Q.In a two-sector economy, the consumption function is $C=60+0.6Y$ (Rs. crore) and autonomous investment is $I=40$ (Rs. crore). Find the equilibrium level of national income using

Solve Y=C+I directly for Y, then independently derive the saving function and solve S=I, confirming both methods give the identical equilibrium income.

1. The Y = C + I approach: substituting the consumption function and the given autonomous investment into the equilibrium condition:

   $Y=C+I=(60+0.6Y)+40$

   $Y=100+0.6Y$

   $Y-0.6Y=100 \Rightarrow 0.4Y=100 \Rightarrow Y=250$

   So the equilibrium level of income is $Y^{*}=Rs.\,250$ crore by this method.
2. The S = I approach (independent check): first derive the saving function from the given consumption function:

   $S=Y-C=Y-(60+0.6Y)=-60+0.4Y$

   Setting planned saving equal to planned investment, $S=I=40$:

   $-60+0.4Y=40 \Rightarrow 0.4Y=100 \Rightarrow Y=250$

   Comparison: both methods independently arrive at EXACTLY the same equilibrium income, $Y^{*}=Rs.\,250$ crore — confirming the two approaches are simply algebraically equivalent restatements of the identical equilibrium condition, and that the answer is correct. …

A common slip when deriving the saving function is to forget to distribute the negative sign correctly across BOTH terms of C — writing S=Y-60+0.6Y (an addition sign error) instead of the corr …