Chapter 6 — Consumer Choices
How do people decide what to buy? Economics models this through utility — a measure of satisfaction. Consumers aim to maximize their total utility given a limited budget, and the key insight is that each additional unit of a good typically brings less additional satisfaction than the one before it. This chapter builds the logical foundations of the demand curve from the ground up.
Table of Contents
1 — Consumption Choices
- 1.1 Budget Constraints
- 1.2 Total Utility and Diminishing Marginal Utility
- 1.3 Choosing to Maximize Utility — Step by Step
- 1.4 Marginal Utility per Dollar
- 1.5 The Utility-Maximizing Rule
2 — How Changes in Income and Prices Affect Choices
- 2.1 How Income Changes Affect Choices
- 2.2 How Price Changes Affect Choices
- 2.3 Substitution Effect and Income Effect
- 2.4 Foundations of the Demand Curve
3 — Behavioral Economics
4 — Advanced: Indifference Curves & Optimization
Glossary — Key Terms at a Glance
| Term | Meaning |
|---|---|
| Utility | A measure of satisfaction or happiness from consumption |
| Total Utility | The overall satisfaction from consuming a given quantity of a good |
| Marginal Utility (MU) | The additional utility from consuming one more unit of a good |
| Diminishing Marginal Utility | Each successive unit consumed adds less to total utility |
| Budget Constraint | The set of all affordable combinations of goods given income and prices |
| Consumer Equilibrium | The utility-maximizing point where MU₁/P₁ = MU₂/P₂ |
| Marginal Utility per Dollar | MU ÷ Price — measures “bang for the buck” |
| Normal Good | Demand increases when income rises |
| Inferior Good | Demand decreases when income rises |
| Substitution Effect | Change in consumption due to a good becoming relatively cheaper/more expensive |
| Income Effect | Change in consumption due to purchasing power changing when price changes |
| Behavioral Economics | Branch integrating psychology into economic decision-making |
| Loss Aversion | People feel losses ~2.25× more strongly than equivalent gains |
| Fungible | Dollars are interchangeable — $1 found = $1 earned (in theory) |
| Mental Accounting | Treating money differently depending on its source or intended use |
1 — Consumption Choices
1.1 Budget Constraints
A budget constraint (or budget line) shows all possible combinations of two goods that a consumer can afford given their income and the prices of the goods.
Example: José has $56 to spend. T-shirts cost $14, movies cost $7.
- If he spends everything on movies: $56 ÷ $7 = 8 movies (vertical intercept)
- If he spends everything on T-shirts: $56 ÷ $14 = 4 T-shirts (horizontal intercept)
- Slope of budget line = −(Price of T-shirts / Price of movies) = −$14/$7 = −2
The slope tells us the opportunity cost: José must give up 2 movies to afford 1 more T-shirt.
Budget Constraint Equation:
\[P_1 Q_1 + P_2 Q_2 = I\] \[14T + 7M = 56\]Solving for M: $M = 8 - 2T$ (slope = −2, intercept = 8)
Diagram — Budget Constraint:
Key Properties of the Budget Constraint:
- Points on the line: spend all income (affordable, no waste)
- Points inside the line: affordable but don’t use all income
- Points outside the line: unaffordable
- The slope = −(P₁/P₂) = the rate at which one good trades for the other
1.2 Total Utility and Diminishing Marginal Utility
Total Utility = the overall satisfaction from consuming a given quantity.
Marginal Utility (MU) = the additional utility from one more unit:
\[MU = \frac{\Delta \text{Total Utility}}{\Delta \text{Quantity}} = TU_n - TU_{n-1}\]José’s Utility from T-Shirts and Movies:
| T-Shirts | Total Utility | Marginal Utility | Movies | Total Utility | Marginal Utility | |
|---|---|---|---|---|---|---|
| 1 | 22 | 22 | 1 | 16 | 16 | |
| 2 | 43 | 21 | 2 | 31 | 15 | |
| 3 | 63 | 20 | 3 | 45 | 14 | |
| 4 | 81 | 18 | 4 | 58 | 13 | |
| 5 | 97 | 16 | 5 | 70 | 12 | |
| 6 | 111 | 14 | 6 | 81 | 11 | |
| 7 | 123 | 12 | 7 | 91 | 10 | |
| 8 | 133 | 10 | 8 | 100 | 9 |
Notice: Total utility always rises, but marginal utility falls with each additional unit. The first T-shirt (MU = 22) gives more satisfaction than the fourth (MU = 18).
Law of Diminishing Marginal Utility: Each additional unit of a good consumed provides less additional utility than the previous unit. This is a specific case of the general law of diminishing returns.
Intuition: Your first slice of pizza is amazing. Your fifth slice is just okay. Your eighth slice may make you feel sick.
Diagram — Total Utility and Marginal Utility:
Utils are subjective. We cannot compare utils between people. If Alice gets 20 utils from coffee and Bob gets 10 utils, we can NOT say Alice enjoys coffee more — they use different personal scales. What matters is that each individual can rank their own preferences.
1.3 Choosing to Maximize Utility — Step by Step
Method 1: Add Up Total Utility for Each Affordable Combination
| Point | T-Shirts | Movies | Total Utility |
|---|---|---|---|
| P | 4 | 0 | 81 + 0 = 81 |
| Q | 3 | 2 | 63 + 31 = 94 |
| R | 2 | 4 | 43 + 58 = 101 |
| S | 1 | 6 | 22 + 81 = 103 ← Maximum! |
| T | 0 | 8 | 0 + 100 = 100 |
José maximizes utility at point S: 1 T-shirt + 6 movies = 103 utils.
Method 2: Compare Marginal Gains and Losses Step by Step
Start at any point and ask: “Would I gain more utility by trading one good for the other?”
| Move | Give Up | Lose | Get | Gain | Net | Better? |
|---|---|---|---|---|---|---|
| P → Q | 1 T-shirt | 18 utils | 2 movies | 31 utils | +13 | ✅ |
| Q → R | 1 T-shirt | 20 utils | 2 movies | 27 utils | +7 | ✅ |
| R → S | 1 T-shirt | 21 utils | 2 movies | 23 utils | +2 | ✅ |
| S → T | 1 T-shirt | 22 utils | 2 movies | 19 utils | −3 | ❌ Stop! |
Again, S is the optimal point. Moving beyond S would reduce total utility.
1.4 Marginal Utility per Dollar
Marginal Utility per Dollar = MU ÷ Price
This measures the “bang for the buck” — how much additional satisfaction you get per dollar spent.
Decision Rule: Always purchase the next item that gives the highest marginal utility per dollar, until the budget is exhausted.
| T-Shirts | MU | MU/$ (÷$14) | Movies | MU | MU/$ (÷$7) | |
|---|---|---|---|---|---|---|
| 1st | 22 | 1.57 | 1st | 16 | 2.29 ← Buy first | |
| 2nd | 21 | 1.50 | 2nd | 15 | 2.14 ← Buy second | |
| 3rd | 20 | 1.43 | 3rd | 14 | 2.00 ← Buy third | |
| 4th | 18 | 1.29 | 4th | 13 | 1.86 ← Buy fourth | |
| 5th | 16 | 1.14 | 5th | 12 | 1.71 ← Buy fifth | |
| 6th | 14 | 1.00 | 6th | 11 | 1.57 ← Tie with T-shirt 1! |
José buys movies 1–6 first (highest MU/$), then the first T-shirt (tied at 1.57). Total spent: 6 × $7 + 1 × $14 = $56. Budget exhausted. → S (1 T-shirt, 6 movies).
1.5 The Utility-Maximizing Rule
At the consumer equilibrium (utility-maximizing point), the marginal utility per dollar is equal across all goods:
\[\frac{MU_1}{P_1} = \frac{MU_2}{P_2}\]Equivalently, the ratio of marginal utilities equals the ratio of prices:
\[\frac{MU_1}{MU_2} = \frac{P_1}{P_2}\]At point S: MU of T-shirt₁ = 22, MU of Movie₆ = 11
\[\frac{22}{14} = \frac{11}{7} = 1.57 \quad ✓\]Why must this hold? If MU₁/P₁ > MU₂/P₂, then good 1 gives more satisfaction per dollar. You should buy more of good 1 and less of good 2. As you do, diminishing marginal utility will lower MU₁ and raise MU₂ until the ratios equalize.
Do We Need to Measure Utils? No! The key assumption is only that individuals can rank their preferences — “I prefer A to B.” We don’t need a “utilimometer.” The step-by-step marginal comparison process mirrors how people actually make decisions: “Would I be happier with a little more of this and a little less of that?”
2 — How Changes in Income and Prices Affect Choices
2.1 How Income Changes Affect Choices
When income rises, the budget constraint shifts outward (parallel shift — prices haven’t changed, only the affordable set has expanded).
| If the good is… | Effect of income increase | Example |
|---|---|---|
| Normal good | Demand increases | Steak, vacations, new cars |
| Inferior good | Demand decreases | Instant noodles, used cars, bus tickets |
Most goods are normal goods — when income rises, people buy more of them.
Kimberly’s Choices: She spends $1,000/year on concert tickets ($50 each) and overnight B&B stays ($200/night). Her optimal choice: 8 concerts + 3 overnight stays.
Income doubles to $2,000. What happens?
- Both normal goods: She buys more of both (e.g., 20 concerts + 5 stays) → choice moves to upper-right
- Stays are inferior: She buys fewer stays but many more concerts → choice moves to upper-left
- Concerts are inferior: She buys fewer concerts but more stays → choice moves to lower-right
The answer depends on her personal preferences. For most goods, both increase (normal goods).
2.2 How Price Changes Affect Choices
When the price of one good rises, the budget constraint rotates inward from the axis of the other good (which hasn’t changed price). The consumer can now afford fewer units of the more expensive good.
Typical response: Buy less of the good whose price rose. But the consumer may also adjust purchases of other goods.
Don’t assume a price change only affects one market! When energy prices soar, people don’t just use less energy — they also cut back on dining out, vacations, and other discretionary spending. The entire budget is interconnected.
2.3 Substitution Effect and Income Effect
When a price changes, two effects operate simultaneously:
| Effect | Mechanism | Direction |
|---|---|---|
| Substitution Effect | The good is now relatively more expensive compared to alternatives → consume less of it and more of substitutes | Always reduces quantity of the more expensive good |
| Income Effect | Higher price reduces purchasing power (even though nominal income hasn’t changed) → effectively poorer | For normal goods: reduces quantity demanded. For inferior goods: could increase it |
For normal goods: Both effects work in the same direction → quantity demanded falls when price rises (law of demand always holds).
For inferior goods: Effects work in opposite directions. In theory, the income effect could dominate (Giffen good), but this is extremely rare.
2.4 Foundations of the Demand Curve
The demand curve is built from utility maximization.
As the price of housing rises from P₀ → P₁ → P₂ → P₃, the budget constraint rotates inward. At each new constraint, the consumer re-optimizes, choosing the combination that maximizes utility. This traces out the relationship:
- P₀ → Q₀ (high quantity)
- P₁ → Q₁ (lower quantity)
- P₂ → Q₂ (even lower)
- P₃ → Q₃ (lowest)
Plot price vs. quantity demanded → you get the demand curve!
The downward-sloping demand curve is not just an empirical observation — it’s a logical consequence of consumers maximizing utility subject to budget constraints.
3 — Behavioral Economics
3.1 Loss Aversion
Loss aversion means people feel the pain of a loss about 2.25 times more intensely than the pleasure of an equivalent gain (Kahneman & Tversky, 1979).
- Lost $10 today and found $10? Traditional economics says you should feel neutral (net $0). But most people feel net negative — the loss hurts more than the gain helps.
- Investment implication: People tend to sell winning stocks too early (to “lock in” gains) and hold losing stocks too long (to avoid realizing losses). This is predictable but “irrational” by traditional standards.
3.2 Mental Accounting and Fungibility
Traditional economics treats all dollars as fungible — interchangeable and equal in value regardless of source.
Mental accounting is the behavioral tendency to treat dollars differently based on context:
Examples of Mental Accounting:
-
Found money vs. earned money: You might spend $25 found on the street frivolously (“mad money”), but you’d never waste $25 earned from 3 hours of work — even though they’re identical in value.
-
Credit card debt + savings account: Someone carries $1,000 in credit card debt (15% interest = −$150/year) while keeping $2,000 in savings (2% interest = +$40/year). Net loss: $110/year. The “rational” move: pay off the debt. But people resist because draining savings feels like a bigger loss than the credit card interest.
3.3 Nudges and Self-Control
People often lack perfect self-control. They:
- Buy cigarettes by the pack (not the cheaper carton) to limit smoking
- Overpay taxes so they get a refund (forced savings, even though it’s giving the government a free loan)
- Procrastinate on retirement enrollment even when it’s clearly beneficial
Nudges are policy designs that guide people toward better decisions without mandating them:
- Opt-out retirement plans: Employees are automatically enrolled in 401(k) plans unless they actively choose not to. Result: nearly 100% enrollment (vs. ~80% with opt-in).
- The monetary incentives haven’t changed — only the default option. Yet behavior changes dramatically.
Which view is right? Both traditional and behavioral approaches have value:
- Traditional economics provides powerful, clean models for prediction
- Behavioral economics explains predictable “irrational” behaviors and designs better policies
- The key insight: context matters. The same dollar amount can mean different things in different situations.
4 — Advanced: Indifference Curves & Optimization
4.1 Indifference Curves and the MRS
An indifference curve connects all bundles of goods that give the consumer the same level of utility. The consumer is “indifferent” between any two points on the same curve.
Properties of Indifference Curves:
- Downward-sloping — to stay at the same utility, getting more of one good requires giving up some of the other
- Higher curves = higher utility — bundles farther from the origin are preferred
- Cannot cross — if two curves crossed at point A, then A is on both curves, implying two different utility levels for the same bundle (contradiction)
- Convex to the origin — reflects diminishing MRS (you value what you have less of more)
Marginal Rate of Substitution (MRS):
\[MRS = -\frac{\Delta Q_2}{\Delta Q_1} = \frac{MU_1}{MU_2}\]The MRS is the rate at which the consumer is willing to trade good 2 for good 1 while staying equally happy. It equals the slope of the indifference curve (in absolute value).
At the optimum: The MRS equals the price ratio:
\[MRS = \frac{MU_1}{MU_2} = \frac{P_1}{P_2}\]This is equivalent to the utility-maximizing rule $\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$.
Diagram — Optimal Consumer Choice (Indifference Curve Tangent to Budget Line):
Worked Example — Cobb-Douglas Utility:
Utility function: $U(x,y) = x^{0.5} \cdot y^{0.5}$. Prices: $P_x = 4$, $P_y = 2$. Income $I = 120$.
Step 1: Find MRS: \(MU_x = 0.5 \cdot x^{-0.5} \cdot y^{0.5} = \frac{0.5y}{x^{0.5} \cdot y^{0.5}} \cdot \frac{y^{0.5}}{1}\)
Simplified: $MU_x = \frac{y}{2x}$, $MU_y = \frac{x}{2y}$
\[MRS = \frac{MU_x}{MU_y} = \frac{y/2x}{x/2y} = \frac{y}{x}\]Step 2: Set MRS = price ratio: $\frac{y}{x} = \frac{P_x}{P_y} = \frac{4}{2} = 2$ → $y = 2x$
Step 3: Substitute into budget constraint: $4x + 2(2x) = 120$ → $8x = 120$ → $x^* = 15$, $y^* = 30$
Step 4: Utility = $15^{0.5} \times 30^{0.5} = \sqrt{450} \approx 21.2$
Result: Consumer buys 15 units of x and 30 units of y, spending $60 on each good. With Cobb-Douglas utility, the consumer always spends equal income shares on each good (when exponents are equal).
4.2 Lagrangian Optimization
For problems with more than two goods, or for rigorous derivations, we use constrained optimization via the Lagrangian method:
\[\mathcal{L} = U(x, y) + \lambda (I - P_x x - P_y y)\]First-order conditions (FOCs):
\[\frac{\partial \mathcal{L}}{\partial x} = MU_x - \lambda P_x = 0 \implies MU_x = \lambda P_x\] \[\frac{\partial \mathcal{L}}{\partial y} = MU_y - \lambda P_y = 0 \implies MU_y = \lambda P_y\] \[\frac{\partial \mathcal{L}}{\partial \lambda} = I - P_x x - P_y y = 0\]Dividing the first two FOCs:
\[\frac{MU_x}{MU_y} = \frac{P_x}{P_y} \quad \text{(the familiar tangency condition)}\]The Lagrange multiplier $\lambda$ represents the marginal utility of income — how much additional utility the consumer gains from one more dollar of budget.
Worked Example — Lagrangian with $U = x^{0.5} y^{0.5}$, $P_x = 4$, $P_y = 2$, $I = 120$:
\[\mathcal{L} = x^{0.5} y^{0.5} + \lambda(120 - 4x - 2y)\]FOC 1: $\frac{\partial \mathcal{L}}{\partial x} = 0.5 x^{-0.5} y^{0.5} - 4\lambda = 0$
FOC 2: $\frac{\partial \mathcal{L}}{\partial y} = 0.5 x^{0.5} y^{-0.5} - 2\lambda = 0$
From FOC 1: $\lambda = \frac{y^{0.5}}{8x^{0.5}}$. From FOC 2: $\lambda = \frac{x^{0.5}}{4y^{0.5}}$
Setting equal: $\frac{y^{0.5}}{8x^{0.5}} = \frac{x^{0.5}}{4y^{0.5}}$ → $4y = 8x$ → $y = 2x$
Budget: $4x + 2(2x) = 120$ → $x^* = 15$, $y^* = 30$ (confirms previous answer)
Shadow price: $\lambda = \frac{30^{0.5}}{8 \times 15^{0.5}} = \frac{\sqrt{30}}{8\sqrt{15}} = \frac{\sqrt{2}}{8} \approx 0.177$
Meaning: one additional dollar of income increases utility by ~0.177 utils.
Key Takeaways
| Section | Core Idea |
|---|---|
| 6.1 | Consumers maximize utility subject to a budget constraint. Marginal utility diminishes. The optimal choice occurs where MU₁/P₁ = MU₂/P₂ — equal “bang for the buck” across all goods. |
| 6.2 | Income increase → buy more of normal goods, less of inferior goods. Price increase → substitution effect (switch to cheaper alternatives) + income effect (reduced purchasing power). Together, they build the demand curve. |
| 6.3 | Behavioral economics: loss aversion (losses hurt 2.25× more), mental accounting (dollars aren’t treated as fungible), and nudges (changing defaults changes behavior without mandates). |
| 6.4 | Indifference curves show bundles of equal utility. Optimal choice occurs where IC is tangent to the budget line (MRS = price ratio). Lagrangian method provides rigorous constrained optimization. |
Practice Questions
Q1. José has $56. T-shirts cost $14, movies cost $7. At point S (1 T-shirt, 6 movies), MU of T-shirt = 22 and MU of 6th movie = 11. Verify that the utility-maximizing rule holds.
A1. MU₁/P₁ = 22/14 = 1.57. MU₂/P₂ = 11/7 = 1.57. Since 1.57 = 1.57, the ratios are equal. ✓ The last dollar spent on each good provides the same marginal utility, confirming this is the utility-maximizing point.
Q2. If José’s income rises from $56 to $70, how does the budget constraint change? If both goods are normal, what direction does his optimal point move?
A2. The budget constraint shifts outward (parallel). Horizontal intercept moves from 4 to 5 T-shirts ($70/$14). Vertical intercept moves from 8 to 10 movies ($70/$7). The slope stays −2 (prices unchanged). If both are normal goods, José buys more of both — his new optimal point is to the upper-right of S.
Q3. Explain why marginal utility diminishes. Give a real-world example.
A3. Each additional unit adds less satisfaction because the most valued use is fulfilled first. Example: The first glass of water when you’re thirsty is incredibly satisfying (high MU). The second is nice. By the fifth glass, you barely want it (low MU). Total utility still rises, but at a decreasing rate.
Q4. If MU of good A / Price of A > MU of good B / Price of B, what should the consumer do?
A4. Buy more of good A and less of good B. Good A provides more utility per dollar. As you consume more A, its MU falls (diminishing marginal utility). As you consume less B, its MU rises. Eventually, MU_A/P_A = MU_B/P_B and you’ve reached the optimum.
Q5. A 10% decrease in the price of ham causes you to buy more ham and less turkey. Is this the substitution effect, the income effect, or both?
A5. Buying more ham because it’s relatively cheaper than turkey is the substitution effect. If the price drop also makes you feel “richer” and you buy more food overall, that’s the income effect. Both operate simultaneously. The switch specifically from turkey to ham is primarily the substitution effect.
Q6. You lose a $20 bill on the way to dinner, but the restaurant gives you an unexpected $20 discount. Are you better off, worse off, or the same? How would a traditional economist vs. a behavioral economist answer?
A6. Traditional economist: You’re exactly the same — net change is $0. Behavioral economist: You likely feel negative because loss aversion means the $20 loss hurts about 2.25× more than the $20 discount pleases you. The net emotional experience is negative even though the financial outcome is neutral.
Q7. Your company switches from opt-in to opt-out retirement enrollment. Explain why this dramatically increases participation using behavioral economics.
A7. People procrastinate and feel overwhelmed by choices. With opt-in, the default is “not enrolled” — inertia keeps many out. With opt-out, the default is “enrolled” — the same inertia keeps people in. The financial incentives haven’t changed at all; only the default option changed. This is a “nudge” — it exploits the gap between intention and action.
Q8. Someone carries $3,000 in credit card debt at 18% APR while keeping $5,000 in a savings account at 1% APR. Calculate the net annual cost of this behavior and explain why someone would do it.
A8. Credit card interest: $3,000 × 18% = $540/year paid. Savings interest: $5,000 × 1% = $50/year earned. Net loss: $490/year. The rational move is to pay off the debt ($2,000 savings + $0 debt earns $20, saving $520). People resist because of mental accounting — they categorize savings as “untouchable safety net” and credit card debt as a separate category. They don’t treat the dollars as fungible.
Q9. Consumer spending data shows the average U.S. household spent ~$16,557 on housing (34% of spending) and ~$3,264 on food at home (7%). Why might housing have such a dominant budget share?
A9. Housing is a necessity with few substitutes and typically inelastic demand. People must have shelter regardless of price. The high budget share reflects both the high price of housing and its essential nature. When housing costs rise, consumers are forced to cut spending in other categories rather than forgo housing — demonstrating the interconnected nature of budget constraints.
Q10. Praxilla has 18 bronze coins. Poems cost 3 coins each and cucumbers cost 1 coin. MU of poems decreases by 3 per poem (30, 27, 24…). MU of cucumbers = 6 for each of the first three, 5 for the next three, 4 for the next three, etc. Find her utility-maximizing choice.
A10. We compare MU per coin: Poem₁ = 30/3 = 10; Cucumber₁₋₃ = 6/1 = 6; Poem₂ = 27/3 = 9; Cucumber₄₋₆ = 5/1 = 5; Poem₃ = 24/3 = 8; Cucumber₇₋₉ = 4/1 = 4. Working step by step: Buy Poem₁ (highest at 10), then Cucumbers 1-3 (all at 6 > Poem₂ at 9? No — Poem₂ at 9 is higher). Actually: Poem₁ (10, cost 3), Poem₂ (9, cost 3), Cucumbers 1-3 (6 each, cost 1 each), Poem₃ (8, cost 3), Cucumbers 4-6 (5 each, cost 1 each). Total: 3 poems (9 coins) + 9 cucumbers (9 coins) = 18 coins. At this point: MU per coin of Poem₄ = 21/3 = 7, MU per coin of next cucumber = 4/1 = 4. Poem₄ is better but costs 3 coins we don’t have. Optimal: 3 poems + 9 cucumbers.
Q11. Given $U(x,y) = x^{0.3} y^{0.7}$, $P_x = 6$, $P_y = 3$, $I = 180$. Find the optimal bundle.
A11. For Cobb-Douglas $U = x^a y^b$, the optimal shares are: spend fraction $\frac{a}{a+b}$ on x and $\frac{b}{a+b}$ on y. So: spend $\frac{0.3}{1.0} \times 180 = $54$ on x → $x^* = 54/6 = 9$. Spend $\frac{0.7}{1.0} \times 180 = $126$ on y → $y^* = 126/3 = 42$. Optimal: x = 9, y = 42.
Q12. Why do indifference curves never cross? Prove it by contradiction.
A12. Suppose IC₁ and IC₂ cross at point A. Pick point B on IC₁ (not on IC₂) and point C on IC₂ (not on IC₁) where IC₂ represents higher utility. Since A and B are on IC₁: $U(A) = U(B)$. Since A and C are on IC₂: $U(A) = U(C)$. By transitivity: $U(B) = U(C)$. But B is on the lower curve and C on the higher curve, so $U(C) > U(B)$ — contradiction. Therefore ICs cannot cross.
Q13. A consumer allocates $500/month between dining out ($25/meal) and streaming services ($15/month each). Their MU for the 8th meal is 50 utils, and MU for the 10th streaming service is 30 utils. Are they optimizing? If not, what should they do?
A13. MU/$ for meals = 50/25 = 2.0. MU/$ for streaming = 30/15 = 2.0. Since MU/$ is equal across both goods, the consumer IS optimizing. They shouldn’t change anything. Budget check: $25(8) + 15(10) = 200 + 150 = $350 < $500, so there’s unspent money — they should keep buying whichever good still has the highest MU/$ until the budget is exhausted or MU drops to zero.