# Advanced Microeconomics/Demand Correspondence

## Demand CorrespondenceEdit

The *demand correspondence* vector assigns a set of consumption bundles to each pair . A single valued demand correspondence is a *demand function*.

### Assumptions on demand correspondencesEdit

- Homogeneity of degree zero:

- Walras's law:

Notice, the homogeneity assumption allows one argument of to be normalized.

### Comparative StaticsEdit

#### The Engel FunctionEdit

Holding the price vector constant, the demand correspondence is the *Engel function*. In the Engel function is known as the *wealth expansion path*, illustrating changes in the demand correspondence at various levels of wealth. The first derivative of the Engel function with respect to wealth for good is the wealth effect.

- for
*normal goods*the wealth effect is nonnegative,

- for
*inferior goods*the wealth effect is negative,

#### Price EffectsEdit

For any two goods the representation of across all prices is the *offer curve*.
Define the price effect of good on good ,