national incom

Question

Given that money supply is 1400 millions, autonomous consumption is 120 million, while the responsiveness of consumption to changes in disposable income is estimated to be 80% by the ministry of planning. Aggregate autonomous investment is 200 million investment while one % increase in interest rate changes investment by 10 millions. The government collected 200 million as tax revenue and wishes to increase expenditure by 10% above the revenue collected. The transactionary and precautionary demand for money function is expressed as mt/p=0.1y while the speculative money demand ms/p is -100r . compute the equilibrium national income, consumption and investments.

 

What is the size of government expenditure multiplier and savings in question c above.

Answer 1

We solve this using the IS–LM framework (goods market equilibrium + money market equilibrium).

1. Given Information

Money Supply

[

M_s = 1400 \text{ million}

]

Consumption Function Parameters

Autonomous consumption:

[

C_0 = 120

]

Marginal propensity to consume:

[

MPC = 0.8

]

Taxes:

[

T = 200

]

Therefore consumption function:

[

C = 120 + 0.8(Y - T)

]

Investment Function

Autonomous investment:

[

I_0 = 200

]

Investment sensitivity:

1% increase in interest → investment falls by 10 million

[

I = 200 - 10r

]

Government Expenditure

Government revenue:

[

T = 200

]

Government plans to spend 10% above revenue

[

G = 200 + (0.1 \times 200)

]

[

G = 220

]

Money Demand Functions

Transaction + precautionary demand:

[

M_t/P = 0.1Y

]

Speculative demand:

[

M_s/P = -100r

]

Total money demand:

[

M_d/P = 0.1Y - 100r

]

Money supply:

[

M_s/P = 1400

]

2. LM Curve (Money Market Equilibrium)

[

M_s = M_d

]

[

1400 = 0.1Y - 100r

]

Solve for ( r ):

[

100r = 0.1Y - 1400

]

[

r = 0.001Y - 14

]

3. Investment Function with r

Substitute ( r ):

[

I = 200 - 10(0.001Y - 14)

]

[

I = 200 - 0.01Y + 140

]

[

I = 340 - 0.01Y

]

4. Consumption Function

[

C = 120 + 0.8(Y - 200)

]

[

C = 120 + 0.8Y - 160

]

[

C = 0.8Y - 40

]

5. Goods Market Equilibrium (IS)

[

Y = C + I + G

]

Substitute values:

[

Y = (0.8Y - 40) + (340 - 0.01Y) + 220

]

Simplify:

[

Y = 0.79Y + 520

]

[

Y - 0.79Y = 520

]

[

0.21Y = 520

]

[

Y = 2476.19

]

6. Equilibrium National Income

[

Y = 2476.19 \text{ million}

]

7. Equilibrium Consumption

[

C = 0.8Y - 40

]

[

C = 0.8(2476.19) - 40

]

[

C = 1980.95 - 40

]

[

C = 1940.95

]

8. Equilibrium Investment

[

I = 340 - 0.01Y

]

[

I = 340 - 0.01(2476.19)

]

[

I = 340 - 24.76

]

[

I = 315.24

]

9. Savings

Savings:

[

S = Y - C - T

]

[

S = 2476.19 - 1940.95 - 200

]

[

S = 335.24

]

10. Government Expenditure Multiplier

Government multiplier:

[

K_G = \frac{1}{1 - MPC}

]

[

K_G = \frac{1}{1 - 0.8}

]

[

K_G = \frac{1}{0.2}

]

[

K_G = 5

]

Final Answers

VariableValue
Equilibrium National Income (Y)	2476.19 million
Consumption (C)	1940.95 million
Investment (I)	315.24 million
Savings (S)	335.24 million
Government Expenditure Multiplier	5

✅ Important Identity Check

[

S = I + (G - T)

]

[

335.24 = 315.24 + (220 - 200)

]

[

335.24 = 335.24

]

✔ Model is consistent.