Advanced Microeconomics/Demand Correspondence

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Demand Correspondence[edit]

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 correspondences[edit]

  1. Homogeneity of degree zero:
  2. Walras's law:

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

Comparative Statics[edit]

The Engel Function[edit]

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 Effects[edit]

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

Aggregation[edit]

Homogeneity Results[edit]

Engel Aggregation[edit]

Cornout Aggregation[edit]