Consider the following economy.

Desired consumption \(\quad C^{d}=200+0.4(Y-T)-400 r\).

Desired investment \(\quad I^{d}=300-400 r\).

Real money demand \(\quad L=0.6 Y-400 i\).

Full-employment output \(\bar{Y}=900\).

Expected inflation \(\quad \pi^{e}=0\).

a. Suppose that \(T=G=175\) and that \(M=11,165\). Find an equation describing the IS curve. Find an equation describing the \(L M\) curve. Finally, find an equation for the aggregate demand curve. What are the equilibrium values of output, consumption, investment, the real interest rate, and the price level? Assume that there are no misperceptions about the price level.

b. Suppose that \(T=G=240\) and that \(M=11,165\). What is the equation for the aggregate demand curve now? What are the equilibrium values of output, consumption, investment, the real interest rate, and the price level? Assume that full employment output, \(\bar{Y}\), is fixed.

c. Repeat part (b) for \(T=G=175\) and \(M=13,195\).