Alfred Marshall is the chief exponent of the cardinal utility approach — option (c).

In consumption analysis two approaches explain consumer behaviour:

• Cardinal utility approach — assumes utility (satisfaction) can be measured in absolute numerical units called utils. Its central tool is the Law of Diminishing Marginal Utility. This approach was developed and made famous by Alfred Marshall.
• Ordinal utility approach — argues utility can only be ranked, not measured, and uses indifference curves. Its main proponents were J. R. Hicks and R. G. D. Allen.

Hence Hicks (a) and Allen (b) belong to the ordinal school, and Stigler (d) is not associated with founding either approach. The cardinal approach's chief exponent is Marshall.

Of the options, a higher subsidy raises demand — option (b).

An increase in demand means consumers are willing to buy more at a given price (a rightward shift of the demand curve). We check each factor:

• (a) Increase in tax — raises the price consumers pay, reducing demand. ✗
• (b) Higher subsidy — a subsidy lowers the effective price and increases consumers' real purchasing power, so they buy more. This increases demand. ✓
• (c) Increase in interest rate — makes borrowing costlier and saving more attractive, cutting spending, so demand falls. ✗
• (d) Decline in population — fewer buyers means smaller total demand. ✗

Therefore only a higher subsidy causes demand to increase.

Salt is a necessity that has no close substitute, so the answer is option (c).

A close substitute is a good that can be used in place of another to satisfy the same want (like tea and coffee, or Coke and Pepsi). When a good has no close substitute, consumers must buy it regardless of price, so its demand is highly inelastic.

Among the options, sugar can be replaced by jaggery, a matchbox by a lighter, and tea by coffee — all have substitutes. Salt, however, has no real substitute in cooking, so households continue to buy roughly the same quantity even if its price rises. This makes salt the standard textbook example of a good with no close substitute.

The Law of Demand is based on the Law of Diminishing Marginal Utility, so the answer is option (b).

The Law of Demand states that, other things being equal, when the price of a good falls its quantity demanded rises, and vice versa. The reason behind this inverse relationship is the Law of Diminishing Marginal Utility: as a consumer buys more units of a good, the marginal (extra) utility of each successive unit declines. Since a consumer will only buy an additional unit when its price falls to match the lower marginal utility, more is bought at lower prices — which is exactly the Law of Demand.

Gossen's First Law is another name for the Law of Diminishing Marginal Utility, but the most direct and standard answer taught for the basis of the Law of Demand is the Law of Diminishing Marginal Utility.

The correct option is (d) Maximum: TU is highest when MU = 0.

Marginal utility (MU) is the addition to total utility (TU) from consuming one more unit. As long as MU is positive, TU keeps increasing; the point where MU falls to zero is the saturation point at which TU stops rising and is therefore at its maximum. If the consumer takes still more units, MU becomes negative and TU begins to fall.

Why the others are wrong: (a)/(b) TU is at a peak, not zero or minimum, and (c) TU turns negative only after MU becomes negative, not when MU is zero.

The correct option is Both statements (A) and (R) are true and R is the correct explanation of (A).

By the law of diminishing marginal utility, as a consumer consumes more units of a good, the marginal utility (extra satisfaction from each additional unit) keeps falling — so assertion (A) is true. Total utility still increases as long as MU is positive, but because each successive unit adds less than the one before, TU rises at a diminishing rate — so reasoning (R) is true. Crucially, TU increasing at a diminishing rate is a direct consequence of MU diminishing (TU is the running sum of falling MU values). Therefore R correctly explains A.

Elasticity of demand equal to one indicates unitary elastic demand.

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price: Ed = percentage change in quantity demanded / percentage change in price. When this ratio equals exactly 1, the two percentage changes are equal, and demand is said to be unitary elastic. If Ed = 0 it is perfectly inelastic, if Ed is greater than 1 it is relatively (more) elastic, and if Ed is infinite it is perfectly elastic. Only a value of one denotes unitary elastic demand.

When marginal utility reaches zero, total utility is maximum.

Marginal utility (MU) is the addition to total utility (TU) from consuming one more unit. As consumption increases, MU falls (Law of Diminishing Marginal Utility). While MU is positive, TU keeps increasing but at a diminishing rate. When MU becomes exactly zero, no further utility is being added, so TU stops rising and is at its highest — this is the point of satiety or maximum satisfaction. If consumption continues beyond this, MU turns negative and TU begins to fall. Hence TU is maximum when MU = 0.

The correct formula is (b) MU = TUn - TUn-1.

Marginal Utility (MU) is the extra satisfaction a consumer gets from consuming one additional unit of a commodity. If TUn is the total utility from consuming n units and TUn-1 is the total utility from consuming (n-1) units, then the utility added by the nth unit is:

MU of nth unit = TUn - TUn-1

For example, if total utility from 3 units is 30 and from 2 units is 24, the marginal utility of the 3rd unit = 30 - 24 = 6 utils.

The other options are incorrect because adding total utilities (options a and d) or subtracting a later value (option c) does not measure the change caused by the last unit consumed. This formula underlies the Law of Diminishing Marginal Utility studied in the TN HSC Class-11 Economics consumption chapter.