Unit 4: The Theory of Consumer Choice
Where the demand curve actually comes from: a budget line, a map of preferences, and the point where they just touch.
12 topics · 43 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Budget Constraint
- How it worksHow do income and the prices of two goods combine into a budget line of affordable bundles?
- Worked exampleFind the two intercepts of a budget line for 40 dollars of income when pizza costs 4 dollars and movies cost 8 dollars.
- Going furtherWhat happens to every point on the budget line when income rises but both prices stay the same?
Your turn1 of 2
A shopper has 51 dollars of income. Pizza costs 5 dollars a slice and movies cost 12 dollars each. If she spends all her income on pizza alone, how many slices can she buy?The Slope of the Budget Line and Relative Price
- How it worksHow does the ratio of two prices become the slope of the budget line?
- Worked exampleFind the slope of a budget line when pizza costs 4 dollars a slice and movie tickets cost 8 dollars.
- Common mistakeWhy isn't the slope of the budget line determined by how much income a person has?
Your turn1 of 2
Find the slope of a budget line, in magnitude, when pizza costs 6 dollars a slice and movie tickets cost 11 dollars.Shifts and Pivots of the Budget Line
- How it worksHow does a change in income shift the entire budget line in or out while keeping its slope the same?
- Going furtherWhat happens to the budget line when the price of only one of the two goods falls?
- Going furtherWhat happens to the horizontal intercept of a budget line when the price of that axis good falls?
- Common mistakeWhy doesn't a price change move the budget line the same parallel way an income change does?
Your turn1 of 2
The price of movies falls while the price of pizza and the consumer's income stay the same. What happens to her budget line?Indifference Curves and Preferences
- How it worksHow does an indifference curve connect every bundle of two goods that gives a consumer the same satisfaction?
- How it worksHow does a whole map of indifference curves rank a consumer's preferences from least to most preferred?
- Common mistakeWhy isn't one bundle on an indifference curve preferred over a different bundle on that same curve?
Your turn1 of 2
A consumer's indifference map shows several indifference curves, each farther from the origin than the last. What does a curve farther from the origin represent?The Shape of Indifference Curves and the Marginal Rate of Substitution
- How it worksHow does a diminishing willingness to trade one good for another bow an indifference curve inward toward the origin?
- Worked exampleFind the marginal rate of substitution when giving up 2 slices of pizza buys exactly 1 more soda.
- How it worksHow does the marginal rate of substitution show up as the slope at a single point on an indifference curve?
- Common mistakeWhy isn't the marginal rate of substitution the same number at every point along one indifference curve?
Your turn1 of 2
A consumer gives up 5 units of good Y to get 2 more units of good X, staying equally satisfied. What is her marginal rate of substitution of Y for X, in units of Y per unit of X?Perfect Substitutes and Perfect Complements
- How it worksHow do straight-line indifference curves describe two goods that are perfect substitutes for each other?
- How it worksHow do right-angle indifference curves describe two goods like left shoes and right shoes that are perfect complements?
- Going furtherWhat happens to the optimal bundle of perfect complements when the price of only one of them rises?
Your turn1 of 2
A consumer views a red pen and a blue pen as completely interchangeable, always willing to trade one for the other at a constant one-to-one rate. What shape do her indifference curves for red and blue pens take?Utility Maximization and the Tangency Condition
- How it worksHow does the tangency between the budget line and the highest reachable indifference curve mark the optimal bundle?
- Worked exampleFind the optimal bundle of two goods priced at 4 dollars and 2 dollars with 40 dollars of income when MRS = Qy / Qx.
- Common mistakeWhy doesn't a consumer just keep buying more of both goods once they've found a bundle they like?
- Going furtherWhat happens to the optimal bundle when a consumer's income rises but both prices stay fixed?
Your turn1 of 2
A consumer has 96 dollars of income to split between two goods priced at 5 dollars and 5 dollars. Using the tangency condition MRS = Qy divided by Qx, what is her optimal quantity of the first good?Deriving the Demand Curve from Consumer Choice
- How it worksHow does pivoting the budget line at each new price generate a new optimal bundle for that price?
- How it worksHow does plotting each price against its optimal quantity of one good build the demand curve from scratch?
- Worked exampleFind two points on a demand curve for a good priced at 2 dollars and then 4 dollars from a consumer's optimal bundles.
- Ties togetherHow does this demand curve built from indifference curves match the same downward-sloping demand curve seen earlier?
Your turn1 of 2
A consumer with 88 dollars of income splits spending evenly between two goods whenever MRS = Qy divided by Qx. At a price of 3 dollars for the first good, how many more units does she buy than at a higher price of 8 dollars?Decomposing the Income and Substitution Effects
- How it worksHow does the substitution effect slide a consumer along the same indifference curve toward the good that got cheaper?
- How it worksHow does the income effect shift a consumer to a new, higher indifference curve once their purchasing power rises?
- Worked exampleFind the substitution and income effects when a price falls from 4 dollars to 2 dollars and quantity rises from 10 to 16 units.
- Common mistakeWhy isn't the entire increase in quantity bought after a price drop just called the substitution effect?
- Going furtherWhat happens to the size of the income effect when a good takes up a much larger share of a consumer's budget?
Your turn1 of 2
A price falls from 6 dollars to 2 dollars, and the quantity bought rises from 12 to 21 units in total. If the substitution effect alone accounts for 0.28 of those extra units, how many units does the income effect account for?Corner Solutions and When Tangency Fails
- How it worksHow does an optimal bundle land on an axis instead of at an interior tangency when preferences are extreme enough?
- How it worksHow do perfect substitutes with very different prices push a consumer to buy only the cheaper one?
- Going furtherWhat happens to a corner solution once the price of the good being bought exclusively starts to rise?
Your turn1 of 2
A consumer's optimal bundle involves buying zero units of one of the two goods and spending her entire income on the other. What does this tell you about where her chosen bundle sits on her budget line?Normal, Inferior, and Giffen Goods
- How it worksHow do the income and substitution effects both push in the same direction for a normal good?
- How it worksHow does the income effect for an inferior good pull against the substitution effect instead of joining it?
- Common mistakeWhy doesn't every good become more attractive to buy once a consumer's income goes up?
- Going furtherWhat happens to the demand curve in the rare Giffen case where the income effect overwhelms the substitution effect?
Your turn1 of 2
A family's income rises, and they respond by buying less ramen and more steak. What does this reveal about ramen for this family?The Income-Consumption Curve and the Engel Curve
- How it worksHow does connecting the optimal bundles at every income level trace out the income-consumption curve?
- Worked exampleFind two points on an Engel curve when a consumer buys 5 units of a good at 20000 dollars of income and 8 units at 30000 dollars.
- Ties togetherHow does the income-consumption curve relate to whether a good counts as normal or inferior?
Your turn1 of 2
At an income of 23482 dollars a consumer buys 8 units of a good, and at 32543 dollars she buys 11 units. What is the income elasticity of demand between these two income levels, using percentage change in quantity over percentage change in income?