Q.A household's consumption function is $C=50+0.8Y$, where C and Y are measured in thousands of rupees.

The MPC is the coefficient of Y (the slope of the line); substitute Y=500 into the consumption function to find C.

(a) MPC = slope = 0.8 (the coefficient of Y). (b) $C=50+0.8(500)=50+400=450$.

(a) The consumption function $C=50+0.8Y$ is in the standard linear form $y=mx+c$, with Y playing the role of x. The slope of this line is the coefficient of Y, which is $0.8$. Since the slope of a linear consumption function IS, by definition, the Marginal Propensity to Consume:

This means that for every extra Rs. 1 of income the household earns, it spends Rs. 0.80 of it on consumption (and, correspondingly, saves the remaining Rs. 0.20).

(b) Substituting $Y=500$ into the consumption function:

Cross-check using the slope directly: starting from a convenient reference point, say $Y=0 \Rightarrow C=50$ (the autonomous/intercept consumption), moving to $Y=500$ is a change of $\Delta Y=500$. Applying the slope: $\Delta C=\text{MPC}\times\Delta Y=0.8\times500=400$, so $C=50+400=450$ — matching the direct substitution exactly.

Students sometimes mistake the INTERCEPT (Rs. 50, the autonomous consumption incurred even at zero income) for the MPC — the MPC is always the SLOPE (the coefficient multiplying Y), not the constant term.