question_answer

The saving function of an economy is\[S=-200+0.25Y.\]The economy is in equilibrium when income is equal to Rs.2,000.Calculate the following :

(i) Investment expenditure at equilibrium level of income

(ii) Autonomous consumption

Or It is given that MPC is 1/3rd of MPS, while consumption at zero level of income is given as Rs.100crore. Derive the consumption and savings functions.

Answer:

(i) At equilibrium, savings (S) are equal to planned investment (I). It is given that,             \[S=-200+\,\,\,\,\,Y\] Equilibrium level of income is 2,000. Substituting the value of Y in the savings function, we get             \[S=-200+0.25\times 2,000\]             \[S=-200+500\Rightarrow S=\]300 or /= 300\[[\therefore \]at equilibrium level of Income Savings (S) = Investment Expenditure (/)] Thus, investment expenditure at equilibrium level of income is 300.         (ii) Autonomous consumption means the level of consumption expenditure when income is zero.             When Y=0,   Savings =-200             Consumption+Savings=Income             \[Consumption+(-\text{ }200)=0\] So, autonomous consumption =200                                                                                      Or According to question, Marginal Propensity to consume (MPC)=\[\frac{1}{3}\] Marginal Propensity of Save(MPS) We know that,             MPC + MPS =1             \[\therefore \]\[\frac{1}{3}\]MPS+MPS=1             MPS=\[\frac{3}{4}\]             MPS =0.75 and MPC =1-0.75 =0.25 Consumption function\[(C)=\overline{C}+bY,\] where, \[\overline{C}\]= Autonomous Consumption =Rs.100crore b= MPC =025 So, consumption function (c)=100+025Y Saving function \[(S)=-\overline{S}+sY,\] where, \[-\overline{S}\]= Dissavings = Autonomous consumption = 100 and S = Marginal Propensity to Save = 075 Therefore, Savings Function (S) =\[-100+0.75Y\]