Christopher Makler
Stanford University Department of Economics
Econ 50: Lecture 11
Part 1:
Comparative Statics
Part 2:
Functional Forms and Behavior
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BL1
We will be solving for the optimal bundle
as a function of income and prices:
The solutions to this problem will be called the demand functions. We have to think about how the optimal bundle will change when \(p_1,p_2,m\) change.
BL2
Plug tangency condition back into constraint:
Tangency Condition: \(MRS = p_1/p_2\)
OPTIMAL BUNDLE
DEMAND FUNCTIONS
(optimization)
(comparative statics)
Remember what you learned about demand and demand curves in Econ 1 / high school:
...its own price changes?
Movement along the demand curve
...the price of another good changes?
Complements
Substitutes
Independent Goods
How does the quantity demanded of a good change when...
...income changes?
Normal goods
Inferior goods
Giffen goods
(possible) shift of the demand curve
...its own price changes?
Movement along the demand curve
How does the quantity demanded of a good change when...
The demand curve for a good
shows the quantity demanded of that good
as a function of its own price
holding all other factors constant
(ceteris paribus)
The price offer curve shows how the optimal bundle changes in good 1-good 2 space as the price of one good changes.
DEMAND CURVE FOR GOOD 1
"Good 1 - Good 2 Space"
"Quantity-Price Space for Good 1"
PRICE OFFER CURVE
...the price of another good changes?
How does the quantity demanded of a good change when...
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.
Demand not related
Complements: \(p_2 \uparrow \Rightarrow x_1^* \downarrow\)
What happens to the quantity of good 1 demanded when the price of good 2 increases?
Substitutes: \(p_2 \uparrow \Rightarrow x_1^* \uparrow\)
COMPLEMENTS:
UPWARD-SLOPING
PRICE OFFER CURVE
SUBSTITUTES:
DOWNWARD-SLOPING
PRICE OFFER CURVE
How does the quantity demanded of a good change when...
...income changes?
When your income goes up,
demand for the good increases.
When your income goes up,
demand for the good decreases.
The income offer curve shows how the optimal bundle changes in good 1-good 2 space as income changes.
Good 1 normal: \(m \uparrow \Rightarrow x_1^* \uparrow\)
What happens to the quantity of good 1 demanded when the income increases?
Good 1 inferior: \(m \uparrow \Rightarrow x_1^* \downarrow\)
BOTH NORMAL GOODS:
UPWARD-SLOPING
INCOME OFFER CURVE
ONE GOOD INFERIOR:
DOWNWARD-SLOPING
PRICE OFFER CURVE
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