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  =  g N and g is a positive constant. The government finances its purchases through lump-sum taxes on consumers, where  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 sis the savings rate, with 0 < s < 1.

a. Derive equations similar to Equations (7.17), (7.18), and (7.19), 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 one 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