Free Income Determination 02 Practice Test - 12th Grade - Commerce 

Multiplier = $\frac{1}{1-MPC}$ 

If the marginal propensity to save decreases, the value of the multiplier will increase.

Multiplier (M) = $\frac{\Delta Y}{\Delta A}$

= $\frac{(4000-3000)}{(600-400)}$

= 5

MPS = $\frac{1}{M}$

= $\frac{1}{5}$

= 0.2

False. Saving can be negative when consumption is greater than income. Negative saving amounts to borrowing.

False. MPC + MPS = 1, it can never be greater than or less than 1.

True, there is a direct relationship between MPC and value of investment multiplier. Higher the value of MPC, higher the investment multiplier and vice cersa. Because,

$M=\frac{1}{1-MPC}$

(i) 75 per cent of the increase in income is spent on consumption.

$\therefore$                   $MPC=\frac{\Delta C}{\Delta Y}=\frac{75}{100}=0.75$

                                Multiplier  $\left(M\right)=\frac{1}{1-MPC}=\frac{1}{1-0.75}=\frac{1}{0.25}=4$

We know,                $M=\frac{\Delta Y}{\Delta I}$

$\Rightarrow$          $\Delta Y=M\times \Delta I$

                                  $\Delta Y=4\times 1,000=4,000$

(ii) Increase in consumption expenditure $\left(\Delta C\right)=MPC.\Delta Y$

                                                              $=0.75\times 4,000$                   $(\because MPC=\frac{\Delta C}{\Delta Y}),$ so that $\Delta C=MPC.\Delta Y)$

                                                              $=\frac{75}{100}\times 4,000=3,000$

(i) Total increase in income = Rs 4,000 crore.

(ii) Total increase in consumption expenditure = Rs 3,000 crore.

$\Delta Y=\frac{1}{1-MPC}.\Delta A$            [Where A is autonomous expenditure by the government]

$=\frac{1}{1-0.5}\times 5,000=\frac{5,000}{0.5}=10,000.$

(i) Given, S = - 50 + 0.5Y

and I = 7,000

At the equilibrium level,

$\Rightarrow$           S = I

             -50 + 0.5Y = 7,000

              0.5Y = 7,000 + 50

               0.5Y = 7,050

               $Y=\frac{7,050}{0.5}$

$\Rightarrow$              Y = 14,100

(ii) At Y = 14,100

                Saving, S = - 50 + 0.5(14,100)   

                 = - 50 + 7,050

$\therefore$              S = 7,000

        Consumption expenditure, C = Y - S

$\Rightarrow$                 $=14,100-7,000$

                                         $=7,100$

Alternative Method

At equilibrium level,

                                  Saving = Investment

                                   Saving = 7,000

        Consumption expenditure, C =  Y - S

                                     = 14,100 - 7,000

                                     = 7,100.

(i) Equilibrium level of national income = 14,100.

(ii) Consumption expenditure at equilibrium level of national income = 7,100.                         

(i) Given, C = 150 + 0.6Y and I = 2,000

At the equilibrium level,

                                   Y = C + I

$\Rightarrow$             Y = 150 + 0.6Y + 2,000           $\Rightarrow$          Y = 2,150 + 0.6Y

                                    Y - 0.6Y = 2,150        $\Rightarrow$            0.4Y = 2,150

                                  $Y=\frac{2,150}{0.4}=5,375$

(ii) Consumption,        C = 150 +0.6(5,375)

                                       = 150 + 3,225 = 3,375

(iii) We know that,       Y = C + S

$\Rightarrow$             S = Y - C = 5,375 - 3,375 = 2,000

Alternatively, 

Given :                         C = 150 + 0.6Y, 

                                     S = -150 + 0.4Y ($\because$ MPC = 0.6, accordingly MPS = 1 - 0.6 = 0.4)

Or,                                S = -150 + 0.4(5,375)

                                        = -150 + 2,150 = 2,000.

(i) Equilibrium level of national income = Rs 5,375.

(ii) Consumption expenditure at equilibrium level of national income = Rs 3,375.

(iii) Saving at equilibrium level of national income = Rs 2,000.