1. Consider the effects of adding a government to the Solow model. Suppose that the government purchases G = PK units of consumption goods in any period, where l" :> {J is constant and hence total purchases grow with the capital stock. The government nances its spending via lump sum taxes T and balances its budget every period. Consumers consume a constant fraction (1 s) of after tax income: 0 = (1 s)(Y T). Output is produced via a Cobb-Douglas production function Y = K \"N 1\" with no productivity growth and the population grows at the constant rate it. (a) Determine the steady state per-worker quantities of capital, output, and con- sumption. (b) What are the eects of an increase in 1" on the steady state per-worker quan- tities of capital, output, and consumption