ECO102 Principles of macroeconomics Question on National Income Determination./Solution

SET 1

Assume C=20+0.8 Yd, I=GHS 50, G=GHS

20, T-GHS 10.

 1) Find the equilibrium

national income by estimating the totalexpenditure function.

 2) Find a balance between spending and saving.

 3)Shows the equality of leakage and inflow from the output flow at equilibrium. 

4) How is GhS 20 government spending financed? 

5) If (a) A flat tax is increased by 100% or

 (b)government spending is reduced by 50% to balance the public budget What is the equilibrium output 

 6) Will changes in flat taxes or government spending in (5) above have a similar impact on equilibrium production?

                                              S0LUTIONS

 To solve these problems, we'll first need to understand the key equations and concepts involved in calculating national income equilibrium. The Aggregate Demand (AD), or Total Expenditure Function, is the sum of Consumption (C), Investment (I), and Government Spending (G).

1) Find the equilibrium national income by estimating the total expenditure function:

AD = C + I + G

Given:

C = 20 + 0.8 Yd (Yd is disposable income)

I = GHS 50

G = GHS 20

T = GHS 10 (Taxes)

First, find disposable income, Yd:

Yd = Y - T, where Y is the national income.

Next, plug Yd into the consumption function:

C = 20 + 0.8(Y - T)

Now, plug the consumption function and given values for I and G into the aggregate demand equation:

AD = (20 + 0.8(Y - 10)) + 50 + 20

Simplify and combine terms:

AD = 0.8Y - 8 + 70

AD = 0.8Y + 62

For equilibrium, Aggregate Demand (AD) = National Income (Y):

Y = 0.8Y + 62

Now, solve for the equilibrium national income Y:

0.2Y = 62

Y = GHS 310

2) Find a balance between spending and saving:

Since Y = C + S, where S is savings, we can find S:

Y = 310 = C + S

C = 20 + 0.8(310 - 10) = GHS 260

S = Y - C = 310 - 260 = GHS 50

Savings, S = GHS 50, which shows a balance between spending and saving.

3) Shows the equality of leakage and inflow from the output flow at equilibrium:

Leakages (T, S) = Injections (G, I)

T + S = G + I

10 + 50 = 20 + 50

The equality of leakages and inflows (60 = 60) at equilibrium is demonstrated.

4) How is GHS 20 government spending financed?

Government spending is financed through taxes (GHS 10) and borrowing (GHS 10, which is the difference between spending and taxes).

5) If (a) a flat tax is increased by 100% or (b) government spending is reduced by 50% to balance the public budget. What is the equilibrium output of 6?

a) If the flat tax is increased by 100%, the new tax becomes 20:

Y = 0.8(Y - 20) + 62

0.2Y = 42

Y = 210 => The new equilibrium output is GHS 210.

b) If government spending is reduced by 50%, the new government spending becomes 10:

Y = 0.8(Y - 10) + 50 + 10

0.2Y = 50

Y = 250 => The new equilibrium output is GHS 250.

6) Will changes in flat taxes or government spending in (5) above have a similar impact on equilibrium production?

No, they have different effects. A 100% increase in the flat tax rate results in a decrease in equilibrium output to GHS 210, while a 50% reduction in government spending leads to a decrease in equilibrium output to GHS 250. Changes in taxes and government spending have different impacts on equilibrium production

👊💪💪💪💪