Production and consumption: The rational consumer

5.1 The rational consumer

"We have budgets and must decide how to spend them. The model of utility theory that economists have constructed to explain consumer choice assumes that consumers will try to maximize their utility....

"Utility theory provides insights into demand. It lets us look behind demand curves to see how utility-maximizing consumers can be expected to respond to price changes. While the focus of this chapter is on consumers making decisions about what goods and services to buy, the same model can be used to understand how individuals make other types of decisions, such as how much to work and how much of their incomes to spend now or to sock away for the future."
- Principles of Microeconomics

Activity

OpenStax College: "Principles of Microeconomics, Chapter 6: Introduction to Consumer Choices"

• Read Chapter 6 for information on consumer choice, including utility, consumer equilibrium, consumer equilibrium demand, consumer surplus, budget constraint, and consumer equilibrium and indifference curves.

Principles of Microeconomics: "Chapter 7 - Introduction, Section 1 and Section 2"

• Read the Chapter 7 Introduction and Sections 7.1 and 7.2. Attempt the "Try It" problems at the end of each section. Take a moment to read through the stated learning outcomes for this chapter of the text, which you can find at the beginning of each section. These outcomes should be your goals as you read through the chapter.

TED Talks: "Sheena Iyengar on the Art of Choosing"

• This is an optional lecture and not a requirement of the course. Please listen to this guest lecture in which the speaker talks about her ground-breaking research on how people make choices and explains attitudes towards their decisions.

Khan Academy: "Marginal Utility"

• Watch this video about marginal utility.

Khan Academy: "Budget Line"

• Watch this video about the budget line.

Khan Academy: "Deriving Demand Curve from Tweaking Marginal Utility per Dollar"

• Watch this video about deriving the demand curve from tweaking marginal utility per dollar.

Wolfram Demonstrations Project: "Constrained Optimization: Cobb-Douglas Utility and Interior Solutions Using a Lagrangian"

• To use this simulation, you must download and install the Mathematica Viewer from the Wolfram Demonstrations Project. Although this software is free, it is a sizable download. This activity is therefore optional.

This simulation presents an excellent illustration of how indifference curves and budget lines interact to produce optimal consumption (highest combined utility) of goods, given a set budget.

Our first task is to avoid letting the title of the simulation and the mathematical expressions fluster us! Once you have downloaded the software to your desktop, open the simulation and read the instructions.

A Lagrangian is an optimal point. Consumer optimization is all about finding the optimal point on the highest indifference curve (the red curve convex to the origin). An indifference curve shows different quantities of much of each of two goods (X₁ and X₂) a person can consume and end up with equivalent utility. You will work with an example of a college student who is trying to optimize his utility derived from eating pizza and drinking beer in the following quiz.

A vital constraint to consider in optimizing utility is budget. The slope of the budget line is controlled by the relative prices of both products. In the simulation, change the sliders that control the relative price of each good (X₁ and X₂) and note how the budget line changes. The cheaper either product is the more of that product can be bought, but that does not necessarily mean utility will respond proportionately. The income slider moves the budget line inward or outward; with more income we can buy proportionately more of both products. Notice how the budget line changes shape or moves up or down different indifference curves are tangent to the budget line. The indifference curve doesn’t move, but we rather encounter different curves to which the budget line becomes tangent.

The “preference strength” for X₁ determines the shape of the indifference curve and consequently where it becomes tangent to the budget line. Experiment with varying preferences and recall that preference is another way of stating tastes. Note that as preferences change, higher or lower indifferences curves intersect the budget line.

Start your exploration by setting all sliders to the middle of their respective bars. Then, try the following:

• Examine the consequence of an overall price decline in both products. (Hint: Move both X sliders in turn, then at the same time.)
• Examine the consequences of an overall price increase in both products in turn and at the same time.
• Reset to the midpoints and explore income increases and decreases. How do these compare with price increases?
• Reset to the midpoints and explore how changing preferences affect quantities purchased.
• How could you represent luxuries and necessities with this demonstration?