lexicographic, cardinal/ordinal utility,envelope,
Hotelling’s lemma, utility maximization
1. In the
context of the usual utility maximization problem involving n(>2) goods,
prove that not all goods can be net complements and that at least one good must
be normal.
2. Prove the
envelope theorem and use it to derive Hotelling’s lemma.
3. Explain:
(a) Why
lexicographic preferences do not yield a continuous utility function.
(b) The
difference between cardinal and ordinal utility.
(c) Why
profit maximization is not an assumption in the competitive general equilibrium
model.
4. Average
costs fall as output increases if and only if the production function is
homogeneous of degree p>1. True or false? Explain your answers.
5. Consider
the problems of maximizing utility u(x) subject to px ≤ y and
minimizing expenditure px subject to u(x) ≥ u. Assuming that the
utility function is continuous and strictly monotonic increasing and that
solutions to both problems exist. Prove that utility maximization implies and
is implied by expenditure minimization.
