An economy is described by the following equations:

Desired consumption \(C^{d}=300+0.5(Y-T)-300 r\).

Desired investment \(\quad I^{d}=100-100 r\).

Government purchases \(\quad G=100\).

Taxes \(T=100\).

Real money demand \(\quad L=0.5 Y-200 r\).

Money supply \(\quad M=6300\).

Full-employment output \(\bar{Y}=700\).

Note that the expected rate of inflation is assumed to equal zero so that money demand depends directly on the real interest rate, which equals the nominal interest rate.

a. Write the equation for the aggregate demand curve. Find the equations describing the goods market and asset market equilibria. Use these two equations to eliminate the real interest rate. For any given price level, the equation of the aggregate demand curve gives the level of output that satisfies both goods market and asset market equilibria.

b. Suppose that \(P=15\). What are the short-run equilibrium values of output, the real interest rate, consumption, and investment?

c. What are the long-run equilibrium values of output, the real interest rate, consumption, investment, and the price level?