Question

Math

Given the saving funstion S = -10 + 0.2Y and autonomous investment I = Rs.50 cores
i) Find the level of consumption
ii) If investment decreases permanently by Rs.5 crore, what is the new level of consumption.

Answer 1

i) We know that consumption (C) and savings (S) are functions profit (Y):

$$Y = C(Y) + S(Y),$$

this equation shows that the portion of income goes to private consumption $C$, and excess takes the form of savings $S$. However, the cost to society can be represented on the one hand, the demand for consumer needs $C$, and on the other – the investment $I$:

$$Y = C'(Y) + I'(Y).$$

We can find the level of investment and savings from this equation:

$$I'(Y) = Y - C'(Y);$$ $$S'(Y) = Y - C'(Y).$$

We know that the saving function is $S = -10 + 0.2Y$, autonomous investment $I = Rs.50$ crores we can see that:

$$I'(Y) = S'(Y) \rightarrow 50 = -10 + 0.2Y.$$

Then we can find the level of profit $Y$

$$Y = \frac{50 + 10}{0.2} = 300,$$

After this we find the level of consumption $C'(Y)$

$$C'(Y) = Y - I'(Y) = 300 - 50 = 250$$

ii) If investment decreases permanently by Rs.5 crore, the new level of investment $I''$ is Rs.55 crores and we find the new level of consumption $C''$ by the same algorithm:

$$I''(Y) = S(Y) \rightarrow 55 = -10 + 0.2Y.$$ $$Y = \frac{55 + 10}{0.2} = 325,$$ $$C''(Y) = Y - I''(Y) = 325 - 55 = 270.$$

Answer: i) Consumption $C'$ is Rs.250 crores, i) Consumption $C''$ is Rs.270 crores.