Chapter 2 Theory Of Consumer Behaviour

Utility

Consumers aim to maximize their satisfaction by deciding how to spend their income on various goods. This involves understanding their preferences and what they can afford.

Cardinal Utility Analysis

This approach quantifies the satisfaction a consumer derives from a good, assigning numerical values to utility levels. It assumes that utility can be measured precisely.

Measures Of Utility

Total Utility (TU): The aggregate satisfaction gained from consuming a specific quantity of a good. As more of a good is consumed, total utility generally increases.

Marginal Utility (MU): The additional satisfaction obtained from consuming one more unit of a good. It is calculated as the change in total utility divided by the change in quantity ($ MU = TU_n - TU_{n-1} $). Marginal utility typically diminishes with increased consumption, a concept known as the Law of Diminishing Marginal Utility.

The relationship between Total Utility and Marginal Utility is that Total Utility is the sum of all Marginal Utilities: $ TU_n = MU_1 + MU_2 + \dots + MU_n $. Typically, marginal utility decreases as consumption increases, causing total utility to rise at a diminishing rate. When marginal utility is zero, total utility is at its maximum. If marginal utility becomes negative, total utility starts to decline.

Derivation Of Demand Curve In The Case Of A Single Commodity (Law Of Diminishing Marginal Utility)

The Law of Diminishing Marginal Utility explains why demand curves slope downwards. As a consumer consumes more units of a good, the additional satisfaction (marginal utility) derived from each successive unit decreases. Consequently, the consumer is willing to pay less for each additional unit. This inverse relationship between price and quantity demanded forms the basis of the demand curve.

Ordinal Utility Analysis

This approach acknowledges that consumers may not be able to assign numerical values to their satisfaction. Instead, they can rank different combinations of goods based on their preferences. This analysis focuses on the relative satisfaction derived from various bundles of goods.

Shape Of An Indifference Curve

An indifference curve represents all the combinations of two goods that provide a consumer with the same level of satisfaction. Indifference curves are typically convex to the origin, reflecting the Law of Diminishing Marginal Rate of Substitution (MRS). MRS is the rate at which a consumer is willing to trade one good for another to maintain the same level of satisfaction. As a consumer has more of one good, they are willing to give up less of the other to gain an additional unit of the first, due to diminishing marginal utility of the good being consumed more.

When goods are perfect substitutes, the indifference curves are straight lines, indicating a constant MRS.

Monotonic Preferences

Monotonic preferences imply that a consumer will always prefer a bundle that contains more of at least one good and no less of the other, compared to another bundle. This means consumers always prefer more to less.

Indifference Map

An indifference map is a collection of several indifference curves, representing a consumer's preferences for various bundles of goods. Higher indifference curves indicate higher levels of satisfaction.

Features Of Indifference Curve

1. Downward Sloping: Indifference curves slope downwards from left to right. To consume more of one good, a consumer must give up some of the other good to maintain the same level of satisfaction.
2. Higher Indifference Curve = Greater Utility: As long as marginal utility is positive, a consumer will always prefer bundles on higher indifference curves, as they offer greater satisfaction.
3. Indifference Curves Do Not Intersect: Two indifference curves cannot intersect. If they did, it would imply that a single bundle provides two different levels of satisfaction, which is a contradiction.

The Consumer’S Budget

Consumers operate within the constraints of their income and the prices of goods. The budget set and budget line define the combinations of goods a consumer can afford.

Budget Set And Budget Line

Budget Constraint: The limitation imposed by the consumer's income (M) and the prices of goods ($p_1$ for good 1 and $p_2$ for good 2). The constraint is represented by the inequality $ p_1x_1 + p_2x_2 \leq M $, where $x_1$ and $x_2$ are the quantities of the two goods.

Budget Set: The collection of all possible bundles of goods that a consumer can afford given their income and the prevailing prices. This includes all combinations satisfying the budget constraint.

Budget Line: A graphical representation of all the bundles that a consumer can purchase if they spend their entire income ($ p_1x_1 + p_2x_2 = M $). It represents the trade-off between the two goods.

Price Ratio And The Slope Of The Budget Line

The slope of the budget line is determined by the ratio of the prices of the two goods ($-\frac{p_1}{p_2}$). This ratio represents the rate at which the market allows the consumer to substitute one good for another. The absolute value of the slope ($|\frac{p_1}{p_2}|$) signifies the market's trade-off rate, or how many units of good 2 must be given up to obtain one additional unit of good 1.

Changes In The Budget Set

Changes in consumer income or the prices of goods alter the budget set:

• Change in Income: An increase in income shifts the budget line outwards (parallel shift), allowing the consumer to afford more of both goods. A decrease in income shifts it inwards.
• Change in Price: A change in the price of one good, while income and the other good's price remain constant, causes the budget line to pivot. An increase in price makes the line steeper and shifts the intercept of that good inwards, while a decrease in price makes it flatter and shifts the intercept outwards.

Optimal Choice Of The Consumer

A rational consumer aims to maximize their satisfaction by choosing the most preferred bundle from their budget set. This optimal choice occurs where the consumer's preferences (indifference curve) align with their purchasing power (budget line).

Equality Of The Marginal Rate Of Substitution And The Ratio Of The Prices

The optimal consumption bundle for a consumer is found at the point where the budget line is tangent to the highest possible indifference curve. At this point of tangency, the Marginal Rate of Substitution (MRS) equals the price ratio ($ MRS = \frac{p_1}{p_2} $). This signifies that the consumer's willingness to trade goods matches the market's trade-off rate, leading to the greatest attainable satisfaction.

Demand

Demand refers to the quantity of a good that a consumer is willing and able to purchase at various prices, given their income, preferences, and the prices of related goods.

Functions

A function describes a relationship where each input value corresponds to exactly one output value. In economics, demand functions express the relationship between the quantity demanded of a good and its determinants, such as price, income, and prices of related goods.

Answer:

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An increasing function's graph slopes upwards, while a decreasing function's graph slopes downwards. In economics, demand curves are typically plotted with price on the vertical axis and quantity on the horizontal axis, showing a downward slope.

Demand Curve And The Law Of Demand

The Law of Demand states that, ceteris paribus (all other factors remaining constant), as the price of a good falls, the quantity demanded increases, and as the price rises, the quantity demanded falls. The demand curve is a graphical representation of this inverse relationship between price and quantity demanded.

Deriving A Demand Curve From Indifference Curves And Budget Constraints

A demand curve can be derived by observing how a consumer's optimal choice changes when the price of a good varies, while income and the price of the other good remain constant. Each price-quantity combination identified from these optimal choices forms a point on the demand curve.

When the price of a good decreases, the budget line pivots outward, allowing the consumer to reach a higher indifference curve. This leads to an increase in the consumption of the cheaper good. This relationship forms the downward-sloping demand curve.

Normal And Inferior Goods

• Normal Goods: For these goods, demand increases as consumer income rises and decreases as income falls. The demand moves in the same direction as income.
• Inferior Goods: For these goods, demand decreases as consumer income rises and increases as income falls. The demand moves in the opposite direction of income.

A good can be normal at lower income levels and inferior at higher income levels.

Substitutes And Complements

• Substitutes: Goods that can be used in place of each other. An increase in the price of a substitute good leads to an increase in the demand for the other good (e.g., tea and coffee).
• Complements: Goods that are consumed together. An increase in the price of a complementary good leads to a decrease in the demand for the other good (e.g., tea and sugar).

Shifts In The Demand Curve

A shift in the demand curve occurs when factors other than the price of the good itself change. These factors include:

• Income: An increase in income shifts the demand curve for normal goods to the right and for inferior goods to the left.
• Prices of Related Goods: An increase in the price of a substitute shifts the demand curve to the right; an increase in the price of a complement shifts it to the left.
• Tastes and Preferences: Favorable changes shift the curve rightward; unfavorable changes shift it leftward.

Movements Along The Demand Curve And Shifts In The Demand Curve

Movement along the demand curve occurs due to a change in the price of the good itself. This is a change in quantity demanded.

Shift in the demand curve occurs due to changes in factors other than the price of the good (income, prices of related goods, tastes, etc.). This represents a change in demand.

Market Demand

Market demand is the aggregate demand for a good from all consumers in the market. It is derived by summing up the individual demands at each price level. Graphically, this is achieved through horizontal summation of individual demand curves.

Adding Up Two Linear Demand Curves

To find the market demand when there are multiple consumers, their individual demand quantities at each price are added together. For linear demand curves, this summation process can be done algebraically or graphically.

Elasticity Of Demand

Elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. It indicates how much demand will change for a given percentage change in price.

Elasticity Along A Linear Demand Curve

On a linear demand curve, price elasticity of demand varies at different points. It is calculated as the ratio of the percentage change in quantity demanded to the percentage change in price. The formula is $ e_D = \frac{\% \Delta Q}{\% \Delta P} $ or $ e_D = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} $.

The elasticity can be different at various points on the curve: elastic ($|e_D| > 1$), inelastic ($|e_D| < 1$), or unit elastic ($|e_D| = 1$).

Constant Elasticity Demand Curve

Some demand curves exhibit constant elasticity at all points:

• Perfectly Inelastic Demand (Vertical Demand Curve): Elasticity is 0. Quantity demanded does not change regardless of price.
• Perfectly Elastic Demand (Horizontal Demand Curve): Elasticity is infinite. Any price increase leads to zero demand, and at a specific price, demand is unlimited.
• Unit Elastic Demand (Rectangular Hyperbola): Elasticity is always 1. A percentage change in price is exactly offset by an equal percentage change in quantity demanded.

Geometric Measure Of Elasticity Along A Linear Demand Curve

The elasticity at any point on a straight-line demand curve can be measured geometrically as the ratio of the segment of the demand curve below the point to the segment above the point.

Factors Determining Price Elasticity Of Demand For A Good

• Availability of Close Substitutes: Goods with many close substitutes tend to have more elastic demand.
• Nature of the Good: Necessities generally have inelastic demand, while luxuries have elastic demand.
• Proportion of Income Spent: Goods that constitute a large portion of income tend to have more elastic demand.
• Time Horizon: Demand tends to be more elastic over longer periods as consumers have more time to adjust their consumption patterns.

Elasticity And Expenditure

The relationship between price changes and total expenditure on a good depends on the price elasticity of demand:

• Elastic Demand ($|e_D| > 1$): An increase in price leads to a decrease in total expenditure, and a decrease in price leads to an increase in total expenditure.
• Inelastic Demand ($|e_D| < 1$): An increase in price leads to an increase in total expenditure, and a decrease in price leads to a decrease in total expenditure.
• Unit Elastic Demand ($|e_D| = 1$): Total expenditure remains unchanged when the price changes.

Rectangular Hyperbola

A demand curve that is a rectangular hyperbola ($pq = c$) has a constant elasticity of 1 at all points. This means that total expenditure on the good remains constant regardless of price changes.