Consumption per worker is 72, depreciation is 12.5%, and capital per w

Consumption per worker is 72, depreciation is 12.5%, and capital per worker is 64. Given the production function y = 20 , show that this economy is in a steady state.

If the saving rate should double, what is the new steady-state level of consumption per worker?

ANSWER

The steady-state capital-labor ratio k* = . Plugging the values above into this equation yields s = 0.1. Putting the given value of k into the production function yields y = 80, so the given value of consumption per worker implies s = 0.1. This is a steady state. (As further confirmation, note that 64 × 0.125 = 8 = saving, so the loss of capital due to depreciation is exactly restored by investment.) If s = 0.2, then k* = 181, so y = 113, and consumption per worker is 113 × 0.8 = 90.