Chapter Notes

Theory of Consumer Behaviour

In economics, we study how people make choices. For an individual consumer, the main challenge is deciding how to spend their limited income on various goods and services to get the most satisfaction possible. This is called the problem of choice.

What a consumer chooses depends on two main things:

1. Preferences: What the consumer likes or dislikes.
2. Budget: What the consumer can afford, which depends on their income and the prices of goods.

This chapter explores two main ways to understand consumer choices: Cardinal Utility Analysis and Ordinal Utility Analysis.

Preliminary Notations and Assumptions

To keep things simple, we'll assume the consumer is choosing between only two goods: bananas and mangoes.

• A combination of these two goods is called a consumption bundle.
• We'll use x₁ for the quantity of bananas and x₂ for the quantity of mangoes.
• A bundle is written as (x₁, x₂). For example, the bundle (5, 10) means 5 bananas and 10 mangoes.

Utility

When you decide to buy something, you do it because you expect to get some satisfaction, or utility, from it.

Utility is the want-satisfying capacity of a commodity. The more you need or want something, the more utility you get from it.

Utility is a subjective concept, meaning it's different for everyone. [!example] Someone who loves chocolate will get a lot of utility from a chocolate bar, while someone who doesn't like chocolate will get very little. Similarly, a room heater provides a lot of utility in Ladakh during winter but almost none in Chennai during summer.

Cardinal Utility Analysis

Cardinal Utility Analysis is an approach that assumes we can measure and express utility in numbers, or "units." For instance, you could say, "This shirt gives me 50 units of utility."

Measures of Utility

There are two key measures of utility:

• Total Utility (TU): This is the total satisfaction you get from consuming a certain quantity of a good. The more you consume, the higher your total utility. For example, the total utility of eating three bananas is the combined satisfaction from all three.
• Marginal Utility (MU): This is the additional satisfaction you get from consuming one more unit of a good.

The formula for marginal utility is: MUₙ = TUₙ - TUₙ₋₁ (Marginal utility of the nth unit = Total utility of n units - Total utility of n-1 units)

Total utility is simply the sum of all the marginal utilities up to that point: TUₙ = MU₁ + MU₂ + ... + MUₙ

Law of Diminishing Marginal Utility

A very important concept in economics is the Law of Diminishing Marginal Utility. This law states that as you consume more and more of a commodity, the marginal utility (or extra satisfaction) from each additional unit starts to decrease.

Why does this happen? Because as you get more of something, your desire for even more of it becomes weaker.

As you can see in the table:

• Total utility increases at first, but at a slower and slower rate.
• Marginal utility steadily decreases.
• At the 5th unit, TU is at its maximum (24), and MU is zero. This is the point of maximum satisfaction.
• At the 6th unit, TU actually starts to fall, and MU becomes negative. Consuming more at this point makes you worse off.

Derivation of Demand Curve (Law of Diminishing Marginal Utility)

The Law of Diminishing Marginal Utility helps explain why demand curves slope downwards.

Demand is the quantity of a commodity that a consumer is willing and able to buy at a certain price, given their income and preferences. A demand curve shows the relationship between the price of a good and the quantity a consumer is willing to buy.

Since each extra unit of a good gives you less marginal utility, you are willing to pay less for it. [!example] If you paid Rs. 40 for the 5th unit of a good, you won't be willing to pay Rs. 40 for the 6th unit because it gives you less satisfaction. You would only buy the 6th unit if the price drops.

This inverse relationship between price and quantity demanded is known as the Law of Demand.

Ordinal Utility Analysis

A major criticism of cardinal utility is that people don't really think in terms of "units" of satisfaction. In real life, we don't say "this apple gives me 20 utils." Instead, we rank our preferences. We might say, "I prefer an apple to an orange," but not by how much.

This is the basis of Ordinal Utility Analysis, which focuses on ranking bundles of goods in order of preference.

Indifference Curve

An indifference curve is a graph that shows all the different combinations of two goods that give a consumer the exact same level of satisfaction. The consumer is "indifferent" to any of these combinations.

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 is called the Marginal Rate of Substitution (MRS). It's the amount of one good (e.g., mangoes) a consumer must give up to get one additional unit of another good (e.g., a banana).

MRS = |ΔY / ΔX| (The amount of Good Y given up / The amount of Good X gained)

Law of Diminishing Marginal Rate of Substitution

As a consumer gets more and more of one good (bananas), they are willing to give up less and less of the other good (mangoes) to get one more banana. This is the Law of Diminishing Marginal Rate of Substitution.

In the table, to go from A to B, the consumer gives up 3 mangoes for 1 banana. From B to C, they only give up 2 mangoes. From C to D, just 1 mango. The MRS is diminishing.

Shape of an Indifference Curve for Perfect Substitutes

What if the goods are perfect substitutes? These are goods that can be used in place of each other and provide the exact same utility.

In this case, the MRS does not diminish; it stays constant. The indifference curve for perfect substitutes is a straight line.

Monotonic Preferences

Economists assume that consumers have monotonic preferences. This is a fancy way of saying "more is better." A consumer will always prefer a bundle that has more of at least one good and no less of the other.

For example, a consumer will always prefer the bundle (10, 10) over the bundle (9, 10) because it has more of the first good.

Indifference Map

A consumer's preferences for all possible bundles can be shown by a family of indifference curves, called an indifference map. Each curve represents a different level of utility. Because of monotonic preferences, bundles on higher indifference curves are always preferred to bundles on lower ones.

Features of Indifference Curves

1. Indifference curves slope downwards from left to right: To get more of one good, you must have less of the other to keep satisfaction constant.
2. Higher indifference curves represent higher utility: This is due to the "more is better" assumption of monotonic preferences.
3. Two indifference curves never intersect: If they did, it would lead to a logical contradiction. A single point of intersection would imply that two different levels of satisfaction are equal, which is impossible.

The Consumer's Budget

A consumer's choices are limited by their income and the prices of goods. They can only buy bundles they can afford.

Budget Set and Budget Line

• The budget set is the collection of all possible bundles of two goods that a consumer can afford with their income at the given market prices.
• The budget line represents all the bundles that a consumer can buy if they spend their entire income. Bundles below the line are affordable but don't use up all the income. Bundles above the line are unaffordable.

The equation for the budget line is: p₁x₁ + p₂x₂ = M (Price of good 1 × Quantity of good 1) + (Price of good 2 × Quantity of good 2) = Income

The slope of the budget line is -p₁/p₂. It tells us the rate at which the market requires you to trade one good for another.

Changes in the Budget Set

The budget set can change if income or prices change.

• Change in Income:
  • If income increases (and prices stay the same), the budget line shifts outward in a parallel way. The consumer can now afford more of both goods.
  • If income decreases, the budget line shifts inward.
• Change in Price:
  • If the price of one good (e.g., bananas) increases, the budget line pivots inward. The consumer can buy fewer bananas if they spend all their money on them, but the maximum amount of mangoes they can buy remains the same. The line becomes steeper.
  • If the price of one good decreases, the budget line pivots outward, becoming flatter.

Optimal Choice of the Consumer

So, how does a rational consumer choose the best bundle? They will choose the bundle from their budget set that gives them the maximum possible satisfaction.

This means the consumer will try to reach the highest possible indifference curve while staying on or below their budget line.

At this point of tangency:

• The slope of the indifference curve (MRS) is equal to the slope of the budget line (price ratio).
• MRS = p₁/p₂
• This means the rate at which the consumer is willing to trade one good for another (MRS) is exactly equal to the rate at which the market allows them to trade (the price ratio).

Any other point on the budget line would be on a lower indifference curve, providing less satisfaction. Any point on a higher indifference curve is unaffordable.

Demand

The consumer's optimal choice of a good depends on its price, the prices of other goods, the consumer's income, and their preferences. The relationship between the price of a good and the quantity the consumer optimally chooses is called the demand function.

Demand Curve and the Law of Demand

The demand curve is a graphical representation of the demand function. It shows the quantity of a good a consumer will buy at different prices, assuming other factors (income, other prices, tastes) remain constant.

Generally, when the price of a good falls, the consumer's optimal choice will involve buying more of it, and when the price rises, they will buy less. This negative relationship is the Law of Demand.

The Law of Demand can be explained by two effects of a price change:

1. Substitution Effect: When a good becomes cheaper, consumers substitute it for other, now relatively more expensive, goods.
2. Income Effect: When the price of a good falls, the consumer's purchasing power increases. They have more "real" income, which allows them to buy more of the good.

Normal and Inferior Goods

How demand changes with income depends on the type of good.

• Normal Goods: For most goods, as income increases, the demand for them also increases. These are normal goods.
• Inferior Goods: There are some goods for which demand decreases as income rises. These are inferior goods. As people get richer, they switch from these low-quality items to better alternatives. [!example] A person with a very low income might buy coarse cereals. If their income increases, they might reduce their consumption of coarse cereals and buy better quality grains instead.
• Giffen Goods: A special and rare type of inferior good where the income effect is so strong that it outweighs the substitution effect. For a Giffen good, when the price rises, the demand for it also rises, violating the Law of Demand.

Substitutes and Complements

The demand for a good is also affected by the prices of related goods.

• Substitutes: These are goods that can be used in place of each other, like tea and coffee. The demand for a good usually moves in the same direction as the price of its substitutes. If the price of coffee goes up, the demand for tea will likely increase.
• Complementary Goods: These are goods that are consumed together, like tea and sugar or shoes and socks. The demand for a good moves in the opposite direction of the price of its complements. If the price of sugar increases, the demand for tea will likely decrease.

Shifts in the Demand Curve vs. Movements along the Demand Curve

It's crucial to understand the difference between a "change in quantity demanded" and a "change in demand."

• Movement along the Demand Curve: This is caused only by a change in the price of the good itself. Moving from one point to another on the same curve.
• Shift in the Demand Curve: This is caused by a change in any other factor besides the good's own price (e.g., income, price of related goods, tastes). The entire curve moves to the right (an increase in demand) or to the left (a decrease in demand).

Market Demand

So far, we've looked at an individual consumer's demand. Market demand is the total demand of all consumers in the market for a good, taken together.

To find the market demand at a specific price, you simply add up the quantities demanded by each individual consumer at that price. Graphically, the market demand curve is the horizontal summation of all the individual demand curves.

Elasticity of Demand

The Law of Demand tells us that if price falls, quantity demanded will rise. But it doesn't tell us by how much. Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price.

The formula is: eᴅ = (Percentage change in quantity demanded) / (Percentage change in price)

Types of Price Elasticity

• Inelastic Demand (|eᴅ| < 1): The percentage change in quantity is less than the percentage change in price. Demand is not very responsive to price changes. This is common for necessities like food.
• Elastic Demand (|eᴅ| > 1): The percentage change in quantity is greater than the percentage change in price. Demand is highly responsive to price changes. This is common for luxury goods.
• Unitary-Elastic Demand (|eᴅ| = 1): The percentage change in quantity is exactly equal to the percentage change in price.

Elasticity along a Linear Demand Curve

On a straight-line (linear) demand curve, the elasticity is different at every point.

• At the top (where it hits the price axis), demand is perfectly elastic (∞).
• At the midpoint, demand is unitary-elastic (1).
• At the bottom (where it hits the quantity axis), demand is perfectly inelastic (0).

Constant Elasticity Demand Curves

Some demand curves have the same elasticity at all points:

• Perfectly Inelastic: A vertical line. Quantity demanded is the same regardless of price (|eᴅ| = 0).
• Perfectly Elastic: A horizontal line. Consumers will buy any amount at one price, but nothing at a higher price (|eᴅ| = ∞).
• Unitary Elastic: A rectangular hyperbola. The percentage change in price and quantity are always equal (|eᴅ| = 1).

Factors Determining Price Elasticity of Demand

1. Nature of the Good: Necessities tend to be inelastic, while luxuries are elastic.
2. Availability of Close Substitutes: If there are many good substitutes available, demand will be more elastic because consumers can easily switch if the price changes. If there are no close substitutes, demand will be inelastic.

Elasticity and Expenditure

Total expenditure on a good is simply Price × Quantity. How total expenditure changes when price changes depends on elasticity.

• If demand is inelastic (|eᴅ| < 1): Price and total expenditure move in the same direction. If price increases, total expenditure also increases.
• If demand is elastic (|eᴅ| > 1): Price and total expenditure move in opposite directions. If price increases, total expenditure decreases.
• If demand is unitary-elastic (|eᴅ| = 1): Total expenditure remains constant when the price changes.