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## Sagot :

**Answer:**

The correct option is **c. raise G by $30 or reduce T by $40**.

**Explanation:**

**Note:** This question is not complete. The complete question is therefore provided before answering the question as follows:

(Advanced analysis) Answer the question on the basis of the following information for a mixed open economy. The letters Y, Ca, Ig, Xn, G, and T stand for GDP, consumption, gross investment, net exports, government purchases, and net taxes respectively. Figures are in billions of dollars.

Ca = 25 + 0.75(Y - T)

Ig = Ig0 = 50

Xn = Xn0 = 10

G = G0 = 70

T = T0 = 30

Refer to the information. If government desired to raise the equilibrium GDP to $650, it could:

a. raise G by $45 or reduce T by $10.

b. raise G by $40 and reduce T by $30.

c. raise G by $30 or reduce T by $40.

d. raise both and T by $40.

e. reduce G by $30 and increase T by $40.

**The explanation of the answer is now provided as follows:**

Equilibrium GDP (Y) can be obtained as follows:

Y = C + G + I + Xn …………………….. (1)

Substituting all the values in the question into equation (1) and solve for Y, we have:

Y = 25 + 0.75(Y - 30) + 70 + 50 + 10

Y = 0.75Y - 22.50 + 155

Y – 0.75Y = 132.50

0.25Y = 132.50

Y = 132.50 / 0.25

Y = 530

Therefore, we have:

Y = Current equilibrium GDP = $530

Amount of increase in equilibrium GDP required = Desired equilibrium GDP – Current equilibrium GDP = 650 - 530 = 120

From the question, we have:

Ca = 25 + 0.75(Y - T) ………………. (2)

The 0.75 in equation (2) is the marginal propensity to consume (MPC). Therefore, we have:

MPC = 0.75

Expenditure multiplier = 1 / (1 - 0.75) = 4

Tax multiplier = - MPC / (1 – MPC) = -0.75 / (1 – 0.75) = -3

Amount of increase in G or government expenditure required = Amount of increase in equilibrium GDP required / Expenditure multiplier = 120 / 4 = $30

Amount of tax cut or decrease in T required = Amount of increase in equilibrium GDP required / Tax multiplier = 120 / (-3) = -$40

Therefore, correct option is **c. raise G by $30 or reduce T by $40**.