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.

(a) Derive equations similar to Equations (7- 18), (7-19), and (7-20), and show in a diagram how the quantity of capital per worker, k*, is determined.

(b) Show that there can be two steady states, one with high k* and the other with low k*.

(c) Ignore the steady state with low k* (it can be shown that this steady state is “unstable”). Determine the effects of an increase in g on capital per worker and on output per worker in the steady state. What are the effects on the growth rates of aggregate output, aggregate consumption, and aggregate investment?