Summary

  1. Utility is the economic concept of consumers’ happiness or well-being, and the utility function is the construct that relates the amount of goods consumed (the inputs) to the consumer’s utility level (the output). There are properties that we expect almost all utility functions to share: the completeness, rankability, and transitivity of utility bundles, that having more of a good is better than having less, and that the more a consumer has of a particular good, the less willing she is to give up something else to get more of that good. [Section 4.1]

  2. Consumers’ preferences are reflected in their indifference curves, which show all the combinations of goods over which a consumer receives equal utility. The set of properties imposed on utility functions imply some restrictions on the shapes of indifference curves. Namely, indifference curves slope downward, never cross for a given individual, and are convex to the origin. [Section 4.2]

  3. The negative of the slope of the indifference curve is the marginal rate of substitution of good X for good Y (MRSXY). The MRS is the ratio of the marginal utilities of the goods in the utility function. [Section 4.2]

  4. Consumer preferences lead to differences in the steepness and curvature of indifference curves. If a consumer views two goods as perfect substitutes or perfect complements, their indifference curves will be shaped like straight lines and right angles, respectively. [Section 4.2]

  5. The consumer’s decision about how much of each good to consume depends not only on utility, but also on how much money that person has to spend (her income) and on the prices of the goods. In analyzing the role of income in consumption decisions, we assume the following: Each good has a fixed price, and any consumer can buy as much of a good as she wants at that price if the consumer has sufficient income to pay for it; the consumer has some fixed amount of income to spend; and the consumer cannot save or borrow.

    The budget constraint captures both a consumer’s income and the relative prices of goods. The constraint shows which consumption bundles are feasible (i.e., affordable given the consumer’s income) and which are infeasible. The slope of the budget constraint is the negative of the ratio of the prices of the two goods (–PX/PY). [Section 4.3]

  6. The consumer’s decision is a constrained optimization problem: to maximize utility while staying within her budget constraint. The utility-maximizing solution is generally to consume the bundle of goods located where an indifference curve is tangent to the budget constraint. At this optimal point, the consumer’s marginal rate of substitution—the ratio of the consumer’s marginal utilities from the goods—equals the goods’ relative price ratio.

    A corner solution, where the optimal quantity consumed of one good is zero, can occur when a consumer’s marginal utility of a good is so low compared to that good’s relative price that she is better off not consuming any of that good at all. In such cases, the MRS does not equal the price ratio even though the consumer is at the utility-maximizing consumption bundle. [Section 4.4]