Consumer theory 1.pdf

# Utility theory and marginal utility Utility theory helps us understand consumer behaviour by examining the satisfaction derived from consuming goods and services and how individuals make choices to maximise this satisfaction. ### 1.1 Consumer choices and the concept of utility * Every day, individuals make choices about how to allocate their limited resources, such as money and time, for example, choosing between pizza or a hamburger, or deciding whether to spend or save [6](#page=6). * These individual decisions are fundamental to understanding demand curves and price elasticity [6](#page=6). * Economics uses these choices to comprehend consumer behaviour: why we buy, what we buy, and how much we are willing to pay [6](#page=6). * Utility is defined as the satisfaction derived from consuming goods and services [7](#page=7). * More precisely, utility refers to how consumers rank different goods and services [7](#page=7). * Consumers aim to choose bundles of goods that provide them with the highest level of utility [7](#page=7). * Utility itself is not directly observable; it is an abstract concept used to explain rational consumer decisions [7](#page=7). * A key assumption in demand theory is that consumers strive to maximise their utility, meaning they choose the bundle of goods they most prefer [7](#page=7). ### 1.2 The marginal revolution * The Marginal Revolution, occurring around the 1870s, was a significant turning point in economics that re-evaluated value and decision-making through the lens of marginal analysis [8](#page=8). * This era introduced the concept that economic decisions are made "at the margin," focusing on the benefits and costs associated with consuming one additional unit of a good, input, or activity [8](#page=8). * The Marginal Revolution shifted the focus of economic thought from classical theories of value based on costs (such as Ricardo's labour theory) to subjective, individual decision-making processes [8](#page=8). * It laid the foundational principles for neoclassical economics, which continues to be the dominant economic framework today [8](#page=8). ### 1.3 Marginal utility * Total utility (TU) represents the overall satisfaction gained from consuming a certain quantity of a good or service [9](#page=9). * Marginal utility (MU) measures the additional satisfaction obtained from consuming one more unit of a good [9](#page=9). * For instance, consuming the first ice cream cone might provide 4 "utils" (a hypothetical unit of satisfaction), the second might add 3 more utils, and the third might add 2 more utils [9](#page=9). * The total utility changes by the amount of the marginal utility of the next unit consumed [9](#page=9). * Marginal utility can be mathematically linked to total utility using the formula: $$MU = \frac{\Delta TU}{\Delta Q}$$ This formula indicates that the change in total utility resulting from a change in quantity is equal to the marginal utility [9](#page=9). * Marginal utility is crucial for understanding the extra benefit derived from each additional unit of consumption [9](#page=9). ### 1.4 Law of diminishing marginal utility * The Law of Diminishing Marginal Utility states that as an individual consumes more units of a particular good, the additional (marginal) satisfaction gained from each successive unit tends to decrease [10](#page=10). * This principle helps explain why demand curves typically slope downwards, as consumers are willing to buy more of a good only if its price falls, reflecting the diminishing additional satisfaction they receive [10](#page=10). * Eventually, consuming further units of a good could even lead to a reduction in overall satisfaction (e.g., feeling unwell from consuming too much ice cream) [10](#page=10). > **Tip:** The Law of Diminishing Marginal Utility is a fundamental concept that underpins much of microeconomic analysis, including consumer choice and market demand. ### 1.5 Numerical example of utility and consumption The relationship between quantity consumed, total utility, and marginal utility can be illustrated with a numerical example: | Quantity (Q) | Total utility (U) | Marginal utility (MU) | | :----------- | :---------------- | :-------------------- | | 0 | 0 | – | | 1 | 4 | 4 | | 2 | 7 | 3 | | 3 | 9 | 2 | | 4 | 10 | 1 | | 5 | 10 | 0 | * In this table, total utility increases with each unit consumed, but the rate of increase slows down [11](#page=11). * Marginal utility is calculated as the change in total utility from consuming one additional unit [11](#page=11). * When marginal utility reaches zero, total utility attains its maximum point [11](#page=11). ### 1.6 Graphical illustration of utility The concepts of total utility and marginal utility can be visualized graphically: * **Total utility curve:** This curve typically exhibits a concave shape, indicating that utility increases as consumption rises but at a diminishing rate. The total utility at any point is the sum of the marginal utilities of all units consumed up to that point [12](#page=12). * **Marginal utility curve:** This curve is generally depicted as a downward-sloping line, illustrating the declining additional satisfaction gained from each successive unit of a good [12](#page=12). * Mathematically, marginal utility is the derivative of the total utility function with respect to quantity ($Q$), and total utility is the integral of the marginal utility function over the relevant range of $Q$ [12](#page=12). > **Example:** If a consumer enjoys the first slice of pizza for a satisfaction level of 5 utils and the second slice for an additional 3 utils, their total utility after two slices is 8 utils, and the marginal utility of the second slice is 3 utils. If the third slice only adds 1 util, their total utility becomes 9 utils, and the marginal utility of the third slice is 1 util. This demonstrates diminishing marginal utility [9](#page=9). --- # Derivation of demand and consumer choice This section explains how utility theory underpins consumer demand by detailing the equimarginal principle for utility maximization and introducing the substitution and income effects as alternative approaches to understanding demand curves [14](#page=14). ### 2.1 Foundations of consumer demand Consumers are assumed to maximize utility, choose their most preferred affordable bundle, and face given prices and a fixed income. A rational consumer allocates spending across goods to maximize satisfaction [14](#page=14). #### 2.1.1 The equimarginal principle The equimarginal principle is the fundamental condition for utility maximization. It states that a consumer maximizes utility by allocating their spending such that the last unit of currency (e.g., pound) spent on each good yields the same marginal utility [15](#page=15). The formal condition for this equilibrium is: $$ \frac{MU_1}{P_1} = \frac{MU_2}{P_2} = \frac{MU_3}{P_3} = \dots = \frac{MU_{\text{per } \text{currency unit}}}{\text{of income}} $$ If a good provides a higher marginal utility per unit of currency, consumers should spend more on it. Conversely, if it provides less, consumption should be reduced. This process continues until all goods offer the same marginal utility per unit of currency [15](#page=15). > **Tip:** This principle ensures that no reallocation of spending could increase overall utility given the prices and income. #### 2.1.2 Marginal utility of income When all goods provide the same marginal utility per unit of currency, the consumer has achieved an optimal allocation. The common value of marginal utility per unit of currency across all goods is known as the marginal utility of income. This represents the additional utility a consumer would gain from one more unit of currency to spend [16](#page=16). **Marginal utility of income:** Utility gained from one extra unit of currency [16](#page=16). #### 2.1.3 Explaining downward-sloping demand curves The equimarginal principle helps explain why demand curves slope downward. If the price of a good (e.g., good 1) increases, the ratio $\frac{MU_1}{P_1}$ becomes lower than that of other goods. To restore equality, the consumer must reduce their consumption of good 1. Due to the law of diminishing marginal utility, reducing consumption of good 1 increases its marginal utility. This continues until $\frac{MU_1}{P_1}$ once again equals the ratio for other goods. Therefore, a higher price leads to a lower quantity demanded, explaining the downward slope of demand curves [17](#page=17). ### 2.2 Alternative approach: Substitution and Income Effects An alternative to the marginal utility approach for explaining consumer choice involves indifference curves and focuses on two key effects: the substitution effect and the income effect. This method not only explains the slope of demand curves but also helps in understanding price elasticity of demand [18](#page=18). #### 2.2.1 The substitution effect The substitution effect describes a consumer's response to a change in relative prices. When the price of a good rises, it becomes more expensive relative to other goods. Consequently, consumers tend to substitute away from the now more expensive good towards relatively cheaper alternatives to maintain their satisfaction at a lower cost [18](#page=18) [19](#page=19). > **Example:** If coffee becomes more expensive than tea, consumers are likely to purchase more tea and less coffee [19](#page=19). The substitution effect is a key insight into why demand curves slope downward [19](#page=19). #### 2.2.2 The income effect A change in the price of a good also affects a consumer's real income, which is the purchasing power of their money. When the price of a good rises, real income falls, meaning consumers can afford to buy less. This reduction in purchasing power leads to a decrease in the demand for most normal goods. The income effect is defined as the change in the quantity demanded that results from a change in real income [20](#page=20). Combined with the substitution effect, the income effect helps explain the downward slope of the demand curve [20](#page=20). #### 2.2.3 The interplay of substitution and income effects The substitution effect is consistently negative: when the price of a good increases, consumers tend to buy less of it and switch to alternatives. However, the income effect can operate in either direction [21](#page=21). * **Normal Goods:** For most goods, a price rise leads to lower real income, causing consumers to buy less. This reinforces the negative substitution effect [21](#page=21). * **Inferior Goods:** For some goods, particularly basic necessities, a fall in real income (due to a price rise of another good) might not lead to a significant reduction in consumption, or consumers might even increase their consumption of cheaper alternatives if they perceive themselves as poorer [21](#page=21). Together, these effects explain changes in demand and can sometimes lead to surprising outcomes [21](#page=21). > **Example:** Consider a low-income family and the prices of ready noodles and fresh vegetables. If the price of noodles rises relative to vegetables, the family might substitute towards vegetables because noodles are now relatively more expensive (substitution effect). However, because noodles are a cheap staple, feeling poorer might lead them to rely more on noodles (a positive income effect for an inferior good). Despite this, the overall quantity of noodles purchased may still decrease if the substitution effect is stronger. Conversely, if vegetables become relatively cheaper, the family substitutes towards them (substitution effect). But if they feel poorer, they might reduce their overall consumption of fresh vegetables because vegetables are typically a normal good, resulting in a negative income effect [22](#page=22). --- # Consumer preferences and indifference curves This section explores the fundamental assumptions economists make about consumer preferences and how these preferences are graphically represented by indifference curves. ### 3.1 Assumptions about consumer preferences Economists assume that consumers are rational and can make consistent decisions about their consumption given limited resources. These preferences are characterized by several key assumptions [24](#page=24): #### 3.1.1 Completeness and rankability This assumption states that consumers can compare any two bundles of goods and determine which bundle they prefer, or if they are indifferent between them. This implies that a consumer can always rank their consumption possibilities in terms of preference. For example, a consumer can compare a bundle of 3 apples and 1 chocolate bar with a bundle of 2 apples and 9 chocolate bars and state a preference. This ability to compare and rank is crucial for making choices [24](#page=24) [25](#page=25) [27](#page=27). #### 3.1.2 More is better (non-satiation) For most goods, it is assumed that consumers prefer to consume more rather than less. This is also referred to as monotonicity. This means that if a bundle contains more of at least one good and no less of any other good, it will be preferred to a bundle with less of that good. However, this assumption does not hold for all goods (e.g., undesirable goods) [24](#page=24) [28](#page=28) [30](#page=30) [31](#page=31) [32](#page=32). #### 3.1.3 Transitivity Transitivity ensures that consumer preferences are logically consistent. If a consumer prefers bundle X to bundle Y, and bundle Y to bundle Z, then they must also prefer bundle X to bundle Z. Without transitivity, a consumer could get caught in a cycle of choices, making consistent decision-making impossible [24](#page=24) [29](#page=29). #### 3.1.4 Diminishing marginal rate of substitution This assumption, explored further with indifference curves, suggests that as a consumer has more of a particular good, they become less willing to give up other goods to acquire even more of it. This reflects a preference for variety [24](#page=24). ### 3.2 Ordinal vs. Cardinal Utility Utility is a concept used by economists to describe preferences, but it provides an **ordinal ranking** rather than a cardinal one [26](#page=26). * **Ordinal Utility:** Allows economists to state which bundle is preferred, but not by how much. This is sufficient for most economic analyses, such as determining consumer choices, as it is not practically possible to measure or compare utility numerically across individuals or bundles [26](#page=26). * **Cardinal Utility:** Would imply the ability to quantify how much more one bundle is liked than another, which is not observable or meaningful in real-world scenarios [26](#page=26). ### 3.3 Visualizing preferences: Indifference curves When preferences are not obvious, such as when comparing bundles with more of one good and less of another, indifference curves are used to graphically represent these trade-offs [33](#page=33). #### 3.3.1 Definition of an indifference curve An indifference curve illustrates all combinations of two goods that provide a consumer with the same level of satisfaction or utility. Each point on an indifference curve represents a bundle that yields equal satisfaction [35](#page=35) [36](#page=36). #### 3.3.2 Characteristics of indifference curves Indifference curves possess four key properties that reflect the assumptions about rational consumer preferences [37](#page=37): 1. **They can be drawn:** This reflects the completeness and rankability assumption, meaning consumers can compare and order consumption bundles [37](#page=37). 2. **Curves further from the origin represent higher utility:** Bundles on indifference curves located further from the origin contain more of at least one good and no less of any other, thus representing higher levels of satisfaction according to the "more is better" assumption. Consumers generally prefer bundles on higher curves [37](#page=37) [38](#page=38). 3. **Curves never cross:** Indifference curves cannot intersect. If they did, it would imply that a single bundle provides two different levels of satisfaction, contradicting the assumption of transitivity and consistent preferences [37](#page=37) [39](#page=39). 4. **Curves are convex to the origin:** This shape signifies a consumer's preference for variety and balanced bundles over extreme combinations of goods. A bundle that is an average of two bundles on the same indifference curve will lie on a higher indifference curve, indicating it is strictly preferred [37](#page=37) [40](#page=40). #### 3.3.3 The slope of an indifference curve: Marginal Rate of Substitution (MRS) The slope of an indifference curve at any point represents the **marginal rate of substitution (MRS)** [42](#page=42). * **Definition:** The MRS tells us how many units of one good (say, Y) a consumer is willing to give up to obtain one additional unit of another good (say, X) while maintaining the same level of utility [42](#page=42) [45](#page=45). * **Formula:** The MRS can be expressed as the negative of the ratio of the change in good Y to the change in good X: $$ \text{MRS}_{XY} = -\frac{\Delta Y}{\Delta X} $$ It is also equal to the ratio of the marginal utilities of the two goods: $$ \text{MRS}_{XY} = \frac{\text{MU}_X}{\text{MU}_Y} $$ where $\text{MU}_X$ is the marginal utility of good X and $\text{MU}_Y$ is the marginal utility of good Y [44](#page=44). * **Diminishing MRS:** Indifference curves are typically convex to the origin, meaning the MRS is not constant but diminishes as one moves along the curve. This reflects the principle of diminishing marginal utility and a decreasing willingness to trade: as a consumer possesses more of one good, they are willing to give up less of the other to gain an additional unit of the first good [41](#page=41) [43](#page=43) [44](#page=44). #### 3.3.4 What the shape of an indifference curve signifies The shape and slope of an indifference curve provide insights into consumer preferences and the relationship between goods: * **Downward Sloping:** Indifference curves are downward sloping because if a consumer gives up some of one good, they must gain more of the other good to maintain the same level of satisfaction, consistent with the non-satiation assumption [47](#page=47). * **Steepness and Flatness:** * **Steeper curves** at a point indicate the consumer requires a large amount of the good on the vertical axis to compensate for a small increase in the good on the horizontal axis. This suggests they value the good on the horizontal axis more at that particular bundle [48](#page=48). * **Flatter curves** indicate the consumer is willing to give up a large amount of the good on the horizontal axis for a small gain in the good on the vertical axis, suggesting they value the good on the vertical axis more at that bundle [48](#page=48). * **Curvature:** The degree of curvature reveals how easily consumers are willing to substitute one good for another [49](#page=49). * **Relatively straight curves** imply the goods are close substitutes, and the consumer is willing to trade them at a nearly constant rate [49](#page=49). * **Strongly convex curves** suggest the goods are less substitutable, and the consumer prefers balanced bundles [49](#page=49). * **Perfect Substitutes:** Lead to straight-line indifference curves, where the MRS is constant. For example, if the MRS is constant at -1, the consumer is always willing to trade one cup of coffee for one cup of tea to maintain utility [49](#page=49) [50](#page=50). * **Perfect Complements:** Lead to L-shaped indifference curves, where goods must be consumed in a fixed proportion. At the "kink" of the L-shape, the MRS is undefined, and along the horizontal or vertical portions, the MRS is 0 or infinity, respectively, as additional units of one good without the other provide no additional utility. An example is left shoes and right shoes, which are consumed in a 1:1 ratio [49](#page=49) [51](#page=51). --- # Budget constraints and consumer limitations The budget constraint defines the limits of what consumers can purchase given their income and the prices of goods [53](#page=53). ### 4.1 The budget constraint and budget line The budget constraint represents all the combinations of goods that a consumer can afford to purchase by spending all of their income. It is typically illustrated graphically as a budget line, which is plotted alongside indifference curves [54](#page=54). #### 4.1.1 Defining the budget constraint To simplify, three assumptions are made: 1. **Fixed Prices:** Each good has a constant price, and consumers can buy any quantity at this price because their individual demand is too small to influence the market [53](#page=53). 2. **Fixed Income:** Consumers have a set amount of income to spend [53](#page=53). 3. **No Borrowing or Saving:** Income must be spent entirely within the current period; otherwise, it is forfeited [53](#page=53). These assumptions allow for the representation of a consumer's economic limitations using a linear equation known as the budget line [53](#page=53). #### 4.1.2 Mathematical representation For a consumer purchasing two goods, say Food (F) and Clothing (C), with prices $P_F$ and $P_C$ respectively, and a given income (let's denote it as $I$), the budget constraint can be expressed mathematically as: $I = P_F Q_F + P_C Q_C$ Where $Q_F$ is the quantity of food and $Q_C$ is the quantity of clothing [54](#page=54). To determine the slope of the budget line, the equation is solved for $Q_C$: $Q_C = \frac{I}{P_C} - \frac{P_F}{P_C} Q_F$ > **Tip:** This equation is in the form of a standard linear equation ($y = mx + c$), where $Q_C$ is the dependent variable (y-axis), $Q_F$ is the independent variable (x-axis), $\frac{I}{P_C}$ is the y-intercept, and $-\frac{P_F}{P_C}$ is the slope. #### 4.1.3 Key features of the budget line The budget line has crucial points and a defining slope: * **Vertical Intercept:** This represents the maximum quantity of the good on the vertical axis (e.g., clothing) that can be purchased if the entire income is spent on that good. For example, if income is 60 dollars and the price of clothing is 6 dollars per unit, the vertical intercept is $\frac{60}{6} = 10$ units of clothing [54](#page=54) [55](#page=55). * **Horizontal Intercept:** This represents the maximum quantity of the good on the horizontal axis (e.g., food) that can be purchased if the entire income is spent on that good. Using the same example, if the price of food is 2 dollars per unit, the horizontal intercept is $\frac{60}{2} = 30$ units of food [55](#page=55). * **Slope:** The slope of the budget constraint is given by the ratio of the price of the good on the horizontal axis to the price of the good on the vertical axis, expressed as $-\frac{P_F}{P_C}$. This slope indicates the rate at which the consumer can trade one good for another in the market while maintaining their total expenditure. For the example given, the slope is $-\frac{2}{6} = -\frac{1}{3}$ [55](#page=55). > **Key Idea:** The absolute value of the slope of the budget constraint equals the relative prices of the two goods, representing the terms of trade offered by the market [55](#page=55). #### 4.1.4 Feasible and infeasible consumption bundles * **Feasible Consumption Bundles:** All combinations of goods that lie on or below the budget line are considered feasible. These bundles cost no more than the consumer's income [55](#page=55). * **Infeasible Consumption Bundles:** Any combination of goods that lies above the budget line is infeasible, as it would require more income than the consumer possesses [55](#page=55). ### 4.2 Factors affecting the budget constraint's position The position and slope of the budget constraint are primarily determined by two factors: the consumer's income and the relative prices of the goods being considered [56](#page=56). #### 4.2.1 Changes in income A change in income causes a **parallel shift** in the budget constraint [56](#page=56) [57](#page=57). * An increase in income shifts the budget line **outward**, expanding the set of feasible consumption bundles [57](#page=57). * A decrease in income shifts the budget line **inward**, contracting the set of feasible consumption bundles [57](#page=57). Crucially, changes in income do not alter the slope of the budget line, meaning the relative prices of the goods remain the same [56](#page=56) [57](#page=57). > **Example:** If income is reduced by 50%, both the food and clothing intercepts decrease by 50%, and the entire budget line shifts inward parallel to its original position [57](#page=57). #### 4.2.2 Changes in prices A change in the price of one good causes the budget line to **pivot**, altering its slope [56](#page=56). * If the price of the good on the horizontal axis increases, the horizontal intercept moves inward, and the budget line pivots inward around the vertical intercept [57](#page=57). * If the price of the good on the vertical axis increases, the vertical intercept moves inward, and the budget line pivots inward around the horizontal intercept [57](#page=57). > **Example:** If the price of food doubles, the horizontal intercept is halved, and the budget line pivots inward around the clothing intercept. The consumer can now afford less food for any given amount of clothing purchased. Similarly, if the price of clothing doubles, the vertical intercept is halved, and the budget line pivots inward around the food intercept [57](#page=57). In all cases where prices increase or income decreases, the area of feasible consumption bundles shrinks, demonstrating a reduction in the consumer's purchasing power. Bundles that were previously affordable may become infeasible [57](#page=57). --- ## Common mistakes to avoid - Review all topics thoroughly before exams - Pay attention to formulas and key definitions - Practice with examples provided in each section - Don't memorize without understanding the underlying concepts

| Term | Definition | |------|------------| | Utility | The satisfaction or benefit a consumer derives from consuming goods and services. It is a construct used to explain rational consumer decisions and represents how consumers rank different goods and services. | | Marginal Utility (MU) | The additional satisfaction gained from consuming one more unit of a good or service. It is calculated as the change in total utility divided by the change in quantity consumed. | | Law of Diminishing Marginal Utility | An economic principle stating that as a consumer consumes more units of a particular good, the additional satisfaction (marginal utility) gained from each subsequent unit tends to decrease. | | Equimarginal Principle | The condition for utility maximization, which states that a consumer allocates their spending across various goods such that the marginal utility per unit of currency spent on each good is equal. Mathematically, this is expressed as $MU_1/P_1 = MU_2/P_2 = \dots$ for all goods. | | Marginal Utility of Income | The additional utility a consumer would gain from having one additional unit of currency to spend. It represents the value of the last unit of money spent on any good in the optimal consumption bundle. | | Substitution Effect | The change in the quantity demanded of a good due solely to a change in its relative price, assuming real income remains constant. Consumers tend to substitute away from relatively more expensive goods towards cheaper alternatives. | | Income Effect | The change in the quantity demanded of a good resulting from a change in real income (purchasing power) caused by a price change. A rise in price reduces real income, typically leading to lower demand for normal goods. | | Preferences | The ranking or ordering of consumption bundles by a consumer based on their subjective satisfaction. Economists assume preferences are complete, transitive, and that more is generally preferred to less (non-satiation). | | Indifference Curve | A graphical representation showing all combinations of two goods that provide a consumer with the same level of utility or satisfaction. Moving along an indifference curve, the consumer is willing to trade one good for another while maintaining constant satisfaction. | | Marginal Rate of Substitution (MRS) | The rate at which a consumer is willing to trade one good for another while maintaining the same level of utility. It is represented by the absolute value of the slope of the indifference curve at a given point. Mathematically, $MRS_{XY} = -\Delta Y / \Delta X$. | | Convexity (of Indifference Curves) | The property where indifference curves typically bow inward towards the origin. This shape reflects a consumer's preference for a variety of goods, meaning they are willing to give up progressively larger amounts of one good to gain an additional unit of another as they consume more of the latter. | | Budget Constraint | A line or curve representing all possible combinations of goods that a consumer can purchase given their fixed income and the prices of those goods. Spending within or on the budget constraint is feasible; spending beyond it is not. | | Budget Line | A specific type of budget constraint, typically represented as a straight line, showing the maximum combinations of two goods a consumer can purchase when spending all of their income. Its slope represents the ratio of the prices of the two goods. | | Perfect Substitutes | Goods that can be used in place of each other in such a way that a consumer gains the same level of utility from consuming them, regardless of the proportion. Their indifference curves are linear, and the MRS is constant. | | Perfect Complements | Goods that must be consumed together in a fixed proportion to provide any additional utility. Their indifference curves are L-shaped, with the "kink" representing the optimal consumption ratio. |