Lecture 4: From Indifference Curves to Demand

Learning Goals

By the end of class, you should be able to:

• Link indifference curves to marginal willingness to pay
• Understand how changes in price affect marginal willingness to pay
• Derive the demand curve from marginal willingness to pay/individual demand
• Define the “law of demand”
• Understand how the income/substitution effects in indifference curves are demand shifters
• Calculate and use the price elasticity of demand

From indifference curves to demand curves

• Indifference curves describe preferences
• But we cannot measure preferences directly
• Instead we can measure what someone is willing to pay for a good
• We can also measure how much of a good was sold at a given price (quantity demanded)
• Today: how one maps into the other

Preferences are about X vs. Y

• Each point is a bundle of goods
• Indifference curves show bundles that are equally good
• Their slope tells us how willing you are to trade one good for another

Indifference Curves give us Willingness to Pay

• At your chosen bundle, you face a tradeoff:

  “How much of one good would I give up for one more of another good?”

That tradeoff is your willingness to pay for the good.

We can measure it in units of the other good, or in dollars.

Prices determine the chosen bundle

A demand curve (Price: p, Quantity: q)

\(q = 100 - 2*p\) Price though often graphed as: \(p = (100 - q)/2\)

Individual vs market demand

• Everything so far works for one person
• People can have different preferences and incomes
• Market demand sums the individual demands at each price to get total quantity demanded

Law of Demand: Negative slope

As price rises:

• Budget lines get steeper
• Chosen bundles shift
• Willingness to pay falls

Lower prices include more units and more buyers.

What shifts demand?

Don’t memorize – think preferences.

• Tastes change → indifference curves change
• Income changes → reachable bundles change
• Prices of other goods change → tradeoffs change
  • If the two goods are “substitutes” (e.g. Coke and Pepsi), a price increase of one will increase the demand for the other
  • If the two goods are “complements” (e.g. Peanut Butter and Jelly), a price increase of one will decrease the demand for the other

Anything that shifts the optimal bundle in the indifference curve picture will shift the demand curve.

Demand vs. quantity demanded

Comprehension check: Do changes in the price of a good “shift” its demand curve, or just move you along it?

Demand is often drawn as a straight line

• It summarizes willingness to pay cleanly
• It’s a good approximation over small ranges
• It makes changes easy to interpret

Straight lines are a tool, not a claim about reality.

Quantifying responsiveness to price changes

• Say demand is given by \(q = 100 - 2*p\)
• How much does a 1 dollar change in price change quantity demanded?

Elasticity = sensitivity

Elasticity asks:

By what percentage does quantity change when price changes by 1%?”

While slope measures unit changes, elasticity measures percent changes—making it easier to compare across goods and prices.

Formula:

\[ \varepsilon = \frac{\% \text{change in quantity demanded}}{\% \text{change in price}} = \frac{\Delta q/q}{\Delta p/p} \]

Elasticities are huge in economics and policymaking – they’re usually what economists actually estimate.

Calculating the change in quantity demanded/price

Price increase: 10 dollars to 11 dollars, quantity demanded decreases: 100 to 90. What is the elasticity?

Elastic vs. inelastic

• Not all goods are equally “elastic”

• Real-world examples:
  • Elastic: Restaurant meals, luxury items (easy to cut back).
  • Inelastic: Insulin, gasoline (hard to cut back when prices rise).

Determinants of elasticity

What do you think determines the elasticity of demand for a good?

How do we use elasticity?

What can elasticity tell us about the effect of a new tax on the quantity of a good demanded?

A good has an elasticity of -15, what will a 1 percent tax on it do to the quantity demanded?

Addiction: Sin taxes vs. ban

Governments often debate whether to tax or ban harmful goods.

• Cigarettes
• Alcohol
• Marijuana
• Opioids

Why?

• To reduce use and harm
• To raise revenue to offset social costs

Elasticity of demand explains whether taxes or bans are more effective.

Cigarettes: taxes reduce use and raise revenue

What policymakers learn from cigarettes

Because demand is inelastic:

• Taxes reduce smoking gradually
• Taxes raise substantial revenue
• Heavy users pay the most tax

This is why cigarette taxes are widely used worldwide.

Elasticity adds a quantitative dimension to an ethical debate.

Alcohol: similar, but not identical

Alcohol demand is also inelastic (Ruhm et al. 2012), but:

• More substitutes than cigarettes
• Less addictive for many users

Elasticity differs by:

• Type (beer vs spirits)
• Group (youth vs adults)
• Result: Taxes reduce drinking
• Effects are stronger for binge drinking and youth

Marijuana legalization: prices fell, use rose

Legalization also changed prices (Miller and Seo 2021). After legalization:

• Production costs fell
• Legal competition increased
• Prices dropped

Use increased — especially among adults.

Marijuana demand is more elastic than cigarette demand

• Lower prices \(\rightarrow\) noticeable increase in use
• Taxes can raise revenue
• But high taxes push consumers back to illegal markets
• Elastic demand limits how high taxes can go.

Partially explains why marijuana policy is so different from cigarette policy.

Opioids: when prices barely matter

The opioid crisis

Because demand is extremely inelastic:

• Taxes don’t meaningfully reduce use
• Supply restrictions can increase harm
• Users substitute toward fentanyl or unsafe sources

Policy implication: Treatment and harm reduction dominate taxation.

Elasticity tells us what tools will fail

Big takeaway

Elasticity tells policymakers whether higher prices change behavior or mainly raise money — or do neither.

So economists and policymakers care about it a ton

One framework, four outcomes

Same policy tool. Different outcomes.

Looking ahead

• Establish theory of a firm and supply curve
• Think about market equilibria and efficiency
• Consider different market structures
• Consider market failures and policy interventions