Desired consumption is Cd = 50 + 0.5Y - 300r - 0.7G, where G = 50 and desired investment is Id = 100 - 400r. Real money demand is Md/P = Y - 1000r Other variables are P = 2 and M = 2100.

a. Find the equilibrium values of the real interest rate, output (Y), consumption, investment.

b. Suppose the money supply increases to 2800. Find the equilibrium values of the real interest rate and output (Y).

a)

IS equation is given by:

C+I+G+Y

50+0.5Y-300r-0.7(50)+100-400r+50=Y

200+0.5y-700R-35=Y

0.5Y=165-700r

Y=330-1400r

LM eqaution

M^d/P=M^S/P

Y-1000r=2100/2

2Y-1000r=2100

Y=1050+1000r

The equilibrium occurs where IS=LM

So,

330-1400r=1050+1000r

-2400r=720

So

r=(-)0.3%

The real interest rate (-)0.3%

Y=330-1400(-0.3)

Y=750

Consumption= 50+0.5(750)-300(-0.3)-0.7(50)

=50+375+90-35

Consumption= $480

Investment= 100-400(-0.3)

Investment= $220

b)

M^s=2800

LM equation(new)

M^d/P=M^S1/P

Y-1000r=2800/2=1400

Y=1400+1000r

IS=LM (in equilibrium)

330-1400r=1400+1000r

-2400r=1070

r= (-) 0.44%

Y= 1400+1000(-0.44)

=1400-445.83

=954.1$

Step-by-step explanation

a)

IS equation is given by:

C+I+G+Y

50+0.5Y-300r-0.7(50)+100-400r+50=Y

200+0.5y-700R-35=Y

0.5Y=165-700r

Y=330-1400r

LM eqaution

M^d/P=M^S/P

Y-1000r=2100/2

2Y-1000r=2100

Y=1050+1000r

The equilibrium occurs where IS=LM

So,

330-1400r=1050+1000r

-2400r=720

So

r=(-)0.3%

The real interest rate (-)0.3%

Y=330-1400(-0.3)

Y=750

Consumption= 50+0.5(750)-300(-0.3)-0.7(50)

=50+375+90-35

Consumption= $480

Investment= 100-400(-0.3)

Investment= $220

b)

M^s=2800

LM equation(new)

M^d/P=M^S1/P

Y-1000r=2800/2=1400

Y=1400+1000r

IS=LM (in equilibrium)

330-1400r=1400+1000r

-2400r=1070

r= (-) 0.44%

The real interest rate (-) 0.44%

Y= 1400+1000(-0.44)

=1400-445.83

=954.1$

Output (Y)= 954.1$