Use the Solow-Swan growth model to answer the following questions. Show your work! Suppose that a government purchases goods in the amount of per worker every year; with Lt workers in year t, total government purchases are Lt . The government has a balanced budget so that its tax revenue in year t, Tt , equals total government purchases. National saving is given by St = s(Yt Tt) Kt , where Y is total output and s is the saving rate (0 < s < 1). The extra term, K, reflects the idea that when wealth (as measured by the capital stock) is higher, saving is lower. The total output is determined by the aggregate production function, Yt = AK t L 1 t , where A is constant, 0 < < 1, and physical capital depreciates at rate > 0. Finally, population growth rate is n > 0. (a) Find the steady-state condition for this economy, and graphically show the steady-state values of per-worker capital (k ) and output (y ). (b) Suppose that the government permanently increases its purchases per worker. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker?