Explanation for Balanced budget and finding capital-labour ratio in a steady state economy.
Consider the following Solow model of growth. Both population and work force grow at the rate of n=1% per year in a closed economy.
Consumption is given by
C=.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 √k
Where y is output per worker and k is the capital-labor ratio. The depreciation rate is δ = 9% per year. Suppose for now that there are no government purchases and that tax rate on income is t=0.
a) In steady state, what are the values of the capital-labor ratio, output per worker, consumption per worker, and investment per worker?
b) Assume that the government purchases goods every year and pays for these using taxes on salary. The government runs a balanced budget in every period and the tax rate on salary is t=.5. Repeat part (a) and comment on the differences.