ECON 302 Lecture 1: Lagrangian
24 Aug 2016
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The lagrangian is a method of solving constrained optimization problem. Examples of constrained optimization include maximizing utility subject to a budget constraint and minimizing costs subject to a level of output. Utility maximization- maximize utility subject to a budget constraint. For more, go to the appendix in chapter 4 of microeconomics by pindyck and rubinfeld. To maximize utility subject to a budget constraint, use the following steps: set up the lagrangian, the lagrangian will have two parts. It can be thought of as the shadow cost of purchasing a unit of a good. For instance, when i buy a unit of good x, i am not able to spend that money to buy good y. The amount of utility i lose from not buying those units of good y represent the shadow cost of buying good x. Solving equation 2. ii. for yields: = . So it must be true that: = .
