Christopher Makler
Stanford University Department of Economics
Econ 50: Lecture 8
Part 1: Brief Overview
Part 2: Worked Examples
Review of what demand is
Demand functions
Demand curves
Complements and Substitutes
Normal and Inferior Goods
Cobb-Douglas
Perfect Complements
Perfect Substitutes
Quadratic Quasilinear
Section: Three goods!
Remember what you learned about demand and demand curves in Econ 1 / high school:
"The demand curve shows the quantity demanded of a good at different prices"
DEMAND CURVE FOR GOOD 1
"Good 1 - Good 2 Space"
"Quantity-Price Space for Good 1"
"The demand curve represents the marginal benefit of an additional unit,
or alternatively the marginal willingness to pay for another unit"
Let's look at the FOC with respect to good 1:
Solve for \(p_1\):
What is the effect of a 1% change
in the price of good 1 \((p_1)\) on the quantity demanded of good 1 \((x_1^*)\)?
no change
perfectly inelastic
less than 1%
inelastic
exactly 1%
unit elastic
more than 1%
elastic
What is the effect of an increase
in the price of good 2 \((p_2)\) on the quantity demanded of good 1 \((x_1^*)\)?
no change
independent
decrease
complements
increase
substitutes
When the price of one good goes up, demand for the other increases.
When the price of one good goes up, demand for the other decreases.
What is the effect of an increase
in income \((m)\) on the quantity demanded of good 1 \((x_1^*)\)?
decrease
good 1 is inferior
increase
good 1 is normal
When your income goes up,
demand for the good increases.
When your income goes up,
demand for the good decreases.
Think about how the behavior described by the demand function translates into the overall shape of the demand curve:
The reason we use different utility functions is because people's relationship with prices depends on the nature of their preferences.
Quantity of Good 1 \((x_1)\)
Price of Good 1 \((p_1)\)
All demand curves must be in this region
Quantity bought at each price if you spent all your money on good 1