1
Utility maximization II
• Example with CES utility function. max 31 + 2 ́1
12
11 +22 − = 0
• Solution:
∗= !
1 3 ́13 ́
−1 2 −1 1
1 1+
∗= !
2 3 ́1 3 ́ 21+ −1 1−1
2
• Special case 1: → −∞ (Perfect Complements)
∗1= =∗2 1 + 2
• Parameterindicatessubstitionpatternbetweengoods: —
0 — Goods are (net) substitutes
— 0 — Goods are (net) complements
2 Utility maximization — tricky cases
1. Non-convex preferences. Example:
2. Example with CES utility function.
max 31 + 2 ́1 12
11 +22 − = 0
● With 1 the interior solution is a minimum!
