Consider the following Keynesian closed economy:

Consumption \(\quad C=388+0.4(Y-T)-600 r\).

Investment \(I=352-400 r\).

Government purchases \(G=280\).

Taxes \(\quad T=300\).

Full-employment output \(\bar{Y}=1400\).

Money supply \(\quad M=12,600\).

Real money demand \(\quad L=1750+0.75 Y\)

\[ -8750\left(r+\pi^{e}\right) . \]

Expected inflation \(\quad \pi^{e}=0.02\).

a. What is the equation of the IS curve?

b. Suppose that the price level is fixed at \(P_{s r}=7\) in the short run. What is the equation of the \(L M\) curve in the short run, while the price level remains fixed?

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

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

\(e\). What is the value of velocity in long-run equilibrium?

f. Suppose that the government wants to increase its purchases to \(G=350\) and to achieve a long-run equilibrium with investment, \(I\), equal to 320 , and the price level, \(P\), equal to 6 . What level of taxes, \(T\), and money supply, \(M\), will achieve this long-run equilibrium? 

The following questions will guide you to the answer. 

(1) What value of the real interest rate leads to \(I=320\) ?

(2) What is the value of consumption in long-run equilibrium when \(I=320\) and \(G=350\) ? 

(3) What value of taxes, \(T\), will lead to the level of consumption, \(C\), in part (2), thereby achieving \(I=320\) and \(G=350\) in long run equilibrium? 

(4) What value of the nominal money supply, \(M\), will lead to a price level of 6 in long-run equilibrium with \(I=320\) and \(G=350\) ? Continue to assume that \(\pi^{e}=0.02\).