In our model specification, we assumed that government expenditure is exogenous (determined outside the model). Let us assume that government expenditure depends on income, y, and interest rate, r, as follows:

G=G(FIXED)+G_Y(Y)+G_R(R)

Let us also assume for the sake of simplicity that

I.The government expands (decrease) its expenditure when income decreases (increases) to stimulate the economy (to suppress aggregate spending).

II.The government expands (decreases) its expenditure when interest rate (r) decreases (increases). The economic rationale is that when the economy slows down, the demand for money falls, and interest rate drops. Thus, the government might expand its public investment to stimulate the economy

Please aware that we will not allow for asymmetric responses to simplify the modeling of the equilibrium.

Explain how the response of y to the change in NX depends on the magnitude of G(r) Make sure to provide your answer with the relevant graphs, mathematical equations, and economic interpretation.