In this class, we assumed that government spending G doesn't provide any benefit to the households and firms. However, in reality, if government spending is used for much needed public projects (for example, education and public transportation), households and firms might benefit from this. Let's incorporate this effect by a stock of public good denoted with KG. The accumulation of public good is similar to the accumulation of capital stock: K1= (1-6) K+ G where G is the government spending at time t and 6c is the depreciation rate of public good. The production at time t is equal to Y = F(A. K. L. KG) = A(K: +acK) L where ac > 0. Individuals pay 7 fraction of their incomes as an income tax, and they consume MPC fraction of their disposable incomes. Government is running a balanced budget, therefore the revenues from this tax is equal to government spending. Assume this is a closed market economy with growth in population and technology: A+1=(1+g)A, and L+1=(1+n)L, for any t such that n>0 and g> 0. Derive steady-state capital stock (aggregate, per capita, or per efficient worker, as you like) as a function of MPC, T. A. L, a, 6, 6g, og using Solow framework. What is the level of r that maximizes steady-state per-capita consumption for any given values of MPC, A. L. a. 8,8c, ac? What is the level of r that maximizes steady-state per-capita government spending for any given values of MPC, A. L. a, 6, 6c, ac? Suppose we are at a steady-state, and then og increased suddenly and permanently. Draw the evolution of real wage rate, real rental rate, real interest rate, per-capita consumption, and investment per efficient worker over time.