# Question

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?

(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?

## Answer to relevant Questions

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