The Law of Equi-Marginal Utility states that a consumer maximizes total utility when the marginal utility per dollar spent is equal across all goods consumed. This principle guides the rational allocation of a limited budget among different goods to achieve maximum satisfaction.

An indifference curve represents various combinations of two commodities that provide the consumer with the same level of utility or satisfaction. Because the consumer is indifferent between these combinations, the curve must slope downward to reflect the trade-off: to consume more of one good, the consumer must sacrifice some of the other to maintain an identical level of total satisfaction.

The historical development of these theories is: 1. Law of Demand (Classical), 3. Law of Diminishing Marginal Utility (Gossen/Marshall), 2. Law of Indifference (Edgeworth), 5. Indifference Curve Analysis (Hicks-Allen), and 4. Revealed Preference Theory (Samuelson). This sequence reflects the evolution from cardinal utility to ordinal utility and finally to behavioral preference theory.

The Law of Equi-Marginal Utility states that a consumer maximizes total utility by allocating income such that the marginal utility per unit of currency spent on each good is equal. It is called the Law of Substitution because it involves substituting goods with higher marginal utility for those with lower marginal utility until equilibrium is reached, ultimately leading to maximum consumer satisfaction.

Consumer equilibrium occurs when a consumer maximizes their total utility given their budget constraint and prevailing market prices. It represents a state where the consumer allocates their limited income in a way that provides the highest possible satisfaction, effectively balancing the marginal utility per dollar spent across all goods.

In indifference curve analysis, a higher curve represents a higher level of satisfaction. Because indifference curves are non-intersecting and downward sloping, any point on a curve further from the origin contains a larger quantity of at least one good without reducing the quantity of the other. According to the assumption of non-satiation, consumers always prefer more of a good, thus higher curves indicate greater utility.

According to the Law of Equi-marginal Utility, a consumer reaches equilibrium when the ratio of marginal utility to price for each good is equal to the marginal utility of money (MUM), ensuring utility is maximized across all purchases.

Inter-temporal allocation of resources refers to the process of distributing consumption or investment across different time periods. It involves making decisions today that affect the availability and utility of resources in the future, balancing current needs against future requirements to optimize overall economic welfare over a specific time horizon.

The Indifference Curve approach relies on several behavioral assumptions regarding consumer choice. Rationality assumes consumers aim to maximize satisfaction. Consistency implies that if a consumer prefers bundle A to B, they will not prefer B to A. Transitivity ensures that if A is preferred to B, and B is preferred to C, then A must be preferred to C. These axioms are essential for modeling consistent consumer preferences.

John Hicks and R.G.D. Allen are widely recognized for their work in ordinal utility theory, where they refined the analysis of consumer behavior by decomposing the total price effect into the substitution effect and the income effect using indifference curve analysis.