Comparative Statics of Demand

This module considers how agents reason about changes in prices or income, and their effects on the quantity of each good they would purchase. We test the classic law of demand, different types of goods (e.g., normal, inferior, and Giffen), and derive Engel curves from first principles. The key tests are to ensure the agent rationally responds to changes in relative prices, and investigate their substitution between goods in a bundle. In practice, these tests involve comparative statics of the argmax from the utility maximization of the previous section on Deriving Demand—i.e., using an Envelope theorem and perturbing prices or income.

Elements

1. Law of Demand

   Predicting the direction of a quantity (or price) change implied by the law of demand.

2. Price Elasticity of Demand

   Computing the price elasticity of demand from a price change and the resulting quantity change.

3. Engel Curves

   Deriving the Engel curve of a good, the income at which a consumer buys each quantity, from a Cobb-Douglas utility and prices.

4. Income Elasticity of Demand

   Computing an income elasticity of demand from percentage changes, or using one to predict a change in quantity or income.

5. Consumption Changes

   Predicting how the share of income spent on a good changes when its price rises, from a CES utility with a stated elasticity of substitution.