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Part II: Considering Which Side You’re On in the Decision-Making Process
You’re happiest when the marginal utility per dollar spent on each good is equal for all goods.
Choosing to Use Calculus with Consumer Choice Dangerous curves ahead. Really! This is the section where I show you how to maximize utility by using calculus and the Lagrangian function. Calculus does make indifference curves dangerous.
Measuring indifference Indifference curves can be described by functions. For example
shows the relationship between the quantity consumed of good x, the quantity consumed of good y, and total utility.
Constraining factors Again, consumers face a budget constraint. For example, a consumer has a weekly budget of $400 for goods x and y. The price of good x is $10 and the price of good y is $8. The budget constraint is
where x and y are the quantities consumed of each good.
Lagrangians can make you happy You’ll recognize this as a constrained optimization problem — the consumer is trying to maximize utility, subject to a budget constraint. This situation is ideal for a Lagrangian. (Go to Chapter 3 for more information on the Lagrangian function and how to set it up.) The consumer wants to maximize utility, subject to the budget constraint, based upon the functions I present earlier in this section. The steps you take in order to determine the quantity of x and y that maximize utility are the following:
