An economy has the per-worker production function
yt = 3kt0.5,
where yt is output per worker and k, is the capital-labour ratio. The depreciation rate is 0.1, and the population growth rate is 0.05. Saving is
St = 0.3Yt,
where St is total national saving, and Y, is total output.
a. What are the steady-state values of the capital-labour 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
yt = 4kt0.5.
Assume that the saving rate and population growth rate are at their original values.