Modify the Solow Growth model by including government spending as follows. The government purchases G units of consumption goods in the current period, were 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 every 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.
1. Derive equations for
(a) The law of motion of capital per worker over time (i.e. the relationship between k0 and k).
(b) The solution for steady state capital per worker k.