Both population and workforce grow at the rate of n=1% per year in a closed economy. Consumption is C=0.5(1-t)Y, where t is the tax rate on income...

 Both population and workforce grow at the rate of n=1% per year in a closed economy. Consumption is C=0.5(1-t)Y, where t is the tax rate on income and Y is total output. The per-worker production function is y=8 k1/2 , where y is output per-worker and k is the capital-labour ratio. The deprecation rate of capital is d=9% per year. Suppose for now that there are no government purchase and the tax rate on income is t=0. 

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 is t=0.5. Report part (a) and compare your results.