Basics of Theory of demand:

The most famous approach in the history of consumer behaviour, after indifference curve approach, is the revealed preference approach. In the revealed preference approach there is no concept of utility function and that is why the approach has no concept of indifference curve. The consumer has only preferences i.e., between any two commodities A and B, she can either prefer A over B or prefer B over A or A and B give same level of utility to the consumer, i.e. consumer is indifference between A and B. The slope of the demand curve of a good can take any algebrical sign. There are five main axioms of revealed preference theory.  In revealed preference approach own price effect can be decomposed into own substitution effect and income effect for a price change. Substitution effect is negative. The demand function is homogeneous of degree zero with respect to prices and money income, i.e., if prices of all goods and money income change proportionately then demand for each commodity remains unchanged, some times this can be put forward as 'Consumer is free from money illusion'.  In uncertain world consumer's objective is to maximise expected utility unlike the certain world where her objective is to maximise her utility.

The consumer preferences can be completely described by five axioms.  There is a duality between utility maximisation and expenditure minimisation, i.e., they both gives the same results. There are three duality theorems. Roy's identity relates optimal commodity demands to the derivatives of the indirect utility function and the optimal value of the Lagrange multiplier.