Title: Microeconomics / Q1 / lecture6

Q: what are fundamental assumptions of a utility function?
A: 1. it is continuous
2. locally non-satiated rational preference relation
3. p>>0
4. preference relation is strictly convex

Q: Hicksian demand properties
A: The second and third properties follow from the fact that e(p, u) is a twice continuously differentiable concave function; it has a symmetric and negative semidefinite Hessian (matrix of second derivatives). Fourth property can be shown by recalling that h(p, u) is homogenous of degree 0 in p.

substitutes

Compliments

Slutsky equation

Q: normal good (walrasian vs hicksian)
A: the impact of a change in price on the Walrasian demand is larger (in absolute value) because the wealth effect reinforces the price effect. For example, an increase in the price will reduce demand both because the relative price has increased and because real wealth has fallen. In contrast, Hicksian demand is less sensitive to price because, to maintain the same utility level, price changes are accompanied by wealth changes in the same direction.

Q: inferior goods
A: The wealth effect for Walrasian demand is the opposite direction of price effects.

Q: when is something a type of Definent?
A: If all the eigenvalues are nonnegative, it is positive semidefinite.
If all the eigenvalues are positive, it is positive definite.
If all the eigenvalues are nonpositive, it is negative semidefinite.
If all the eigenvalues are negative, it is negative definite.
Otherwise, it is indefinite.

Roy’s identity

Q: Go from indirect utility function to walrasian
A: Roy's identity

Summary of lecture 6