Q.A household's consumption function is $C=100+0.75Y$ (in Rs. crore). At income Y = Rs. 800 crore, find

An increment in income is either consumed or saved, so MPC + MPS = 1; the answer is (b).

In the consumption and investment functions topic of the Tamil Nadu HSC Commerce syllabus:

• Marginal Propensity to Consume (MPC) = change in consumption ÷ change in income = dC/dY
• Marginal Propensity to Save (MPS) = change in saving ÷ change in income = dS/dY

Because every extra rupee of income is either spent on consumption or set aside as saving, the change in income equals the change in consumption plus the change in saving:

dY = dC + dS

Dividing throughout by dY:

dC/dY + dS/dY = 1

i.e. MPC + MPS = 1

For example, if MPC = 0.8 then MPS = 0.2, and 0.8 + 0.2 = 1. So the sum is always exactly one.

The marginal propensity to consume (MPC) and the marginal propensity to save (MPS) always sum to 1.

An increase in income (change in Y) is disposed of in only two ways: it is either spent on consumption (change in C) or set aside as saving (change in S). Therefore change in Y = change in C + change in S.

• MPC = change in C / change in Y (the fraction of extra income consumed).
• MPS = change in S / change in Y (the fraction of extra income saved).

Dividing the identity change in Y = change in C + change in S throughout by change in Y gives: 1 = MPC + MPS. This is why the options 0.1, 1.1 and 2 are wrong — the two propensities can only exhaust exactly one whole unit of the extra income.

The average propensity to consume (APC) is measured as C divided by Y.

The average propensity to consume is the ratio of total consumption expenditure to total income at a given level of income. It tells us the proportion of income that is consumed.

APC = C / Y, where C = total consumption and Y = total income.

For example, if income is 1000 and consumption is 800, then APC = 800 / 1000 = 0.8. The inverted ratio Y/C is not the consumption ratio, and C + Y or C x Y have no meaning as a propensity. So the correct measure is C/Y.

APC is consumption divided by income, i.e. C/Y, so option (b) is correct.

The Average Propensity to Consume (APC) measures the proportion of total income (Y) that is devoted to consumption (C):

APC = C / Y

For example, if income is 1000 and consumption is 800, APC = 800 / 1000 = 0.8. The other options (Y/C, C+Y, C x Y) do not express this ratio of consumption to income.