Y = C + I + G + X - IM C = 250 + 0.75DI I = 250 G = 250 T = 200 DI = Y T X = IM

Question

Y = C + I + G + X - IM

   C = 250 + 0.75DI

   I = 250

   G = 250

   T = 200

   DI = Y T

   X = IM

15A) What is the equilibrium level of income?

   a. 2000

   b. 2200

   c. 2400

   d. 2600

15B) What is the simple spending multiplier?

   a. 1/2

   b. 2

   c. 3

   d. 4

15C) If you needed to increase the equilibrium level of income by $200, this could be achieved by a

   a. tax cut of 200

   b. tax increase of 100

   c. government spending increase of 50

   d. government spending increase of 200

15D) An increase in government spending of $200B increased real GDP by $1000B. If the fiscal stimulus had come from a tax cut of the same size, real GDP would have increased by

   a. 1000B

   b. 900B

   c. 800B

   d. 200B

Explanation / Answer

15(A) To determine the equilibrium level of income(Y) we need to put the value in the following function

Y = C + I + G + X - IM   

Y = (250 + 0.75DI) + 250 + 250 [as X = IM, so it will be cancelled out]

Y = 750 + 0.75 (Y - T) [Putting the value of DI = Y - T]

0.25Y = 750 - 0.75 * 200 [As T = 200]

Y = 2400.

So, the equilibrium level of income is 2400, that is option c.

15(B). To calculate the spending multiplier we need to calculate the Marginal propensity to consume (MPC) i.e

changes in consumption divided by changes in income i.e. first order differentiation of consumption function.

C = 250 + 0.75 DI

C = 250 + 0.75 Y - 0.75 T

dC / dY = 0.75

MPC = 0.75

Spending multiplier is 1 / (1 - MPC) = 1 / (1 - 0.75) = 4.

So, the spending multiplier is 4, that is option d.

15(C). If you needed to increase the equilibrium level of income by $200, this could be achieved by a government spending increase of 50, that is option c.

This is because change in level of income = spending multiplier * Change in government spending.

So, Change in government spending = change in level of income / spending multiplier

Change in government spending = 200 / 4 = 50.

15(D). An increase in government spending of $200B increased real GDP by $1000B, that means government spending multiplier is 5.

So, 1 / (1 - MPC) = 5

MPC = 0.80

Now, tax multiplier is [- MPC / (1 - MPC)]

Tax multiplier = - 0.80 / 0.20 = - 4.

That means a tax cut of $200 billion will lead to an increase of (4 * 200) = $800 billion in real GDP.

So, the correct answer is option $800 billion that is option c.

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