Law of Demand and Elasticity of Demand: Comprehensive Study Guide

Chapter Overview and Introduction to Business Economics

• The study of Theory of Demand and Supply is a foundational pillar of business economics, as market economies are governed by the interaction between buyers (demand) and sellers (supply). These two forces determine the price and quantity of goods and services sold.

• Business owners and managers face complex questions regarding product diversification and market positioning. For instance, Aroma Tea Limited CEO Rajeev Aggarwal asked marketing head Sanjeev Bhandari several critical questions before entering the green tea market:

  • What does the market pulse say and who are the competitors?

  • How will the demand for green tea affect black tea (substitution effect)?

  • Is the product a luxury or a necessity?

  • Will consumers of coffee or soft drinks shift to green tea?

• The answers to such questions reside in understanding the determinants of demand and how factors like weather, pandemics, or wars cause price fluctuations.

• Fundamental components of Market Mechanism:

  • Demand: Represents the behavior of buyers. Quantities purchased at a given price determine the market size.

  • Supply: Represents the behavior of sellers.

  • Interaction: The two determine the clearing price and quantity sold.

Meaning of Demand

• In Economics, Demand is distinct from a mere desire or wish. It refers to the quantity of a good or service that buyers are willing and able to purchase at various prices during a given period of time.

• Effective Demand must consist of three essential elements:

  1. Desire for the commodity.

  2. Means to purchase (Ability to pay/purchasing power).

  3. Willingness to use those means for the purchase.

• Key characteristics of quantity demanded:

  • It is always expressed at a given price.

  • It is a flow concept, not a single instance. It must be expressed per period of time (e.g., $1000$ dozen oranges per day).

• Formal Definition: "By demand, we mean the various quantities of a given commodity or service which consumers would buy in one market during a given period of time, at various prices, or at various incomes, or at various prices of related goods."

Determinants of Demand

• Price of the commodity: Under the principle of Ceteris Paribus (other things being equal), demand is inversely related to price. A rise in price leads to a fall in quantity purchased due to income and substitution effects.

• Price of related commodities:

  • Complementary Goods: Goods consumed together (e.g., tea and sugar, automobiles and petrol, printers and ink). There is an inverse relation between the demand for a good and the price of its complement. If the price of petrol cars falls, the demand for petrol rises.

  • Substitute (Competing) Goods: Goods that satisfy the same want (e.g., tea and coffee, ball pens and ink pens). There is a direct (positive) relation between the demand for a product and the price of its substitutes. If the price of tea falls, people substitute tea for coffee, causing coffee demand to fall.

• Disposable Income of the consumer:

  • Normal Goods: Demand increases as income increases (e.g., furniture, automobiles, clothing).

  • Inferior Goods: Demand rises up to a certain income level but decreases as income rises further because consumers switch to superior substitutes.

  • Necessities: Essential goods (food grains, fuel) show an increase in demand with income, but the increase is less than proportionate to the income rise.

  • Luxuries/Prestige Goods: Demand arises only beyond certain income thresholds and continues to rise with wealth.

• Tastes and Preferences:

  • Demand is higher for goods that are modern or in fashion.

  • Demonstration Effect: Termed by James Duesenberry; referring to the desire to emulate the consumption of others.

  • Bandwagon Effect: Purchasing a commodity because others are doing so to stay fashionable/stylish.

  • Snob Effect: A decrease in demand for a good because others are consuming it; a desire to be exclusive or different.

  • Veblen Effect: Named after Thorstein Veblen; high-priced goods (diamonds, luxury cars) are consumed by the rich for status/conspicuous consumption. Utility is measured by price.

• Consumer Expectations:

  • If consumers expect future price hikes, income increases, or supply shortages, current demand increases.

  • If expectations involve falling prices or incomes, current demand for non-essential goods falls.

• Other Factors:

  • Size of Population: Larger populations generally mean higher demand.

  • Age Distribution: An aging population increases demand for geriatric care/walking sticks; a younger population increases demand for baby food/toys.

  • National Income Distribution: Uneven distribution (few rich, many poor) leads to lower overall propensity to consume and lower demand for consumer goods. Equal distribution leads to higher aggregate demand.

  • Credit Facilities: Low interest rates and availability of credit induce higher demand for expensive durables.

  • Government Policy: Taxes increase prices (decreasing demand); subsidies decrease prices (increasing demand). Bans or regulations (e.g., on cigarettes) directly restrict demand.

The Demand Function

• The demand function is a symbolic statement expressing the relationship between quantity demanded (dependent variable) and its determinants (independent variables).

• A simple demand function is expressed as:     $Q_x = f(P_x, Y, P_r)$     Where:

  • $Q_x$ = Quantity demanded of product $X$

  • $P_x$ = Price of commodity $X$

  • $Y$ = Money income of the consumer

  • $P_r$ = Price of related goods

• An algebraic example of a specific demand function:     $Q_x = 45 + 2y + 1P_r - 2P$

The Law of Demand

• Prof. Alfred Marshall's Definition: "The greater the amount to be sold, the smaller must be the price at which it is offered in order that it may find purchasers or in other words the amount demanded increases with a fall in price and diminishes with a rise in price."

• The law states an inverse relationship between price and quantity demanded, assuming Ceteris Paribus (related prices, income, and tastes remain constant).

• Demand Schedule: A tabular representation of quantities demanded at different prices.

  • Example: Ice-cream demand at price $\text{Rs. } 60$ is $0$ cups; at $\text{Rs. } 0$ (free), it is $12$ cups.

• Demand Curve: A graphical presentation of the demand schedule.

  • Vertical axis ($Y$) = Price per unit.

  • Horizontal axis ($X$) = Quantity demanded per time period.

  • The slope is negative ($-\frac{\Delta P}{\Delta Q}$), indicating the inverse relationship.

  • Curves can be linear or curvilinear.

• Market Demand: The total quantity that all buyers in the market are willing to buy at a given price.

  • Market Demand Schedule: Obtained by adding individual quantities demanded (e.g., If Buyer A wants $3$ units and Buyer B wants $2$ units at price $0$, market demand is $5$).

  • Market Demand Curve: The horizontal summation (lateral summation) of all individual demand curves.

• Linear Demand Equation:     $Q = a - bP$     Where $a$ is the vertical intercept and $b$ is the slope.

Rationale of the Law of Demand

1. Price Effect (Substitution + Income Effects):

   • Substitution Effect: When a good's price falls, it becomes relatively cheaper than others, inducing buyers to substitute it for more expensive goods. This effect is stronger if goods are close substitutes and switching costs are low.

   • Income Effect: A fall in price increases the consumer's real income (purchasing power), allowing them to buy more of the good with the same money.

2. Utility Maximizing Behavior: Consumers reach equilibrium when Marginal Utility equals price ($MU = P$). Due to diminishing marginal utility, consumers will only buy additional units if the price is lowered.

3. New Consumers: A price fall allows lower-income consumers, who previously could not afford the product, to enter the market.

4. Different Uses: Commodities with multiple uses (e.g., electricity) are used only for essential purposes when prices are high, but for more varied purposes when prices fall.

Exceptions to the Law of Demand

• Conspicuous Goods (Veblen Effect): Prestige items (diamonds, luxury cars) become more attractive as their prices rise because they serve as status symbols.

• Giffen Goods: Named after Sir Robert Giffen. These are inferior goods with no close substitutes that occupy a large part of the consumer's budget. As the price of bread rose for British workers, they bought more of it because it was still the cheapest option compared to meat.

• Conspicuous Necessities: Goods like TVs or refrigerators that become perceived necessities due to social group consumption patterns, causing demand to persist despite rising prices.

• Future Price Expectations: If households expect prices to rise further (e.g., during a drought), they demand more even as prices increase currently.

• Irrationality/Incomplete Information: Consumers may impulsively buy at high prices or assume high price equates to high quality.

• Necessaries of Life: Minimum quantities of basic goods (salt, essential food) must be consumed regardless of price.

• Speculative Goods: In stock markets, rising prices often lead to more demand as buyers expect further gains.

Movements vs. Shifts in Demand

• Expansion and Contraction of Demand:

  • Caused only by a change in the price of the commodity itself, while other factors remain constant.

  • Expansion: Quantity demanded increases due to a fall in price (downward movement on the same curve).

  • Contraction: Quantity demanded decreases due to a rise in price (upward movement on the same curve).

• Increase and Decrease in Demand:

  • Caused by changes in non-price factors (income, tastes, related prices).

  • The entire demand curve shifts.

  • Increase: Curve shifts to the right. More is demanded at each price (e.g., due to a rise in income for normal goods).

  • Decrease: Curve shifts to the left. Less is demanded at each price (e.g., due to a rise in the price of a complement).

Price Elasticity of Demand (PED)

• Elasticity measures the degree of responsiveness of quantity demanded to a change in a determinant variable.

• Formula:     E_p = \frac{\text{% change in quantity demanded}}{\text{% change in price}}

• Symbolic Equation:     $E_p = \frac{\Delta q}{q} \times \frac{p}{\Delta p}$

• Types of Price Elasticity:

  1. Perfectly Inelastic ($E_p = 0$): Quantity demanded does not change at all regardless of price. Curve is vertical.

  2. Inelastic (0 < E_p < 1): % change in quantity is smaller than % change in price. Curve is steep. (e.g., wheat, salt).

  3. Unitary Elastic ($E_p = 1$): % change in quantity equals % change in price. Curve is a rectangular hyperbola.

  4. Elastic (1 < E_p < \infty): % change in quantity is larger than % change in price. Curve is flat. (e.g., headphones, TVs).

  5. Perfectly Elastic ($E_p = \infty$): Buyers will buy everything at one price, but nothing if the price rises slightly. Curve is horizontal. (Occurs in perfect competition).

Methods to Measure Elasticity

• Point Elasticity: Used for infinitesimal changes in price. Measured as the product of the price-quantity ratio and the reciprocal of the slope.

  • Geometric Method on a linear curve: $E_p = \frac{\text{Lower segment (RT)}}{\text{Upper segment (Rt)}}$.

  • Elasticity is $\infty$ at the vertical intercept, $1$ at the midpoint, and $0$ at the horizontal intercept.

• Arc Elasticity: Used for discrete/large price changes between two points. It uses the midpoint method to ensure consistency regardless of direction.

  • Formula: $E_p = \frac{q_2 - q_1}{q_2 + q_1} \times \frac{p_2 + p_1}{p_2 - p_1}$

• Total Outlay Method: Analyzes changes in total expenditure ($\text{Price} \times \text{Quantity}$).

  • If Price $\uparrow$ and Total Revenue ($TR$) remains same: $E_p = 1$.

  • If Price $\uparrow$ and $TR \downarrow$: E_p > 1 (Elastic).

  • If Price $\uparrow$ and $TR \uparrow$: E_p < 1 (Inelastic).

Determinants of Price Elasticity

• Substitutes: More substitutes leads to higher elasticity (e.g., specific tea brands). Single brands are more elastic than generic product categories (e.g., Indian Oil petrol vs. petrol in general).

• Budget Share: Goods taking a large share of income (rent, clothing) are more elastic than minor items (matches, salt).

• Nature of Need: Luxuries (Home theatre) are elastic; necessities (food, housing) are inelastic.

• Number of Uses: More uses (milk, electricity) lead to higher elasticity.

• Time Period: Demand is more elastic in the long run as consumers find substitutes or change habits (e.g., buying a more fuel-efficient car over time).

• Consumer Habits: Habitual consumption (addiction) makes demand inelastic.

• Tied Demand: Goods used with others (ink cartridges for printers) have inelastic demand.

Income Elasticity of Demand ($E_i$)

• Measures responsiveness of demand to changes in consumer income.

• Equation:     $E_i = \frac{\Delta Q}{Q} \times \frac{Y}{\Delta Y}$

• Values and Interpretations:

  • Positive (E_i > 0): Normal Goods.

  • Greater than One (E_i > 1): Luxury goods; spending increases faster than income.

  • Less than One (0 < E_i < 1): Necessities; spending increases slower than income (e.g., wheat).

  • Zero ($E_i = 0$): Demand is unresponsive to income (e.g., buttons).

  • Negative (E_i < 0): Inferior goods (e.g., bajra, used cars).

Cross-Price Elasticity of Demand ($E_c$)

• Measures how demand for Good $X$ changes in response to the price of Good $Y$.

• Equation:     $E_c = \frac{\Delta q_x}{\Delta p_y} \times \frac{p_y}{q_x}$

• Classifications:

  • Substitutes: $E_c$ is positive. Large positive values indicate close substitutes (e.g., Royal vs. Imperial notebooks).

  • Complements: $E_c$ is negative. Very low negative values indicate strong complements (e.g., tea and sugar).

  • Unrelated Goods: $E_c = 0$.

Advertisement Elasticity ($E_a$)

• Also called promotional elasticity; measures the effectiveness of advertising spending on sales.

• Formula:     $E_a = \frac{\% \text{ Change in quantity demanded}}{\% \text{ Change in advertisement spending}}$     $E_a = \frac{\Delta Q_d}{Q_d} \times \frac{A}{\Delta A}$

• Interpretations:

  • $E_a = 0$: No response to ads.

  • E_a > 1: Demand increases at a higher rate than ad spending.

• Helps managers determine the optimum level of advertisement expenditure.

Questions & Discussion

• Scenario Study: A shopkeeper sells Imperial and Royal notebooks. Price of Imperial rises by $10\%$, demand for Royal rises by $15\%$.

  • Calculation: $E_c = \frac{15\%}{10\%} = +1.5$.

  • Conclusion: Significant substitutability.

• Calculations on Quantity: A consumer buys $80$ units at $\text{Rs. } 4$. If $E_d = -4$, at what price will he buy $60$ units?

  • Solution: Using $E_d = \frac{\Delta q}{q} \times \frac{p}{\Delta p}$, we find $-4 = \frac{-20}{80} \times \frac{4}{x - 4}$. Solving for $x$ gives $\text{Rs. } 4.2$.

• Data on New vs Used Cars: Real incomes rise by $10\%$. New car sales rise from $400$ to $500$ ($+25\%$). Used car sales fall from $4000$ to $3850$ ($-3.75\%$).

  • Result: New car $E_i = \frac{25}{10} = +2.5$ (Normal/Elastic). Used car $E_i = \frac{-3.75}{10} = -0.375$ (Inferior).