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

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.

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