The correct answer is: A. Cardinal measurability of the utility.
Cardinal measurability of utility is the assumption that utility can be measured on a cardinal scale, meaning that it can be represented by a number that indicates the relative satisfaction that a consumer receives from consuming a good or service. This assumption is necessary for the Marshallian utility analysis to be valid, as it allows economists to compare the utility that consumers receive from different goods and services.
However, there is some debate about whether or not cardinal measurability of utility is a valid assumption. Some economists argue that it is not possible to measure utility on a cardinal scale, as it is a subjective concept that cannot be directly observed. Others argue that it is possible to measure utility on a cardinal scale, but that the measurements are not always accurate.
Despite the debate, the Marshallian utility analysis is still widely used in economics. This is because it is a simple and elegant model that can be used to explain a wide range of economic phenomena.
The other options are not as valid assumptions as cardinal measurability of utility.
B. Given marginal utility of money is the assumption that the marginal utility of money is constant. This means that the additional satisfaction that a consumer receives from consuming an additional unit of money is always the same. This assumption is not as valid as cardinal measurability of utility, as it is not always true that the marginal utility of money is constant.
C. Diminishing marginal utility of the goods is the assumption that the marginal utility of a good declines as the consumer consumes more of that good. This means that the additional satisfaction that a consumer receives from consuming an additional unit of a good declines as the consumer consumes more of that good. This assumption is more valid than cardinal measurability of utility, as it is more likely to be true in the real world.
D. Additivity of the utility is the assumption that the utility that a consumer receives from consuming two goods is equal to the sum of the utilities that the consumer receives from consuming each good individually. This assumption is not as valid as cardinal measurability of utility, as it is not always true that the utility that a consumer receives from consuming two goods is equal to the sum of the utilities that the consumer receives from consuming each good individually.