N3

4. Consider an economy described by the following production function: Y=AK^0.3L^0.7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Y is total output, A is technological progress, K is capital stock and L is labor supply.

a) What is the per-worker production function?

b) Show that this production function has constant returns to scale.

C) Assuming no population growth or technological growth, and assuming that the change in capital per worker is zero and/or that investment equals capital depreciation, find the capital stock per worker and output per worker as a function of the saving rate and the depreciation rate. Hint: let investment: i = sy

D) What results in (c) above suggest for economic growth?