(2) Use the Solow-Swan growth model to answer the following questions. Suppose that a government purchases goods in the amount of 0 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) wkt, where Y is total output and s is the saving rate (0 < s < 1). The extra term, -wK, 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, Y =K La AKEL- where A is constant, 0 < a < 1, and physical capital depreciates at rate > 0. Finally, population growth rate is n > 0. (a) When markets are perfectly competitive, find the labor share of national income. What happen to the labor share, when capital per worker (k = K/L) rises? (b) Find the steady-state condition for this economy, and graphically show the steady- state values of per-worker capital (k*) and output (y*). Suppose that the government permanently increases its purchases per worker. What are the effects on the steady-state levels of capital per worker and output per worker?