5. An economy has the per-worker production function

= y k 3 t t0.5 where yt is output per worker and kt is the capital labor ratio. The depreciation rate is 0.1, and the popu lation growth rate is 0.05. Saving is

= S Y 0.3 , t t where St is total national saving and Yt is total output.

a. What are the steady-state values of the capital–

labor ratio, output per worker, and consumption per worker?

The rest of the problem shows the effects of changes in the three fundamental determinants of long-run living standards.

b. Repeat Part ( ) a for a saving rate of 0.4 instead of 0.3.

c. Repeat Part ( ) a for a population growth rate of 0.08 (with a saving rate of 0.3).

d. Repeat Part ( ) a for a production function of

= y k 4 . t t0.5 Assume that the saving rate and population growth rate are at their original values.