Demand Curve: The relationship between the price charged for a good and the consumer's desired quantity of the good.

Optimization Condition: MRS = MRT

-S/C = -P_C/P_S = -2/4 = -1/2
→ S = C/2 ... (Equation 1)

Budget Constraint:

24 = 4S + 2C
Substitute (1): 24 = 4(C/2) + 2C = 4C
→ C* = 6, S* = 3

Figure 4-1: Deriving the Demand Curve from Utility Maximization

Key Insight: The demand curve is derived by optimizing utility at different prices and finding which quantity you want at each price.

"Great point. Someone noticed. That as we varied the price of cookies, the number of slices of pizza did not change. That is not a general law. That is a specific feature of this utility function."

This is called a flat cross-price consumption curve — a special property of this particular utility function that makes calculations simpler.

ε = (ΔQ/Q) / (ΔP/P) ≈ (dQ/dP) × (P/Q)

"How responsive is demand to price changes?"

"Here's the key feature that differentiates elasticity. It's substitutability. Goods with no substitutes are not elastic. Goods with lots of substitutes are very elastic."

Student: "Gas?"

Gruber: "Gas would be somewhat inelastic because you got to get to work. On the other hand, there's a bus, there's your bike. You could walk, you could buy a new car. So it's not perfectly inelastic."

Student: "Insulin?"

Gruber: "Insulin is the classic example we use. There's no substitute. When you're having diabetic trauma for insulin, you will not say, 'it's $1 more, I'm just going to die.'"

Key: Price ratio unchanged → MRS = MRT condition unchanged

Budget line shifts parallel (not pivots)

Figure 4-4: Generating an Engel Curve

Definition: The relationship between income and quantity demanded

γ = (ΔQ/Q) / (ΔY/Y) ≈ (dQ/dY) × (Y/Q)

Income Elasticity of Demand

"Gamma is much more interesting than epsilon. Epsilon, some negative number, 0 to minus infinity. Gamma can have a much larger range."

"Ramen is the example. Ramen is the ultimate inferior good. No one wants to eat ramen. I realize there's fancy ramen restaurants, but nobody should go there."

"People eat ramen because it's cheap. As you get richer, you consume less ramen."

"Rent is the perfect example. Richer people have nicer apartments than poorer people, but richer people spend a smaller share of their budget on apartments than do poorer people."

"When a price changes, two things happen simultaneously. You may not realize it, but actually when a price changes, two things happen."

"When a price changes, two things happen. Goods become differentially attractive and you're richer or poorer. And both things drive your response to that price change."

Definition: Change in quantity holding utility constant

ΔQ|_Ū

Figure 4-5: Income and Substitution Effects for a Normal Good

"We're showing you the change in quantity you get at a constant utility. How do we keep utility constant? We stay on the same indifference curve."

Mathematical Proof:

1. At tangency: MU_C/MU_S = P_C/P_S
2. P_C/P_S went up (cookies more expensive)
3. MU_C/MU_S must go up to maintain equality
4. To raise MU_C → consume fewer cookies (diminishing MU!)
5. To lower MU_S → consume more pizza

Conclusion: Price↑ → Substitution effect is always negative

Why are you "effectively poorer"?

"Your income itself hasn't fallen, but your resources have, what you can buy with that income has fallen. You're effectively poor."

Student: "Your opportunity set has been constricted."

Gruber: "Your opportunity set has been constricted."

"Figure 4.6 is no longer pizza and cookies. Figure 4.6 is now steak and potatoes. Because pizza and cookies are both normal goods."

"Potatoes is the classic inferior good. Poor people, especially back in the day, used to have to eat potatoes because they were cheap to grow and very filling."

Figure 4-6: Income and Substitution Effects for an Inferior Good (Potatoes)

"The income effect goes the other way because potatoes are an inferior good. In other words, now that you're so poor, now potatoes are so expensive, you don't have enough money for steak anymore. So you got to have more potatoes. It's ironic, right?"

A Giffen good is an inferior good where the income effect dominates the substitution effect, resulting in an upward-sloping demand curve.

Price↑ → Demand↑ (violates law of demand!)

"I like the name Giffen because it rhymes with Griffin. And Griffins are imaginary. Giffen goods are also largely imaginary. It's a great theoretical concept, but they don't really exist."

Claim: During the potato blight, potato prices rose but per capita potato consumption rose. Therefore, potatoes are a Giffen good!

Gruber's Rebuttal:

"Here's what they got wrong. Here's where empirical economics is fun. They miss the fact that what other effect did the potato blight have? It chased all the people who could afford it out of Ireland. The only people who were left were super poor."

"So yeah, on average, potatoes per person went up. It's a Giffen good. What you're missing is the capitas are different. Each person needs more potatoes. It's just the non-potato eaters left."

Student: "A Veblen good?"

Gruber: "A Veblen good is a totally different concept. That's the concept that basically you want more when the price is up because you care about your social standing. But that's a behavioral economics thing. We'll come back to that type of behavior. It's not a standard economics effect."

"I'll tell you why we care in about six lectures. Because it turns out when you make your decisions about how hard you're going to work or how much you're going to save, income substitution effects are going to start to work against each other."