The marginal utilities of a consumer from successive units of a good are 20, 14, 8, 2 and –4. If she gets the good free of cost and wants the highest total utility, how many units will she consume, and what is the marginal utility of the last unit she consumes?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 units; 2
Total utility rises as long as marginal utility is positive. When MU turns negative, TU starts falling. So a free good is used until the last unit with positive MU.
MU of units 1 to 4: 20, 14, 8, 2, all positive, so TU keeps rising
MU of unit 5 = −4, so the 5th unit lowers TU
She consumes 4 units; MU of the 4th unit = 2
TU at 4 units is 20 + 14 + 8 + 2 = 44, but 44 is the total, not the marginal utility of the last unit.
NCERT (2026-27): “Measures of Utility … In general, MUn = TUn – TUn-1, where subscript n refers to the nth unit of the commodity …” “Notice that MU3 is less than MU2. You may also notice that total utility increases but at a diminishing rate: The rate of change in total utility due to change in quantity of commodity consumed is a measure of marginal utility. … MU becomes zero at a level when TU remains constant. In the example, TU does not change at 5th unit of consumption and therefore MU5= 0. Thereafter, TU starts falling and MU becomes negative.” |