Solved Problems on Consumption and Income

Calculate APC, MPC, MPS and APS from the following data:

Solution:

Complete the following table:

Solution:

Complete the following table:

Solution:

Complete the following table:

Solution:

Remember C = a + cY = 90 + .6Y

Given C = 300 + 0.8Y, and Y = 4,000, find the level of consumption:
Solution:  C = 300 + 0.8Y
                    = 300 + .8 x 4000 = 300 + 3200 = 3,500

Given that C = 60 + 0.8Y and I = 60, calculate (i) Equilibrium level of income, (ii) Consumption at equilibrium level and (iii) Saving at equilibrium level.
Solution:
(i) In equilibrium,      Y = C + I
∴                              Y = 60 + 0.8Y + 60
=>                  Y - .8Y = 120
=>                        .2Y = 120
=>               Y = 120 x 1 / 0.2 = 600

(ii)    C = 60 + 0.8Y
            = 60 + .8 x 600
            = 60 + 480 = 540

(iii) S = Y - C
          = 600 - 540 = 60

In an economy, S = - 50 + 0.5 Y, and investment expenditure is ₹7,000. Calculate: (i) Equilibrium level of income (ii) Consumption expenditure at equilibrium.
Solution:
(i) For equilibrium, S = I
∴              -50 + 0.5Y = 7,000
=>                      0.5Y = 7,000 + 50 = 7,050
=>                               \[\mathrm{Y}=7,050\times\frac{10}{5}=14,100\]

(ii) C = Y - S
         = 14,100 - (-50 + 0.5 x 14,100)
=>     = 14,100 - 7,000 = 7,100

What will the value of multiplier when
(i) MPC = 1, (ii) MPC = 0, (iii) MPC = MPS?
Solution:
\[\mathrm{K}=\frac{1}{1-\mathrm{MPC}}\]
∴  (i)  \[\mathrm{K}=\frac{1}{1-1}=\frac{1}{0}=\infty\]
    (ii)  \[\mathrm{K}=\frac{1}{1-0}=\frac{1}{1}=1\]
    (iii)  MPC +MPS= 1 
       ∴    \[\mathrm{MPC}=\mathrm{MPS}=\frac{1}{2}\]
                 \[\mathrm{K}=\frac{1}{1-\mathrm{MPC}}=\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=2\]

In an economy, MPC = 0.75. If investment is increased by ₹10 crore; how much would be the increase in income.
Solution:
\[\mathrm{K}=\frac{1}{1-\mathrm{MPC}}\]
∴   \[\mathrm{K}=\frac{1}{1-0.75}=\frac{1}{.25}=\frac{1\times100}{25}=4\]
Increase in income = K.ΔI = 4 x 10 = ₹40 crore

In an economy, national income increases by ₹500 crore as a result of increase in investment by ₹125. Calculate MPC.
Solution:
\[\mathrm{K}=\frac{\Delta\mathrm{Y}}{\Delta\mathrm{I}}\]
\[\mathrm{K}=\frac{500}{125}=4\]
Now,  \[\mathrm{K}=\frac{1}{1-\mathrm{MPC}}\]
=>      \[\mathrm{4}=\frac{1}{1-\mathrm{MPC}}\] 
=>      4 - 4 MPC = 1 
=>      4 MPC = 4 - 1 = 3 
or          \[\mathrm{MPC}=\frac{3}{4}=0.75\]

Find the value of additional investment made by government, when MPC = 0.5 and increase in income (ΔY) = ₹1000 (ISC 2015)
Solution:
We know that K (Multiplier) =  \[\frac{1}{1-\mathrm{c}}=\frac{1}{1-0.5}\]
\[=\frac{10}{5}=2\]
Now, ΔY = K x ΔI
=>  1000 = 2 x ΔI
=>  \[\Delta\mathrm{I}=\frac{1000}{2}=\bar{\mathrm{₹}}500\]