Utility Theory
Learning Objectives
By the end of this page you will be able to:
- Define utility, total utility, and marginal utility, and distinguish cardinal from ordinal utility.
- Calculate marginal utility from a total utility schedule and identify the point of satiation.
- State the law of diminishing marginal utility and explain why it holds for most goods.
- Derive and apply the consumer equilibrium condition (equi-marginal principle) to allocate a budget across two goods.
- Explain consumer surplus, compute it in a simple example, and relate it to policy analysis.
- Identify the main limitations of utility theory as a model of real consumer behaviour.
Quick Answer
Utility theory is the branch of microeconomics that explains how consumers decide what to buy when they have limited income and goods have prices. It models consumption as a trade-off between the satisfaction (utility) a good provides and its cost, and shows that a rational consumer keeps buying a good only as long as the extra satisfaction from one more unit is worth the price. It matters because it is the foundation for the downward-sloping demand curve, for consumer surplus (used to measure the welfare cost of taxes and monopolies), and for arguments like progressive taxation and risk aversion. The two main variants are cardinal utility (satisfaction measured in numbers, called "utils") and ordinal utility (only rankings matter, used in indifference curve analysis).
Overview
Every day, consumers with a fixed income face the same underlying problem: prices are given, wants are unlimited, and money isn't. Utility theory is economics' answer to "how does a rational person solve this problem?" It starts from a simple idea — consuming goods and services gives people satisfaction, which economists call utility — and builds a set of tools to predict what a consumer will buy, how much, and how their choices change when prices or income change.
Historically, economists first tried to measure utility directly in numbers (the cardinal approach, associated with Alfred Marshall). Later economists (Hicks and Allen) showed you don't need to measure satisfaction in numbers at all — you only need to know whether a consumer prefers one bundle of goods to another (the ordinal approach). Modern microeconomics relies mostly on the ordinal approach through indifference curves, but the cardinal approach remains the easiest way to build intuition for concepts like diminishing marginal utility and consumer surplus, so most courses (and this page) start there.
Why does this matter beyond the exam? Utility theory explains why demand curves slope downward, why a rupee matters more to a poor household than a rich one (the basis for progressive taxation), why insurance and gambling both exist, and how economists measure the welfare gains and losses from taxes, subsidies, and market power.
Core Concepts
Cardinal vs. Ordinal Utility
Definition Cardinal utility assumes satisfaction can be measured in specific numerical units called "utils" (e.g., an apple gives 10 utils, a mango gives 15 utils). Ordinal utility assumes satisfaction cannot be measured in absolute numbers — a consumer can only rank bundles as "preferred," "less preferred," or "indifferent."
Explanation Under the cardinal approach, if apple = 10 utils and mango = 15 utils, we can say the mango gives exactly 5 more utils of satisfaction — a precise, comparable, addable quantity. Under the ordinal approach, we only know the consumer prefers the mango to the apple; we cannot say by "how much." This distinction matters because cardinal utility permits arithmetic (adding, subtracting utils across goods and people), while ordinal utility only permits ranking. Since real satisfaction cannot actually be measured with a ruler, modern theory prefers the more modest, ordinal claim.
| Cardinal Utility | Ordinal Utility | |
|---|---|---|
| Measurement | Assigns a specific number ("utils") to satisfaction | Ranks preferences without assigning numbers |
| Developed by | Marshall | Hicks, Allen |
| Assumption | Utility is measurable and comparable | Only the ranking matters |
| Used for | Law of diminishing marginal utility, consumer surplus | Indifference curve analysis |
Example Suppose a student says "watching a movie gives me 20 utils and reading a book gives me 12 utils" — that's cardinal utility (a claimed exact number). If the student instead says "I prefer the movie to the book, and the book to scrolling on the phone," that is ordinal utility — only the order is stated, not the size of the gap.
Real-World Example When a market research survey in India asks respondents to rate a masala-flavoured snack on a 1–10 "satisfaction score," it is (loosely) applying cardinal utility. When the same survey instead asks respondents to rank five flavours from most to least preferred, it is applying ordinal utility — closer to how economists model choice today because it avoids the (shaky) assumption that satisfaction can be measured like temperature.
Why It Matters The distinction decides which tools you can legitimately use. Cardinal utility gives you the law of diminishing marginal utility and consumer surplus directly. Ordinal utility is more realistic (nobody actually knows their utility in numbers) and underlies indifference curve analysis, which is the standard modern treatment of consumer choice — see Indifference Curves.
Common Misunderstanding Students often think cardinal utility has been "proven wrong" and should be ignored. It hasn't been proven wrong — it's just a stronger, less realistic assumption than ordinal utility. Economists still use cardinal-style reasoning (e.g., "marginal utility of income") in welfare economics and public finance because it is a useful simplification, even though it isn't literally measurable.
Total Utility and Marginal Utility
Definition Total Utility (TU) is the total satisfaction a consumer gets from consuming a given quantity of a good. Marginal Utility (MU) is the additional satisfaction gained from consuming one more unit of that good.
Explanation Marginal utility is calculated as:
MU = ΔTU / ΔQ
(the change in total utility divided by the change in quantity consumed). As long as MU is positive, each additional unit adds to total utility, so TU keeps rising — but typically at a slower and slower rate, because MU itself falls as consumption increases (see the law of diminishing marginal utility below). When MU hits zero, TU is at its maximum — the consumer is fully "satiated." If MU turns negative, TU actually starts to fall, because the extra unit creates discomfort rather than satisfaction.
Example: Consuming samosas
| Units consumed | Total Utility (utils) | Marginal Utility (utils) |
|---|---|---|
| 0 | 0 | — |
| 1 | 10 | 10 |
| 2 | 18 | 8 |
| 3 | 24 | 6 |
| 4 | 28 | 4 |
| 5 | 28 | 0 |
| 6 | 26 | -2 |
TU rises, peaks at 5 units (MU = 0), then falls when MU turns negative (the 6th samosa is unpleasant — perhaps the consumer now feels overfull).
Real-World Example Think of a cricket fan watching back-to-back IPL matches on a Sunday. The first match delivers huge enjoyment (high MU). The second match is still enjoyable but a bit less thrilling because the fan is already satisfied. By the fourth or fifth consecutive match, the fan is tired, distracted, and the "extra" match may even feel like a chore rather than entertainment — MU has fallen to zero or turned negative, even though total hours of "entertainment consumed" keep rising.
Why It Matters This TU/MU relationship is the mechanical engine behind almost every other result in this topic: the law of diminishing marginal utility, the consumer equilibrium condition, and the downward-sloping demand curve all follow directly from how MU behaves as quantity increases.
Common Misunderstanding Students often confuse "marginal utility is falling" with "total utility is falling." These are different: as long as MU is positive (even if small), TU is still rising — just more slowly. TU only falls once MU actually goes negative. Look at units 4 and 5 in the table: MU falls from 4 to 0, but TU is still rising (28 is more than 24) until MU actually reaches zero.
Law of Diminishing Marginal Utility
Definition The law of diminishing marginal utility states that as a consumer consumes more and more units of a good, ceteris paribus (holding everything else constant), the marginal utility derived from each additional unit eventually declines.
Explanation The intuition is satiation: the first unit of a good satisfies the most urgent want; each subsequent unit satisfies a progressively less urgent want, because the most pressing need has already been met. This is why the samosa table above shows MU falling steadily from 10 to 8 to 6 to 4 to 0 to -2 as more samosas are eaten in one sitting. The law generally requires that consumption happens within a reasonable time period (not spread over months) and that the good itself doesn't change in character.
Example On a hot day, the first glass of water quenches real thirst (very high MU). The second glass is still nice but less urgently needed. By the fifth or sixth glass, the person may feel uncomfortably full, and MU could even turn negative.
Real-World Example Telecom companies in India offer tiered data plans (1GB, 2GB, 3GB/day) partly because they understand diminishing marginal utility: the value a user places on the first GB of daily data (needed for calls, essential apps, work) is far higher than the value of the tenth GB in the same day, which may just be idle background usage. This is also why "unlimited" plans are priced only modestly above capped ones — providers know MU beyond a certain point is close to zero for most users.
Why It Matters
- It explains why demand curves slope downward — consumers are only willing to buy additional units at successively lower prices, because each additional unit is worth less to them.
- It justifies progressive taxation — the marginal utility of an extra rupee of income is higher for a poor household than a rich one, so taking a rupee from the rich causes a smaller utility loss than taking it from the poor.
- It explains risk aversion — because the marginal utility of income diminishes, losing ₹100 hurts more than gaining ₹100 helps, which is why people buy insurance even when it has a negative expected monetary value.
Common Misunderstanding Some students think this law means marginal utility is always negative after a certain point, or that it applies to literally every good instantly (e.g., money, or a rare stamp collection). In reality, MU only declines — it does not have to become negative, and it may decline very slowly for some goods (like money) or take unusual forms for goods people collect (like art or coins), where the law is often assumed to apply only loosely or over a longer horizon.
Consumer Equilibrium (Cardinal Approach) — The Equi-Marginal Principle
Definition A consumer maximizes total utility from a fixed budget when the marginal utility per rupee spent is equal across all goods purchased:
MU_x / P_x = MU_y / P_y = λ
where λ (lambda) represents the marginal utility of money income — the extra satisfaction from one more rupee if it were spent optimally.
Explanation This is often called the equi-marginal principle (or the law of equi-marginal utility). The logic is simple reallocation: if MU_x/P_x > MU_y/P_y, the consumer is getting more "bang per rupee" from good X than from good Y. A rational consumer should shift spending away from Y and toward X. As more X is bought, MU_x falls (diminishing marginal utility); as less Y is bought, MU_y rises. The consumer keeps reallocating until MU_x/P_x = MU_y/P_y — at that point, no further reallocation can increase total utility, so the budget is being spent optimally.
Example Suppose tea costs ₹10/cup with MU = 40 utils, and biscuits cost ₹5/packet with MU = 30 utils.
- MU per rupee on tea = 40/10 = 4
- MU per rupee on biscuits = 30/5 = 6
Biscuits give more utility per rupee, so the consumer should buy more biscuits and less tea. As biscuit consumption rises, MU_biscuit falls (say to 24); as tea consumption falls, MU_tea rises (say to 48). Now MU per rupee on tea = 48/10 = 4.8 and on biscuits = 24/5 = 4.8 — equilibrium reached, since both ratios are now equal.
Real-World Example A college student in India with a fixed monthly allowance of ₹3,000 deciding how to split spending between mobile data recharges and canteen food is implicitly applying this principle. If an extra ₹100 of data gives more "value" (marginal utility) than an extra ₹100 of canteen snacks, a rational student shifts money toward data — until the last rupee spent on each gives roughly equal satisfaction. Firms use the same principle in reverse: an advertiser with a fixed budget allocates spend across Instagram, Google, and TV ads until the marginal return per rupee is equalized across channels.
Why It Matters This condition is the cardinal-utility version of "optimal choice," and it generalizes directly to the ordinal (indifference curve) approach, where equilibrium occurs where the budget line is tangent to the highest attainable indifference curve — see Indifference Curves and Budget Constraints.
Common Misunderstanding Students often think equilibrium means "equal marginal utility" (MU_x = MU_y) rather than "equal marginal utility per rupee" (MU_x/P_x = MU_y/P_y). These are different whenever the two goods have different prices — you must always divide by price before comparing.
Consumer Surplus
Definition Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good (reflecting the utility they get from it) and the price they actually have to pay.
Explanation Because of diminishing marginal utility, a consumer would have been willing to pay more for the first few units of a good than the market price actually charges — they only pay the same market price for every unit. The "extra" value they get on those earlier units, over and above what they paid, is consumer surplus. Graphically, it is the area below the demand curve (which reflects willingness to pay) and above the horizontal price line, up to the quantity actually purchased.
Example Suppose a consumer's willingness to pay for successive cups of tea is ₹20, ₹15, ₹10, and ₹5 for the 1st, 2nd, 3rd, and 4th cups. If the market price is ₹10/cup, the consumer buys 3 cups (since the 4th cup is worth only ₹5, less than its price). Consumer surplus = (20−10) + (15−10) + (10−10) = 10 + 5 + 0 = ₹15.
Real-World Example When Indian Railways prices a Rajdhani Express ticket at, say, ₹2,000, a business traveller who would have paid ₹5,000 to avoid a costly flight captures ₹3,000 of consumer surplus. Airlines and e-commerce platforms try to reduce consumer surplus (and capture it as profit) through price discrimination — for example, surge pricing or personalized discounts — by charging different consumers closer to their own maximum willingness to pay.
Why It Matters Consumer surplus is the standard tool economists use to measure the welfare impact of taxes, subsidies, price controls, and monopoly pricing. For example, a tax typically shrinks consumer surplus (and producer surplus) by more than the government collects in revenue — this "extra" loss is called deadweight loss.
Common Misunderstanding Students sometimes think consumer surplus is money the consumer literally saves or receives. It isn't cash in hand — it is a measure of extra satisfaction/value the consumer enjoys beyond what they paid, existing only conceptually (though it can be converted into a monetary measure for comparison purposes).
Limitations of Utility Theory
Definition The limitations of utility theory are the assumptions and simplifications in the model that make it an imperfect description of real consumer behaviour.
Explanation The main limitations are:
- Utility is subjective and hard to measure — cardinal "utils" are not observable or verifiable in the real world; no instrument can measure someone's satisfaction directly.
- Assumes rational maximization — behavioural economics (see Related Topics) shows people often use mental shortcuts, get influenced by framing, and don't always maximize utility consistently.
- Ignores social effects — a consumer's utility can depend on what others consume, as in Veblen goods (utility rises with price/exclusivity, e.g., luxury watches) or the bandwagon effect (utility rises because "everyone has it").
- Static model — the basic model doesn't capture how preferences change with experience, addiction, habit formation, or over time.
Example Two people buy the exact same smartphone at the exact same price. Basic utility theory assumes we can meaningfully compare or predict behaviour based on "utils," but in reality, one buyer may want it purely for functionality, the other purely because it signals social status (a Veblen-type effect) — the model doesn't distinguish these very different sources of "utility."
Real-World Example Studies on Indian consumers' festive-season (Diwali) gold purchases show behaviour that plain utility maximization struggles to explain fully: gold buying often continues even when prices are historically high, partly due to social custom, habit, and status signalling rather than a strict marginal-utility-per-rupee calculation. This illustrates why behavioural economics has grown as a complement to classical utility theory.
Why It Matters Recognizing these limitations doesn't mean discarding the model — it means using it as a first approximation while being aware that real-world predictions may need adjustment for social, psychological, and dynamic factors.
Common Misunderstanding Students often think "limitations" mean the theory is useless. In reality, utility theory is still the backbone of demand theory and welfare economics — its limitations simply mark where more advanced tools (indifference curves, behavioural economics) are needed for a fuller picture.
Visual Learning
Key Terms
| Term | Definition | Context/Related Concepts |
|---|---|---|
| Utility | Satisfaction or benefit derived from consuming a good/service | Foundation of consumer choice theory |
| Total Utility (TU) | Total satisfaction from consuming a given quantity of a good | Rises while MU > 0, peaks when MU = 0 |
| Marginal Utility (MU) | Additional satisfaction from one more unit; MU = ΔTU/ΔQ | Declines due to Law of Diminishing Marginal Utility |
| Cardinal Utility | Utility measured in specific numerical units ("utils") | Marshall; used for MU/consumer surplus analysis |
| Ordinal Utility | Utility expressed only as a ranking of preferences | Hicks & Allen; basis of indifference curve analysis |
| Law of Diminishing Marginal Utility | MU falls as more units of a good are consumed, ceteris paribus | Explains downward-sloping demand, progressive taxation |
| Equi-Marginal Principle | Utility is maximized when MU per rupee is equal across all goods | MU_x/P_x = MU_y/P_y = λ |
| Consumer Surplus | Difference between willingness to pay and price actually paid | Used in welfare/tax/subsidy analysis; area under demand curve above price |
| Deadweight Loss | Loss of total surplus caused by market distortions (e.g., taxes) | Related to consumer and producer surplus reduction |
| Veblen Good | A good for which higher price/exclusivity increases utility/demand | Limitation of standard utility theory |
Common Mistakes
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Misconception: Marginal utility falling means total utility is also falling. Why it's wrong: As long as MU is positive, each additional unit still adds to total utility, even if by a smaller amount than before. Correct explanation: TU only starts falling once MU turns negative. In the samosa example, TU keeps rising through unit 5 (where MU = 0) and only falls at unit 6 (where MU = -2).
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Misconception: Consumer equilibrium requires MU_x = MU_y (equal marginal utilities across goods). Why it's wrong: This ignores price differences between goods; it's only correct if the two goods happen to have identical prices. Correct explanation: The correct equilibrium condition is MU per rupee spent, i.e., MU_x/P_x = MU_y/P_y, since the consumer is really comparing "value gained per rupee" not "value gained per unit."
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Misconception: Consumer surplus is actual money the consumer gets to keep or save. Why it's wrong: Consumer surplus is a conceptual/welfare measure of extra satisfaction, not a cash transaction. Correct explanation: It represents the gap between what a consumer would have paid (reflecting their utility) and what they actually pay — useful for comparing welfare across policies, but not literal money in the consumer's pocket.
Comparison and Connections
| Concept | Cardinal Utility Approach | Ordinal Utility Approach (Indifference Curves) |
|---|---|---|
| Measurability | Assumes utility can be measured in utils | Assumes only rankings/preferences can be observed |
| Key tool | Marginal utility, MU/P ratio | Marginal Rate of Substitution (MRS), indifference curves |
| Equilibrium condition | MU_x/P_x = MU_y/P_y | Budget line tangent to highest indifference curve (MRS = P_x/P_y) |
| Realism | Less realistic (satisfaction isn't literally numeric) | More realistic; matches how people actually compare choices |
| Best used for | Building intuition, consumer surplus, progressive taxation logic | Rigorous consumer choice theory, income/substitution effects |
| Related page | This page | Indifference Curves |
Utility theory (cardinal) is also frequently confused with demand theory: utility theory explains why a consumer values a good, while demand theory (built partly on utility theory) shows how much consumers will buy at each price. See Demand and Supply for how MU and diminishing marginal utility connect to the derivation of the demand curve.
Practice Questions
Recall
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Define marginal utility and state its formula. Answer guidance: Marginal utility (MU) is the additional satisfaction gained from consuming one more unit of a good. Formula: MU = ΔTU/ΔQ (change in total utility divided by change in quantity).
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State the law of diminishing marginal utility. Answer guidance: As a consumer consumes successive units of a good, ceteris paribus, the marginal utility derived from each additional unit eventually declines.
Understanding
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Explain why total utility can still be rising even though marginal utility is falling. Answer guidance: MU falling just means each new unit adds less extra satisfaction than the previous one — but as long as MU stays positive, TU keeps increasing (by a shrinking amount each time). TU only decreases once MU becomes negative.
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Why is the consumer equilibrium condition MU_x/P_x = MU_y/P_y rather than MU_x = MU_y? Answer guidance: Because the consumer is choosing how to allocate limited rupees, not limited units. Dividing by price converts MU into "utility per rupee," which is the correct basis for comparing goods with different prices. If prices differ, comparing raw MU values would be misleading.
Application
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A consumer has ₹50 to spend on tea (₹10/cup) and biscuits (₹5/packet). MU of tea = 30 utils, MU of biscuits = 20 utils. Is the consumer at equilibrium? If not, what should they do? Answer guidance: MU/P for tea = 30/10 = 3; MU/P for biscuits = 20/5 = 4. Since biscuits give more utility per rupee, the consumer is not at equilibrium — they should buy more biscuits and less tea until the ratios equalize (as biscuit MU falls and tea MU rises).
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Using the samosa table in this page, calculate the marginal utility of the 4th samosa and state whether the consumer should eat a 4th samosa if each samosa costs "3 utils worth" of money. Answer guidance: MU of the 4th samosa = TU(4) − TU(3) = 28 − 24 = 4 utils. Since 4 > 3 (the utility "cost"), the consumer should eat the 4th samosa, as it still adds more satisfaction than its cost.
Analysis
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A government wants to justify a progressive income tax using utility theory. Construct the argument, and mention one limitation of this argument. Answer guidance: Argument: Diminishing marginal utility of income means an extra rupee is worth more (in utility terms) to a poor person than a rich person. Taxing the rich more heavily therefore causes a smaller total utility loss than taxing everyone equally, while the revenue raised can fund transfers/services that raise a poor household's utility by more. Limitation: this assumes utility is comparable across different people (interpersonal comparison of utility), which cardinal utility theory itself struggles to justify rigorously, since utility isn't actually measurable or comparable between different individuals.
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A firm raises the price of a good, but sales barely fall, and demand actually seems to rise slightly. Using the concept of Veblen goods, analyze why standard utility theory might fail here, and suggest what additional factor should be considered. Answer guidance: Standard utility theory assumes MU per rupee governs demand, so higher price should reduce quantity demanded (all else equal) as consumers reallocate toward cheaper alternatives. If demand rises with price, the good may be a Veblen good, where the price itself is a source of utility (via exclusivity/status signaling), violating the standard assumption that utility comes only from consumption of the good's inherent features. Additional factor: social/status utility and reference-group effects should be incorporated, which is where behavioural economics extensions to utility theory become useful.
FAQ
1. Is utility theory the same as demand theory? No. Utility theory explains the psychological/economic basis of consumer satisfaction and choice; demand theory (the relationship between price and quantity demanded) is built on utility theory (especially diminishing marginal utility) but is a distinct, related concept.
2. Why do economists prefer ordinal utility over cardinal utility today? Because ordinal utility makes a much weaker, more defensible assumption — that consumers can only rank bundles of goods, not assign exact numeric satisfaction values to them. This avoids the unrealistic claim that satisfaction is literally measurable, while still producing all the same core predictions (like downward-sloping demand) through indifference curve analysis.
3. Can marginal utility ever be negative in real life? Yes — think of eating past the point of comfort, or an activity you initially enjoy that becomes unpleasant with over-exposure (like too much loud music). Negative MU means total utility is now falling, i.e., the "good" has effectively become a "bad" at that quantity.
4. How is consumer surplus useful outside of exams? It's the standard tool for cost-benefit and welfare analysis in real policymaking — e.g., estimating how much value consumers lose from a tax on fuel, or how much value they gain from a government subsidy on food grains, compared to the cost/revenue involved.
5. Does the law of diminishing marginal utility apply to money itself? Largely yes, in the sense used for progressive taxation: an extra ₹1,000 typically matters more (in utility terms) to someone earning ₹15,000/month than to someone earning ₹15,00,000/month. However, this is a more debated application than for physical goods like food, since money is not "consumed" directly but used to acquire other goods.
Quick Revision
- Utility = satisfaction from consuming a good; cardinal utility measures it in "utils," ordinal utility only ranks preferences.
- Total Utility (TU) = total satisfaction from a given quantity; Marginal Utility (MU) = ΔTU/ΔQ = extra satisfaction from one more unit.
- TU rises while MU > 0, peaks when MU = 0, and falls when MU < 0.
- Law of Diminishing Marginal Utility: MU falls as consumption of a good increases, ceteris paribus.
- This law explains downward-sloping demand, progressive taxation, and risk aversion.
- Consumer equilibrium (cardinal approach): MU_x/P_x = MU_y/P_y = λ — utility per rupee must be equal across all goods.
- If MU_x/P_x > MU_y/P_y, shift spending from Y to X until the ratios equalize.
- Consumer Surplus = willingness to pay − price actually paid; shown as the area below the demand curve, above the price line.
- Consumer surplus is used to evaluate the welfare effects of taxes, subsidies, price controls, and monopoly.
- Limitations: utility isn't directly measurable, consumers aren't always perfectly rational, social effects (Veblen goods, bandwagon) matter, and the model is static.
- Modern theory generally replaces the cardinal approach with ordinal utility and indifference curves for rigorous analysis.