 > 0

=> 200s > 0.12*100

=> s > 12/200 = 0.06

=> saving rate > 6 percent.

Hence saving rate should be greater than 6%.

Hence, the correct answer is (a) 6 percent