Question

1) An economy has the production function ?=20?^(1/2) The current capital stock is 100, the depreciation rate is 10%, and the population growth rate is 2%.

For income per person to grow, what rate must the saving rate exceed?

2) If the economy has more capital than in the Golden Rule steady state, reducing the saving rate will

decrease steady-state income but increase steady-state consumption.

decrease both steady-state income and steady-state consumption.

increase both steady-state income and steady-state consumption.

increase steady-state income but decrease steady-state consumption.

Answer 1

1)

The correct answer is (a) decrease steady-state income but increase steady-state consumption

Income per person (y) will increase if 20?^(1/2) increase => k increase

=> k = sy - (d + n)k > 0 ,where d = depreciation rate = 0.1 and n = population growth rate = 0.02

=> k = s(20*10) - 0.12*100 > 0

=> s > 0.06

Hence saving rate should be greater than 6% in order to income per person to grow.

2)

As level of Capital is greater than gold rule level of capital, this implies golden rule will be reached if we reduce capital. Golden rule level of capital is that level of steady state capital at which consumption per person is maximum. Hence If we reduce saving rate and according to above formula, k will decrease and will reach golden rule level of capital, steady state consumption per worker will increase and as level of capital is reduced steady state level of income will reduced.

Hence, the correct answer is (a) decrease steady-state income but increase steady-state consumption