Question

C = 100 + 0.8 Yd

I = 500        X = 600         M = 650

G = G₀ - 0.05Y

G_{0 =} 557.5

T = T₀ + .25Y

What T0 would make income equal to the same value as in Question 1? (Hint: T0 could be negative) Q1 = T=400

If Investment falls from 500 to 499, what is change in Y? (ie what is investment multiplier?)

Answer 1

Y = 100 + 0.8 ( Y-T) + 500 + 557.5 - 0.05Y + X-M

Y = 600 + 557.5 + 600 - 650 + 0.8(Y- T) -0.05Y

1.05Y = 1107.5 + 0.8(Y-T) = 1107.5 + 0.8Y - 0.8T

1.05Y -0.8Y = 1107.5 -0.8T

0.25Y = 1107.5 - 0.8T

For question 1), T = 400

==> 0.25Y = 1107.5 - 0.8(400) = 1107.5 - 320 = 787.5

Y = 787.5/0.25 = 3150

Now, when T = T0 + 0.25Y

1.05Y = 1107.5 + 0.8(Y - T0 - 0.25Y) = 1107.5 + 0.6Y - 0.8T0

(1.05 - 0.6)Y = 1107.5 - 0.8T0

Putting in Y = 3150 ; 0.45(3150) = 1107.5 - 0.8T0

1417.5 -1107.5 = -0.8T0

- 387.5 = T0

(ii)

Y = 100 + 0.8( 0.75Y-T0) + I + (X-M) + G0 - 0.05Y

Y - 0.6Y + 0.05Y = I + R

( R includes the rest of the terms)

0.45Y = I + R

==> 0.45dY = dI dY/dI = 1/0.45 = 2.222

In case T = T0 + 0.25Y , investment multiplier is 2.222

In case we just take T, we have 0.25dY = dI

Then multiplier will be = 1/0.25 = 4