Definition
Slutsky matrix, also known as Substitution matrix is the matrix of substitution effects.
Where the (l, k) th entry is:
: consumption change when price changes
: wealth adjusts to compensate
Proposition 2. F. 2 - MWG
If a differentiable Walrasian demand function x(p, w) satisfies Walras's law, homogeneity of degree 0, and the weak axiom, then at any (p, w,) the Slutsky matrix S(p, w) satisfies 
for any 
Interpretation
- The diagonal entries must be negative, but it does not state S is symmetric
- A good can be Giffen only if it is inferior
Proposition 2. F. 3 - MWG
Suppose that the Walrasian demand function x(p, w) is differentiable, homogeneous of degree zero, and satisfies Walras's law. Then
and 
for any (p, w).
Explain: it is associated with the "price and wealth effect cancel off" of Walrasian demand.