# Integrability of Demand

I wondered if someone would be willing to provide an intuitive presentation of the so-called integrability of demand/integrability conditions.

My own knowledge of these conditions is that they're the conditions required of an individual (and subsequently a market) to be acting 'rationally', (i.e. consistently maximising/or minimising welfare using price signals)

My own interpretation is that these conditions are required so that economics is an economic science, adhering to certain predictable laws (such as the compensated law of demand).

Economic behaviour should therefore be time-invariant, path-independent , universal, and not subject to illusion.

For example,

• Homogeneity of degree should hold (money units do not matter in economic decision making, instead it is relative prices).

• Individuals maximise consumption (MRS = price ratio)

• Behaviour is characterised by symmetry (universality). Compensated change in demand for X, given a change in Y is the same as the compensated change in demand for Y, given the change in X.

I wondered if my interpretation here is the correct one?

I am especially interested to here some intuitive explanations of Slutsky Symmetry with real world examples, and also an intuitive explanation of 'negative semidefinite' beyond that it must chracterise a 'concave utility function'.

Would be nice to hear everybody's input on these matters, and really get to the essence of the topic matter.

Best,

Andrew