Properties of Utility Functions

In this section, we test the ability of the agent to use utility functions as a means to compare preferences over different “bundles” of goods or services. A key feature of economic reasoning in this context is for agents to consider how substitution between different goods in a bundle might achieve the same utility (i.e., map out the “indifference curves”). Key tests include correctly distinguishing between substitutes and complements in consumption, and calculating the marginal rate of substitution at a point on an indifference curve. This logic is essential for both agents acting as a planner as we will see in Evaluating Equilibria and Externalities and when fulfilling the role of choice under budget and income constraints, in Deriving Demand.

Elements

1. Diminishing Marginal Utility

   Describing how the marginal utility of a good changes as its quantity rises with the other good fixed.

2. Marginal Utility

   Computing the marginal utilities of both goods for a Cobb-Douglas utility function.

3. Marginal Rate of Substitution

   Computing the marginal rate of substitution between two goods for a Cobb-Douglas utility.

4. Tangency and the Marginal Rate of Substitution

   Using the tangency of the budget line and an indifference curve: the marginal rate of substitution at the optimum equals the price ratio.

5. Substitutes and Complements

   Telling gross substitutes from complements by the sign of the cross-price effect, and computing a cross-price elasticity.