Representing consumer preferences


·        A preference ordering over the consumption set

·        Conditions under which a continuous utility function can represent the preference ordering

·        The marginal rate of substitution

·        Program: v(p1,p2,m), the indirect utility function, is the maximum utility obtainable under the budget constraint determined by p1,p2,m.

·        If we can solve explicitly for the ordinary demand functions in the maximization, we substitute them into the utility function to obtain the indirect utility function.

·        If we can solve for the ordinary demand functions we can explore their properties directly by, for example, taking their derivatives if they exist.

·        Even if we cannot solve for the ordinary demand functions we can use the implicit function theorem to explore the characteristics of the implied ordinary demand functions at the equilibrium. (This involves treating the first order conditions as identities assuming the x1, x2, and λ are implicitly functions of p1,p2,m, differentiating the resulting system of identities with respect to a parameter, solving the resulting linear equations using Cramer’s rule and using the second order condition in investigating the direction of an effect.)

·        Properties of the indirect utility function (see p. 102)

·        Program: e(p1,p2,u), the expenditure function is the minimum expenditure necessary to obtain a specified level of utility.

·        This function is similar in its properties to the cost function (see p. 105). These properties are important aids in analysis.

·        The demands generated by solving this program are called Hicksian demand functions (aka compensated demand functions or constant utility demand functions). The sign of their response to their own price is non-positive.


·        Four important identities (see class notes)

·        Using the identities to prove Roy’s identity and the Slutsky equation

·        Elasticity relationships

·        Deriving the Slutsky equation using the first order conditions, second order conditions and the implicit function theorem

·        The integrability problem and the Slutsky equation


·        The money metric utility function (direct and indirect) and the money metric expenditure function (direct and indirect)

·        Compensating variation and equivalent variations

·        Consumer’s surplus

o       Quasi-linear utility

o       As an approximation to a variation measure.

·        Brief review of Kuhn-Tucker conditions in solving for the indirect utility function with a quasi-linear utility function

·        Discussing above concepts in context of the illustrative problems 2.

·        Endowments in the definition of the budget set

o       Slutsky compensation

o       Expenditure functions with endowments

§         Generalized income

o       Demand for leisure and labour supply

·        Homothetic utility functions

o       Separability in expenditure and indirect utility functions

·        Aggregation

o       Hicksian aggregation

o       Aggregation and weak separability

o       Across consumers

·        Inverse demand functions