Desired consumption is \(C^{d}=2000+0.9 Y-\) \(100,000 r-G\), and desired investment is \(I^{d}=1000\) \(-45,000 r\). Real money demand is \(M^{d} / P=Y-6000 i\). Other variables are \(\pi^{e}=0.03, G=500, \bar{Y}=1000\), and \(M=2100\).

a. Find the equilibrium values of the real interest rate, consumption, investment, and the price level.

b. Suppose government purchases decline to 400 . What happens to the variables listed in part (a)?

c. Suppose government purchases rise to 600 . What happens to the variables listed in part (a)?

d. What feature in this example leads to the result that you don't need to know the amount of taxes collected by the government to find the equilibrium?