# Question: Modify the Solow growth model by including government spending as

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?

**View Solution:**## Answer to relevant Questions

Consider a numerical example using the Solow growth model. Suppose that F(K, N) = K0.5 N0.5, with d = 0.1, s = 0.2, n = 0.01, and z = 1, and take a period to be a year.(a) Determine capital per worker, income per capita, and ...Suppose that the depreciation rate increases. In the Solow growth model, determine the effects of this on the quantity of capital per worker and on output per worker in the steady state. Explain the economic intuition behind ...Introduce government activity in the endogenous growth model as follows. In addition to working u units of time in producing goods, the representative consumer works v units of time for the government and produces gvH goods ...Consider the following effects of an increase in taxes for a consumer.(a) The consumer’s taxes increase by ∆t in the current period. How does this affect current consumption, future consumption, and current saving?(b) ...Suppose in our two-period model of the economy that the government, instead of borrowing in the current period, runs a government loan program. That is, loans are made to consumers at the market real interest rate r, with ...Post your question