Question

# 17. Solow growth The production function in your country is: Y = K^0.5(LE)^0.5. Your economy saves...

17. Solow growth The production function in your country is: Y = K^0.5(LE)^0.5.

Your economy saves 24% of output each period, and 5% of the capital stock depreciates each period. The population grows 2% annually. Technology grows 1% annually. You begin with 1000 workers and 1 unit of capital, and a tech- nology level equal to 1.

a) Write the production function in per-eective-worker terms, so that per-effective-worker output (y = Y/LE ) is a function of per-effective-worker capital (k= K/LE ).
b) Compute the initial levels of output and per-worker output. Will per-effective worker output rise or fall next period?
c) Compute steady state capital-per-eective worker, output-per-eective worker,
and consumption-pe-effective worker
d) In the steady-state, at what rate does output grow? At what rate does
output-per-worker grow?
e) Compute the Golden rule level of capital-per-eective worker, and saving
rate needed to achieve that steady-state. Should more or less saving be
encouraged?