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

  1. Homogeneity of degree zero:
     
  2. 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  ,  

AggregationEdit

Homogeneity ResultsEdit

Engel AggregationEdit

Cornout AggregationEdit