NOTE: for part a, assume the tax rate,t, is 0.

Both population and the work force grow at the rate ofn= 1% per year in a closed economy. Consumption isC= 0.5(1t)Y, wheretis the tax rate on income andYis total output. The per-worker production function isy= 8k, whereyis output per worker andkis the capital-labor ratio. The depreciation rate of capital isd= 9% per year. Suppose for now that there are no government purchases and the tax rate on income ist= 0.

a. Find expressions for national saving per worker and the steady-state level of investment per worker as functions of the capital-labor ratio,k. In the steady state, what are the values of the capital-labor ratio, output per worker, consumption per worker, and investment per worker?

b. Suppose that the government purchases goods each year and pays for these purchases using taxes on income. The government runs a balanced budget in each period and the tax rate on income ist= 0.5. Repeat Part (a) and compare your results.