OPTIMIZATION

Today’s lecture is about optimization. Useful references are chapters 1-5 of Dixit (1990), chapters 16-19 of Simon and Blume (1994), and chapter 5 of Carter (2001). We typicallymodel economic agents as optimizing some objective function. Consumers maximize utility. Example 0.1. A consumer with income y chooses a bundle of goods x1,..., xn with prices p1,..., pn to maximize utility u(x). max x1,...,xn u(x1,..., xn) s.t. p1x1 + + pnxn y Firms maximize profits. Example 0.2. A firm produces a good y with price p, and uses inputs x 2 Rk with prices w 2 Rk. The firm’s production function is f: Rk!R. The firm’s problem is max y,x py wTx s.t. f (x) =