Slutsky substitution matrix is negative semidefinite
E746878
The Slutsky substitution matrix is negative semidefinite is a core result in consumer theory stating that, under standard assumptions, the matrix of compensated price effects has non-positive eigenvalues, reflecting the law of demand in a multigood setting.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Slutsky substitution matrix is negative semidefinite canonical | 1 |
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
result in microeconomic theory
ⓘ
theorem in consumer theory ⓘ |
| appliesTo | finite-dimensional commodity spaces ⓘ |
| assumes |
convex preferences
ⓘ
differentiable utility or demand functions ⓘ locally non-satiated preferences ⓘ standard consumer theory assumptions ⓘ |
| concerns |
Hicksian demand functions
NERFINISHED
ⓘ
Slutsky substitution matrix NERFINISHED ⓘ compensated price effects ⓘ |
| connectedTo | Afriat–Varian revealed preference conditions in differential form ⓘ |
| contrastsWith | positive semidefinite matrices in production theory ⓘ |
| describes | curvature property of the expenditure function ⓘ |
| equivalentTo |
Hicksian demand satisfies the law of compensated demand
NERFINISHED
ⓘ
expenditure function is concave in prices ⓘ |
| field |
consumer theory
ⓘ
microeconomics ⓘ |
| guarantees | consistency of observed Hicksian demand with utility maximization ⓘ |
| historicalOrigin | work of Eugen Slutsky on demand theory ⓘ |
| holdsUnder |
interior solutions to the consumer problem
ⓘ
well-behaved preferences ⓘ |
| implies |
eigenvalues of the Slutsky substitution matrix are non-positive
ⓘ
for any price change vector the associated quadratic form is non-positive ⓘ law of demand in a multigood setting ⓘ own-price compensated effects are non-positive ⓘ substitution terms cannot generate positive quadratic forms ⓘ |
| isPropertyOf | matrix of partial derivatives of Hicksian demand with respect to prices ⓘ |
| isSpecialCaseOf | curvature restrictions in applied demand analysis ⓘ |
| logicalStatus |
necessary condition for rationalizable Hicksian demand
ⓘ
not sufficient alone for full integrability ⓘ |
| mathematicalForm | Slutsky matrix is symmetric and negative semidefinite NERFINISHED ⓘ |
| motivates | imposition of curvature constraints in econometric models of demand ⓘ |
| refersTo | negative semidefiniteness of the Slutsky substitution matrix ⓘ |
| relatedTo |
Hicksian substitution effect
NERFINISHED
ⓘ
Marshallian demand functions NERFINISHED ⓘ Slutsky equation NERFINISHED ⓘ integrability conditions for demand ⓘ |
| requires | twice differentiable expenditure function ⓘ |
| testedIn | empirical demand system estimation ⓘ |
| usedIn |
comparative statics of consumer demand
ⓘ
duality theory in microeconomics ⓘ welfare analysis ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.