Question

solve it:

Consumption : C = 40 + 0.75Y

Investment : I = 140 – 10i

Government Expenditure : G = 100

Tax : T = 80

Money Demand : Md = 0.2Y – 5i

Money Supply : Ms = 85

(i is % interest rate; other figures in Rs. Crores)

a) Find out the equilibrium income, Y and interest rate i.

b) Suppose the government increases its expenditure on education by Rs. 65 Crores?

What would be its effect on equilibrium income and rate of interest.

Answer 1

Answer:

mujhe maths nai aata sorry

Answer 2

Given:

$\text { In order to obtain equilibrium income, we have to find out first the equations for } I S$$\text { and } L M \text { curves. }$

$Y=C+I+G$

$\text { where } C=40+0.75 Y_{d} \text { and } I=140-10 i \text { and } G=100$

$\begin{aligned}Y &=40+0.75 Y_{d}+140-10 i+100 \\&=40+0.75(Y-80)+140-10 i+100 \\&=40+0.75 Y-60+140-10 i+100 \\Y-0.75 Y &=220-10 i \\0.25 Y &=220-10 i\end{aligned}$

$\begin{array}{l}\frac{1}{4} Y=220-10 i \\Y=880-40 i\end{array}$

$\text { Thus } I S \text { equation: } Y=880-40 i$

$\text { To obtain } L M \text { function, we equate demand for money with supply of money. }$

$\begin{aligned}M^{t} &=M^{5} \\0.2 Y-5 i &=85 \\5 i &=0.2 Y-85 \\i &=\frac{0.2}{5} Y-17\end{aligned}$

$\text { Thus, } L M \text { function is }$

$i=0.04 Y-17$

$\text { Substituting the value of } i \text { in the } I S \text { function equation ( } i \text { ) we have }$

$\begin{array}{l}Y=880-40(0.04 Y-17) \\=880-1.6 Y+680 \\Y+1.6 Y=880+680 \\2.6 Y=1560 \\\quad Y=1560 \times \frac{10}{26}=600\end{array}$

$\text { Substituting the value of } 600 \text { for } Y \text { in } I S \text { equation (i) we have }$

$\begin{aligned}600 &=880-40 i \\40 i &=880-600=280 \\i &=\frac{280}{40}=7\end{aligned}$

$\text { (b) With the increase in Government expenditure by Rs. } 65 \text { crores }$

$\begin{aligned}Y^{\prime}=C+I+G+\Delta G \\Y^{\prime}=40+0.75\left(Y^{\prime}-80\right)+140-10 i+100+65 \\=& 40+0.75 Y^{\prime}-60+140-10 i+100+65 \\\quad Y^{\prime}-0.75 Y^{\prime}=285-10 i \\Y^{\prime}(1-0.75)=285-10 i \\\quad \frac{1}{4} Y^{\prime}=285-10 i \\Y^{\prime}=1140-40 i\end{aligned}$

$\text { New equation for } I S \text { curve is }=Y^{\prime}=1140-40 i$

$\text { Substituting the value of } i \text { from } L M \text { function equation (ii) we have }$

$\begin{aligned}Y^{\prime} &=1140-40\left(0.04 Y^{\prime}-17\right) \\Y^{\prime} &=1140-1.6 Y^{\prime}+680 \\Y^{\prime}+1.6 Y^{\prime} &=1820 \\Y^{\prime}(1+1.6) &=1820 \\2.6 Y^{\prime} &=1820\end{aligned}$

$Y^{\prime}=1820 \times \frac{10}{26}=700$

$\text { Now, substituting the value of } Y \text { in the } L M \text { equation (ii) we have }$

$\text { New interest } i=0.04(700)-17$

$\begin{array}{l}=28.00-17=11 \\=11\end{array}$

$\text { Thus, the new equilibrium income is } 700 \text { crores and interest rate is } 11 \text { per cent }$