Question

Suppose that the following equations describe an economy (C,I,G,T, and Y are measured in billions of dollars, and r is measured as a percent; for example, r = 10 = 10%):

C = 170+.6(Y-T)

T = 200

I = 100-4r

G = 350

(M/P)d= L = .75Y – 6r

Ms/P = M/P = 735

a.   Derive the equation for the IS curve and explain all your work. (Hint: It is easier

to solve for Y here.)

b.   Derive the equation for the LM curve and explain all your work. (Hint: It is

easier to solve for Y here.)

c.   Now, express both the IS and the LM equations in terms of r. Graph both curves and calculate their slopes.

d.   Use the equations from parts a and b to calculate the equilibrium levels of real output, the interest rate, planned investment, and consumption.

e.   At the equilibrium level of real output, calculate the value of the government budget surplus.

Answer 1

(a) In goods market equilibrium, Y = C + I + G

Y = 170 + 0.6(Y - 200) + 100 - 4r + 350

Y = 620 + 0.6Y - 120 - 4r

0.4Y = 500 - 4r

Y = 1,250 - 10r..........[Equation of IS curve]

(b) In money market equilibrium, L(Y, r) = M/P

0.75Y - 6r = 735

0.75Y = 735 + 6r

Y = 980 + 8r........[Equation of LM curve]

(c)

From IS equation:

10r = 1,250 - Y

r = 125 - 0.1Y

Slope of IS equation = dr/dY = - 0.1

From LM equation:

8r = Y - 980

r = 0.125Y - 122.5

Slope of LM equation = dr/dY = 0.125

Data table:

Y	r(IS)	r(LM)
0	125	-122.5
250	100	-91.25
500	75	-60
750	50	-28.75
1000	25	2.5
1250	0	33.75

Graph:

(d) In equilibrum, IS equals LM.

1,250 - 10r = 980 + 8r

18r = 270

r = 15

Y = 1,250 - (10 x 15) = 1,250 - 150 = 1,100

I = 100 - (4 x 15) = 100 - 60 = 40

C = 170 + 0.6(1,100 - 200) = 170 + 0.6 x 900 = 170 + 540 = 710

(e) Budget surplus = T - G = 200 - 350 = -150 (i.e. a budget deficit)