By Sydney N. Afriat
The software proposal has had a protracted heritage in economics, specifically within the clarification of call for and in welfare economics. In a finished survey and critique of the Slutsky idea and the trend to which it belongs within the fiscal context, S. N. Afriat bargains a solution of questions relevant to its major inspiration, together with enough stipulations as well.
Originally released in 1980.
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Extra info for Demand Functions and the Slutsky Matrix. (PSME-7)
Conditions For a utility order Rand a demand (x, p), the H'=yRx~py~px and H" =px ~PY ~xRy are such that: (i) if R is complete and xR is closed, then H" (ii) If z
The Antonelli conditions for an inverse demand function have the form of a symmetry similar to Slutsky's conditions for a 19 INTRODUCTION direct demand function. They are in fact just the original Frobenius symmetry conditions applied to an inverse demand function. But the Slutsky conditions make sense even if the demand function is without an inverse and so do the Pfaff classical conditions that are equivalent to the Frobenius symmetry condition and, as shown here, to the Slutsky symmetry condition.
Not every demand function has a utility function at all, and Slutsky's concern was with conditions on a demand function necessary for it to have one, especially one having certain properties. He considered a demand function with a utility function having continuous second derivatives, and, as will be seen, such a demand function must have continuous first derivatives and be invertible. He deduced necessary conditions in terms of the well-known coefficients he formed with the derivatives. These consist in the symmetry condition s = s', and restrictions on the sign of the quadratic form with matrix s.
Demand Functions and the Slutsky Matrix. (PSME-7) by Sydney N. Afriat