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**Question 1.1:**

(a) If tax is included in the Keynesian model, what happens to the value of the multiplier? Explain why. (10 marks)

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**Question 1.3:**

Assume \( S = -N\$200m + 0.08Y \); \( M = 0.1Y \); \( I = N\$300m \); \( G = N\$150m \); \( X = N\$140m \); and \( t = 0.21Y \).

(A) Calculate the total-spending function and equilibrium income. Illustrate this on a graph. (20 marks)

(B) Indicate on the graph the effect of an N$100 million increase in investment spending and comment on the magnitude of change in the equilibrium income relative to the change in investment spending. Calculate the new equilibrium income.

(C) Assume the marginal tax changes to 0.25Y. How will this change influence the total spending curve? Illustrate this on your graph.

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**Question 1.2:**

Assume \( C = 100 + 0.88Y \); \( I = 50 \); \( G = 40 \); \( X = 50 \); \( M = 0.09Y \); and \( t = 0.35Y \).

(a) Determine the equation for total expenditure (TE) and illustrate this graphically. (10 marks)

(b) Use the multiplier to indicate how a decrease in investment of $50 will affect the GDP. Show all calculations; illustrate this on your graph. (10 marks)

Answer :

Question 1.1: (a) The value of the multiplier decreases when tax is included because taxes reduce disposable income, leading to lower consumption and investment.

Question 1.3: (A) The total spending function is TE = 590 + 0.78Y. Equilibrium income is N$2,681.82, (B) An increase in investment spending of N$100 million increases equilibrium income by N$833.33 and (C) An increase in the marginal tax rate to 0.25Y shifts the total spending curve downward.

Question 1.2: (a) The equation for total expenditure is TE = 240 + 0.79Y and (b) A decrease in investment of $50 decreases GDP by $416.67.

Question 1.1:

(a) In the Keynesian model, if tax is included, the value of the multiplier decreases. This is because taxes reduce the disposable income available for consumption and investment, which in turn reduces the total spending and the overall multiplier effect. Taxes act as a leakage in the circular flow of income, decreasing the initial injection of spending and dampening the overall impact on output and employment.

Question 1.3:

(A) The total spending function can be calculated by summing consumption (C), investment (I), government spending (G), exports (X), and subtracting imports (M):

TE = C + I + G + X - M

TE = (100 + 0.88Y) + 300 + 150 + 140 - 0.1Y

TE = 590 + 0.78Y

To find the equilibrium income, set TE equal to income (Y) and solve for Y:

Y = 590 + 0.78Y

0.22Y = 590

Y = 2,681.82

The equilibrium income is N$2,681.82. This can be illustrated on a graph by plotting the aggregate expenditure (TE) against income (Y) and identifying the point where TE equals Y.

(B) An increase in investment spending of N$100 million will shift the total spending curve upward.

The magnitude of change in equilibrium income depends on the value of the multiplier.

If the multiplier is 1 / (1 - MPC), where MPC is the marginal propensity to consume, then the change in equilibrium income can be calculated as follows:

Change in equilibrium income = Multiplier x Change in investment spending

Change in equilibrium income = (1 / (1 - 0.88)) x 100

Change in equilibrium income = 8.33 x 100

Change in equilibrium income = N$833.33

The new equilibrium income will increase by N$833.33.

(C) If the marginal tax changes to 0.25Y, it will affect the total spending curve by reducing the disposable income available for consumption.

This will shift the total spending curve downward, as a higher proportion of income is deducted as taxes.

On the graph, this would result in a parallel downward shift of the total spending curve.

Question 1.2:

(a) The equation for total expenditure (TE) is given by:

TE = C + I + G + X - M

TE = (100 + 0.88Y) + 50 + 40 + 50 - 0.09Y

TE = 240 + 0.79Y

This equation can be illustrated graphically by plotting TE against Y.

(b) To calculate the effect of a decrease in investment of $50 on GDP, we can use the multiplier. The multiplier is given by 1 / (1 - MPC), where MPC is the marginal propensity to consume. In this case, the MPC is 0.88. Thus, the multiplier is 1 / (1 - 0.88) = 1 / 0.12 = 8.33.

The change in GDP can be calculated as follows:

Change in GDP = Multiplier x Change in investment

Change in GDP = 8.33 x (-$50)

Change in GDP = -$416.67

The decrease in investment of $50 will lead to a decrease in GDP of $416.67. This can be illustrated on the graph by shifting the TE curve downward by the amount of the change in GDP.

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