NUMERICAL PROBLEMS ON CLASSICAL AND

NUMERICAL PROBLEMS ON CLASSICAL AND KEYNESIAN ECONOMICS
Basic Information:
𝑑𝐢
o
π‘šπ‘π‘ =
o
π‘šπ‘π‘  =
o
π‘šπ‘π‘ + π‘šπ‘π‘  = 1
o
π‘Žπ‘π‘ =
o
π‘Žπ‘π‘  =
o
π‘Žπ‘π‘ + π‘Žπ‘π‘  = 1
o
πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ π‘€π‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ (𝐾) =
o
π‘‘π‘Œ = 𝐾 βˆ— 𝑑𝐼 = (
o
At equilibrium, income = expenditure
π‘‘π‘Œ
𝑑𝑆
π‘‘π‘Œ
𝐢
π‘Œ
𝑆
π‘Œ
1
1βˆ’π‘šπ‘π‘
1
1βˆ’π‘šπ‘π‘
) βˆ— 𝑑𝐼 = (
1
π‘šπ‘π‘ 
Here, S stands for saving
C stands for consumption
I stands for investment
Y stands for income
mpc stands for marginal propensity to consume
mps stands for marginal propensity to save
apc stands for average propensity to consume
aps stands for average propensity to save
=
1
π‘šπ‘π‘ 
) βˆ— 𝑑𝐼
=
π‘‘π‘Œ
𝑑𝐼
1. If mpc is 0.75, calculate the value of mps and investment multiplier.
Solution: given mpc= 0.75
mps = 1- mpc= 1- 0.75 = 0.25
πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ π‘€π‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ =
1
1βˆ’π‘šπ‘π‘
=
1
1 βˆ’ 0.75
=
1
1 βˆ’ 0.75
=4
2. If value of multiplier is 5, calculate mpc.
Solution: given, investment multiplier (K)= 5
We have, 𝐾 =
1
1βˆ’π‘šπ‘π‘
π‘œπ‘Ÿ , 5 =
1
1 βˆ’ π‘šπ‘π‘
π‘œπ‘Ÿ,
π‘šπ‘π‘ = 0.8
3. In an economy, investment increases by Rs 200 crores. As a result of it, total income increases by
Rs. 1000 crores. Calculate mpc.
Given, π‘–π‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ 𝑖𝑛 π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ = 𝑑𝐼 = 200π‘π‘Ÿπ‘œπ‘Ÿπ‘’π‘ 
π‘–π‘›π‘π‘Ÿπ‘’π‘ π‘’ 𝑖𝑛 π‘–π‘›π‘π‘œπ‘šπ‘’ = π‘‘π‘Œ = 1000π‘π‘Ÿπ‘œπ‘Ÿπ‘’π‘ 
We have,
πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ π‘€π‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ =
π‘œπ‘Ÿ,
π‘œπ‘Ÿ,
π‘œπ‘Ÿ,
π‘‘π‘Œ
𝑑𝐼
1
π‘‘π‘Œ
=
1 βˆ’ π‘šπ‘π‘
𝑑𝐼
1
1000
=
1 βˆ’ π‘šπ‘π‘
200
1
1000
=
1 βˆ’ π‘šπ‘π‘
200
π‘šπ‘π‘ = 0.8
4. In an economy, investment increases from Rs 300 crores to 500 crores As a result of it, total income
increases from Rs. 1000 to Rs. 2000 crores. Calculate value of investment multiplier and mps.
Given, initial investment (I1) = Rs 300 crores
Final investment (I2) = Rs 500 crores
Increase in investment = I2 – I1= dI= 200 crores
initial income (Y1) = Rs 1000 crores
Final investment (Y2) = Rs 2000 crores
Increase in investment = Y2 – Y1= dY =1000 crores
𝑑𝐼 = 200π‘π‘Ÿπ‘œπ‘Ÿπ‘’π‘ 
We have,
πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ π‘€π‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ (𝐾) =
πΉπ‘Ÿπ‘’π‘‘β„Žπ‘’π‘Ÿ, 𝐾 =
π‘‘π‘Œ 1000
=
𝑑𝐼
500
1
π‘‘π‘Œ
=
π‘šπ‘π‘ 
𝑑𝐼
π‘œπ‘Ÿ,
1
1000
=
π‘šπ‘π‘ 
200
π‘œπ‘Ÿ,
1
1000
=
π‘šπ‘π‘ 
200
π‘šπ‘π‘  = 0.2
5. In an economy, mpc = 0.75. In this economy what will be the effect on total income if investment
increases by Rs 300.
Given,
mpc = 0.75
Increase in investment= dI
Increase in income =dY?
1
We have, π‘‘π‘Œ = (
) βˆ— 𝑑𝐼
1βˆ’π‘šπ‘π‘
1
π‘‘π‘Œ = (
) βˆ— 300
1 βˆ’ 0.75
π‘‘π‘Œ = 1200 π‘π‘Ÿπ‘œπ‘Ÿπ‘’π‘ 
6. Suppose you have the following information about a closed economy:
C = 50 + 0.80 Y
I =200
G = 100
Where C is consumption, I is investment, G is Government expenditure and Y is income.
a) Find out the equilibrium level of income.
b) Suppose G increases to 125 what is the new equilibrium level of income?
c) What level of G is needed to achieve a target income of 2000?
a)
At equilibrium, Income = Expenditure
i.e. Y = C + I + G
or, Y = 50 + 0.80 Y + 200 + 100
or, Y (1 – 0.80) = 350
Y= 1750
which is the equilibrium level of income.
b) When G increases to 125
At equilibrium, Income = Expenditure
i.e. Y = C + I + G
or, Y = 50 + 0.80 Y + 200 + 125
or, Y (1 – 0.80) = 375
or, Y = I 875 which is the new equilibrium level of income when G increases to 125
c)
To achieve a target income of 2000, G=?
At equilibrium, income = expenditure
Y=C+I+G
or, 2000 = 50 + 0.80 *2000 + 200 + G
or, G = 2000 –50 – 1600 – 200
or, G= 150
Hence government expenditure should be 150 to achieve income target of Rs. 150
6. Suppose that the economy is characterized by the following structural Equations:
C = 160 + 0.6 (Y –T)
I =150; G = 150; T = 100.
Where C is consumption, I is investment, G is Government expenditure, T is income tax and Y is income
or output.
a) Determine the equilibrium output level.
b) If G rises to 200, what is the how equilibrium level of output? What is the
Value of the govt. expenditure multiplier? Interpret the results.
c) If tax falls to 50, by how much will equilibrium output rise?
What is the value of tax multiplier?
Solution:
a)
At equilibrium, output (income) = Expenditure
i.e. Y = C + I + G
or, Y = 160 + 0.6 (Y – 100) + 150 + 150
Y (1 – 0.6) = 460 – 60
Y = 1000 which is the equilibrium level of output
b) When G increases to 200
At equilibrium, output = expenditure
Y=C+I+G
or, Y = 160 + 0.6 (Y – 100) + 150 + 200
Y (1 – 0.6) = 510 – 60
Y = 1125 which is the new equilibrium output when G increases to 200
Now, increase in G = dG = 200 - 150
Increase in output Y = dY = 1125- 1000 = 125
πΊπ‘œπ‘£π‘’π‘Ÿπ‘›π‘šπ‘’π‘›π‘‘ 𝑒π‘₯π‘π‘’π‘›π‘‘π‘–π‘‘π‘’π‘Ÿπ‘’ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ =
π‘‘π‘Œ
𝑑𝐺
=
125
50
= 2.5
Hence with an increase in government expenditure, real output increases. Output increases by 2.5 times
of increase in government expenditure.
c)
When T falls to 50
At equilibrium, output = expenditure
i.e. Y = C + I + G
or, Y = 160 + 0.6 (Y – 50) + 150 + 150
or, Y (1 – 0.6) = 460 – 30
or, Y = 1075 which is the new equilibrium output when T falls to 50
Hence due to fall in tax to 50, real output will increase to 1075
Now, decrease in T = dT= 100 – 50 = 50
Increase in output Y = dY = 1075 – 1000 = 125
π‘‘π‘Žπ‘₯ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘–π‘’π‘Ÿ =
75
50
= 1.5
Hence with a decrease in tax, real output increases. Real output increases by 1.5 times of decrease in
tax.