Question

These are the equations for the goods, and money market in a hypothetical economy:

C = 250 + .8(Y-T)

I = 100 - 50r

T = G = 100.

Ms = 200

Md = 0.2Y – 100r

ANSWER FROM PART C AND LATER

---a) What is the equation of the IS curve? Is this upward or downward sloping?

----b) If T falls to 50 and everything else is unchanged, what is the equation of the new IS curve?

c) Draw the S+T, I+G and the IS curves for both parts (a) and (b). Keynesian Economics.

d) By how much has the IS curve shifted in part (c)? Does it match up with what is suggested by the multiplier?

e) Derive the LM curve from the Md and Ms equations given above. Is this upward or downward sloping?

f) Using the equation of the IS curve in part (a) and the LM curve in part (e) find the equilibrium levels of Y, r, M, C, S, I, G and T.

g) Using the LM curve in part (e) and the IS curve in part (b), find the equilibrium levels of Y, r, M, C, S, I, G and T.

h) Explain the adjustment process from the old to the new equilibrium when (1) at the same r, you have a different Y, and (2) at the same Y, you have a different r. You might find it helpful to draw IS and LM curves for both equilibria first. Use numbers as much as possible.

i) Suppose the equation of the new LM curve is Y = 1500 + 500r. State one factor that can change the LM curve this way and be as specific as possible. Compare the new and the old LM curves.

j) Using the new LM curve and the IS curve in (b), in other words, both IS and LM have changed. Solve for the equilibrium levels of Y, r, M, C, S, I, G and T.

k) From your answers in part (j), which curve has shifted more? How can you tell? Compare this to the original equilibrium in part (f).

Answer 1

a) IS = C + I +G

Y = 250 + 0.8(Y-T) + 100 - 50r + 100

Y = 250 +0.8Y - 0.8T + 100 - 50r + 100

0.2Y = 250 -80 +200 - 50r

Y = 1850 - 250r

IS curve is downward sloping.

b) Y^' = 250 +0.8Y - 0.8T + 100 - 50r + 100

0.2Y^' = 250 -0.8*50 +200 - 50r

0.2Y^'= 250-40+200-50r

Y^' = 410-50r

Y^' = 2050 - 250r

c) d) The IS curve has moved upward. There has been a parallel shift in IS curve. The slope of IS curve remains the same. The IS curve has shifted 200 units with slope remaining same.

e) LM Curve

Md = 0.2Y - 100r

Ms = 200

At Equilibrium,

Md = Ms

0.2Y - 100r = 200

0.2Y = 200 + 100r

Y = 1000 + 500r

f) From a)

Y = 1850 - 250r and from e) Y = 1000 + 500r.

Therefore, 1850-250r = 1000 + 500r

750r = 850

r = (850/750) = 1.13

Y = 1850 - 250*1.13 = 1566.67

C = 250 + .8(Y-T) = 250+0.8(1566.67 - 100) = 1423.34

I = 100 - 50r = 100 - 50*1.13 = 43.5

I = S = 43.5

T=G = 100

Md = 0.2Y – 100r = 0.2*1566.67 - 100*1.13 = 313.34 - 113 = 200.34

g)  Y^'   = 2050 - 250r (from b)

Y = 1000 + 500r (from e)

  Y =  Y^'

2050 - 250r = 1000 + 500r

750r = 1050

r = 1.4

Y = 2050 - 250*1.4 = 1700

C = 250 + .8(Y-T) = 250+0.8(1700 - 50) = 1570

I = 100 - 50r = 100 - 50*1.4 = 30

I = S = 30

T=50 and G = 100

Md = 0.2Y – 100r = 0.2*1700 - 100*1.4 = 340 - 140 = 200