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Solow model with a government [20 marks] Consider a version of the basic Solow model which is the same as that discussed in the lec- tures except there is now a government

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Solow model with a government [20 marks] Consider a version of the basic Solow model which is the same as that discussed in the lec- tures except there is now a government. Suppose that a government purchases goods in the amount of g per worker every year; with N? workers in year t, total government purchases are gNt. The government has a balanced budget so that its tax revenue in year t, Tt, equals total government purchases. Total national saving St is St = s(Y4 – Tt), where Yt is total output and s is the national saving rate. (a) Derive the equation for the dynamics of capital per worker in this economy. Illustrate the steady-state for this economy on a diagram. (b) Suppose that the government permanently increases its purchases per worker and con- tinues to balance its budget. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker? Illustrate with a diagram. (c) Describe how the economy moves from the original steady state to the new one. What happens to the total capital stock during this process? (d) Now suppose that the government receives annual foreign aid that exactly covers the cost of its purchases. How will this affect the steady state levels of capital, output and consumption per worker?