Explain about the integrability problem, Microeconomics

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Explain about the integrability problem.

The Integrability Problem:

Provide a system of demand functions x(p, m). Is there essentially a utility function by which such demand functions can be derived? That question is termed as the integrability problem. This problem can be solving by a differential equation and integrating back, eventually to the utility function. The Slutsky matrix plays a important role into this process.

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