# Intermediate Microeconomics

## 3. Utility Maximization

Utility is the amount of satisfaction that a consumer derives from consuming a bundle of goods. While utility is not directly measurable, it is a useful abstraction that can be used to describe optimal consumer behavior. The model that we develop is an individual model, which helps us to better understand how individuals make choices based on their preferences and the constraints that they face. In the Pencasts for this topic, we define utility, explore its properties, and make predictions for optimal consumer behavior.

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## Properties of Consumer PreferencesThis Screencast describes the assumptions made regarding consumer preferences, including completeness, transitivity, and more is better. |

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## Utility: Definition and AssumptionsUtility is defined as satisfaction that consumers derive from consuming goods, services, and even leisure. In this pencast, we further explore the concept of utility and discuss some common assumptions. |

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## Utility and Indifference CurvesIndifference curves are graphical representations of bundles of goods for which consumers are indifference between. That is, quantities for two difference goods (for a two-dimensional indifference curve) that yield the same level of utility. We will use this concept in subsequent pencasts to derive consumers' utility maximizing choices for consumption and leisure. In this pencast, we are introduced to indifference curves and explore some of their properties. |

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## Willingness to Substitute between GoodsThis Pencast uses calculus to derive the marginal rate of substitution, i.e. a measure of how much a consumer will trade of one good to obtain one additional unit of another good. |

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## Curvature of Indifference Curves: Part IThis Pencast illustrates different shaped indifference curves, including perfect substitutes, perfect complements, and imperfect substitutes. |

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## Curvature of Indifference Curves: Part IIThis Pencast illustrates two different consumers, which have different markedly different preferences for two goods. One consumer has very steep indifference curves, while the other has relatively flat indifference curves. |

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## Plotting Indifference CurvesUsing a particular utility function, this Pencast shows how plot an indifference curve for an individual consumer. |

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## Budget ConstraintThis Pencast covers the budget that constrains consumer choice. It covers the mathematics of the budget constraint and illustrates how to plot the budget line. |

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## Changes in the Budget ConstraintThis Pencast illustrates how the budget constraint and, hence, the budget line are altered when (a) income changes and (b) when the relative prices of two goods change. |

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## Constrained Optimization: Equating Marginal Rates of Substitution and TransformationThis Pencast shows how to compute the optimal consumption bundle for a consumer by equating the marginal rates of substitution and transformation. |

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## Lagrangian Method: First-Order ConditionsThis Pencast illustrates how to derive the first-order conditions and find the utility maximizing condition, which is given by the Lagrange multiplier. |

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## Lagrangian Method: Finding Optimal BundleThis Pencast shows how to derive the optimal consumption bundle using the Lagrangian method. It involves using the first-order conditions to find the optimal quantities of both goods. |

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## Graphical Representation of the Optimal Consumption BundleThis Pencast illustrates how to find a consumer’s optimal consumption bundle graphically. Interior and corner solutions are covered. |

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## Minimizing an Expenditure Function to Find a Consumer's Optimal BundleThis Pencast illustrates how to derive the first-order conditions and determine a consumer's optimal consumption bundle by minimizing an expenditure function. |

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## Deriving Demand CurvesThis Pencast illustrates graphically how to use a model of individual consumer behavior to derive a demand curve. |

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## Income and Shifts in DemandThis Pencast illustrates graphically how increases in a consumer’s income results in shifts in their demand curve. In addition, it is shown how to derive a Engel curve, which relates income and consumption. |

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## Increases in Income and Normal/Inferior GoodsThis Pencast shows how an increase in income affects the consumption of two goods under three different scenarios: Z and X are normal goods; Z is a normal good and X is an inferior good; and Z is an inferior good and X is a normal good. |

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## Goods Can be Both Normal and InferiorThis Pencast provides an example of a good that is both normal and inferior. |

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## Weighted Income ElasticitiesThis Pencast illustrates how to use a consumer’s budget constraint to derive weighted income elasticities, which is the sum of budget shares multiplied by the income elasticities of demand. |

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## Weighted Income Elasticities: An ApplicationThis Pencast illustrates how information on income elasticities and budget shares can be used to infer income elasticities on other goods for which the same information is not available. |

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## Effects of a Price IncreaseThis Screencast describes how a change in price generates two effects: substitution and income effects. The definitions and intuition behind such effects are discussed. |

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## Effects of a Price Increase: Graphical RepresentationThis Pencast illustrates how to isolate substitution and income effects graphically. |

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## Effects of Changes in Relative Prices: An Application using Cost-of-Living Adjustments (Part I)This Pencast shows how to compute the optimal consumption bundle using initial income and prices. |

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## Effects of Changes in Relative Prices: An Application using Cost-of-Living Adjustments (Part II)This Pencast shows how to compute the optimal consumption bundle using adjusted income and new prices. |

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## Effects of Changes in Relative Prices: An Application using Cost-of-Living Adjustments (Part III)This Pencast shows how to compute the consumption bundle holding utility constant at its initial level using the new prices. |

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## Effects of Changes in Relative Prices: An Application using Cost-of-Living Adjustments (Part IV)This Pencast shows how to compute substitution, income and total effects using the information in Parts I, II and III of this series of Pencasts. |

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## Effects of Changes in Relative Prices: An Application using Cost-of-Living Adjustments (Part V)This Pencast shows that the cost-of-living adjustment allows the consumer to move to a higher indifference curve. |