Modify the Solow growth model by including government spending, as follows. The government purchases G units of consumption goods in the current period, where G = gN and g is a positive constant. The government finances its purchases through lump-sum taxes on consumers, where T denotes total taxes, and the government budget is balanced each period, so that G = T. Consumers consume a constant fraction of disposable income, that is: C = (1 - s)(Y - T), where s is the savings rate, with 0 < s < 1.
Derive the equations that: i) determine the future stock of capital per worker (k') as a function of the current stock of capital per worker (k); ii) solve for the steady state capital stock per worker (k*); and show in a diagram how the latter, k*, is determined.