Elasticity

Chapter 4: Elasticity

Chapter Objectives

To explain the concept of elasticities.
To calculate elasticities of demand (price, income, and cross) and elasticity of supply.

Definition of Elasticity

Elasticity measures the responsiveness/sensitivity of quantity demanded or quantity supplied due to changes in its determinants.

Elasticity of Demand

Measures the responsiveness/sensitivity of quantity demanded due to changes in its determinants.
Three types:
- Price elasticity of demand
- Income elasticity of demand
- Cross elasticity of demand

Price Elasticity of Demand ( $\varepsilon_d$ )

Definition: Measures the sensitivity/responsiveness of the quantity demanded due to a change in its price.
Formula:
- $\varepsilon_d = \frac{\% \Delta \text{ Quantity Demanded}}{\% \Delta \text{ Price}}$
- $\varepsilond = \frac{Q2 – Q1}{Q1} \times \frac{P1}{P2 – P_1}$
 - Where:
 - $Q_1$ = Original Quantity Demanded
 - $Q_2$ = New Quantity Demanded
 - $P_1$ = Original Price
 - $P_2$ = New Price
- Note: Negative coefficient value turns into positive.

Degree of Price Elasticity

Elastic Demand: A small percentage change in price leads to a larger percentage change in quantity demanded. \varepsilon_d > 1
Inelastic Demand: A large percentage change in price leads to a small percentage change in quantity demanded. \varepsilon_d < 1
Unitary Elastic Demand: Percentage changes in price equal percentage changes in quantity demanded. $\varepsilon_d = 1$
Perfectly Inelastic Demand: Quantity demanded does not change as the price changes. $\varepsilon_d = 0$
Perfectly Elastic Demand: A small percentage change in price leads to an infinite percentage change in quantity demanded. $\varepsilon_d = \infty$

5 Degrees of Price Elasticity of Demand

Elasticity	Degree of Elasticity	% Changes	Interpretation
\varepsilon_d > 1	Elastic	\Delta\%P < \Delta\%Q	A smaller % change in the price of a product will lead to a bigger % change in Qd
\varepsilon_d < 1	Inelastic	\Delta\%P > \Delta\%Q	A bigger % change in the price of a product will lead to a smaller % change in Qd
$\varepsilon_d = 1$	Unitary elastic	$\Delta\%P = \Delta\%Q$	A % change in price equals a % change in Qd
$\varepsilon_d = 0$	Perfectly inelastic	$\Delta\%Q = 0$	The Qd does not change even though the price changes.
$\varepsilon_d = \infty$	Perfectly elastic	$\Delta\%P = 0$	A small % change in price leads to an infinite % change in Qd

Income Elasticity of Demand ( $\varepsilon_Y$ )

Definition: Measures the sensitivity/responsiveness of the quantity demanded due to a change in income.
Formula:
- $\varepsilon_Y = \frac{\% \Delta \text{ Quantity Demanded}}{\% \Delta \text{ Income}}$
- $\varepsilonY = \frac{Q2 – Q1}{Q1} \times \frac{Y1}{Y2 – Y_1}$
 - Where:
 - $Q_1$ = Original Quantity Demanded
 - $Q_2$ = New Quantity Demanded
 - $Y_1$ = Original Income Level
 - $Y_2$ = New Income Level

Responses of Income Elasticity

\varepsilon_y < 0: Negative Income Elasticity
- Type of good: Giffen/Inferior goods (e.g., used car and low-grade potatoes)
0 < \varepsilon_y < 1: Inelastic Income
- Type of good: Normal goods (e.g., food and clothing)
$\varepsilon_y = 0$ : Zero Income Elasticity
- Type of good: Necessity Goods (e.g., rice and vegetables)
\varepsilon_y > 1: Elastic Income
- Type of good: Luxury goods (e.g., antique furniture and diamonds)

Income Elasticity of Demand ( $\varepsilon_Y$ ) - Examples

Elasticity	Interpretation	Examples
\varepsilon_y > 1	Luxury goods	Diamonds, luxury cars
0< \varepsilon_y < 1	Normal goods	Shirt, shoes, pen
$\varepsilon_y = 0$	Necessities goods	Rice, vegetables
\varepsilon_y < 0	Inferior/giffen goods	Used car, low-grade fruits

Cross Elasticity of Demand

Definition: Measures the sensitivity/responsiveness of the quantity demanded of one product due to a change in the price of a related product.
Formula:
- $\varepsilon_X = \frac{\% \Delta \text{ Quantity Demanded of good X}}{\% \Delta \text{ Price of good Y}}$
- $\varepsilonx = \frac{Q{x2} – Q{x1}}{Q{x1}} \times \frac{P{y1}}{P{y2} – P_{y1}}$

Responses of Cross Elasticity

\varepsilon_x < 0: Negative Cross Elasticity
- Good X and Y are complementary goods.
\varepsilon_x > 0: Positive Cross Elasticity
- Good X and Y are substitute goods.
$\varepsilon_x = 0$ : Zero Cross Elasticity
- Good X and Y have no relationship.

Cross Elasticity of Demand - Interpretation

Elasticity	Interpretation
\varepsilon_x > 0	Substitute goods
\varepsilon_x < 0	Complementary goods
$\varepsilon_x = 0$	Not related goods

Price Elasticity of Supply ( $\varepsilon_s$ )

Definition: Measures the sensitivity/responsiveness of the quantity supplied due to a change in its price.
Formula:
- $\varepsilon_{ss} = \frac{\% \Delta \text{ Quantity Supplied}}{\% \Delta \text{ Price}}$
- $\varepsilon{ss} = \frac{Q2 – Q1}{Q1} \times \frac{P1}{P2 – P_1}$
 - Where:
 - $Q_1$ = Original Quantity Supplied
 - $Q_2$ = New Quantity Supplied
 - $P_1$ = Original Price Level
 - $P_2$ = New Price Level

Degree of Price Elasticity of Supply

Elastic Supply: A small percentage change in price leads to a larger percentage change in quantity supplied. \varepsilon_{ss} > 1
Inelastic Supply: A large percentage change in price leads to a small percentage change in quantity supplied. \varepsilon_{ss} < 1
Unitary Elastic Supply: Percentage change in price equals the percentage change in the quantity supplied. $\varepsilon_{ss} = 1$
Perfectly Inelastic Supply: A percentage change in price has no effect on the percentage change in the quantity supplied. $\varepsilon_{ss} = 0$
Perfectly Elastic Supply: An almost zero percentage change in price brings a very large percentage change in the quantity supplied. $\varepsilon_{ss} = \infty$

Degrees of Price Elasticity of Supply

Elasticity	Interpretation	Diagram
\varepsilon_p > 1	Elastic supply	A smaller % change in the price of a product will lead to a bigger % change in the Qs
\varepsilon_p < 1	Inelastic supply	A bigger % change in the price of a product will lead to a smaller % change in the Qs
$\varepsilon_p = 1$	Unitary elastic	A % change in price equals a % change in Qs
$\varepsilon_p = \infty$	Perfectly elastic supply	A small % change in price leads to an infinite % change in Qs
$\varepsilon_p = 0$	Perfectly inelastic	The Qs does not change even though the price changes.

Determinants of Price Elasticity of Demand

Existence of Substitutes: Goods with more substitutes have more elastic demand compared to goods with fewer substitutes.
Complementary Goods: Goods that are used together normally have more inelastic demand.
Importance of the good: Demand for necessity goods is inelastic compared to demand for less essential goods.
Income level: Higher-income consumers tend to have inelastic demand because they become less sensitive to price changes.
Time dimensions for purchase: The shorter the period to decide on buying, the more inelastic the demand for the goods.
Habits: When people develop habits around certain goods or services, their demand becomes more inelastic.
Proportion of the good in one’s budget share: Goods that take a higher portion of a consumer’s expenditure or budget will have more elastic demand compared to goods that take a smaller portion.

Determinants of Price Elasticity of Supply

Period of the production process: If the production process takes a longer time to complete, then the response to price change will be small (inelastic).
Time frame to decide on selling: The shorter the time period to decide on selling, the more inelastic will be supply.
Availability and mobility of input for production: When inputs required for production are readily available (e.g., labor, raw materials), producers can easily adjust production levels in response to changes in market conditions. Therefore, more elastic.
Degree of Perishability: If the product is easily damaged or has a short expiration date, then the supply will be inelastic.
Technology Advancement: If more advanced technology is used in production, supply will be more elastic since producers can easily respond to price changes.
Nature of market: If the producer has multiple markets for its product, supply will be more elastic. OR if the market has a low barrier to entry, the supply will be more elastic.

Price Elasticity of Demand ( $E_d$ ) & Relation to Total Revenue (TR)

$TR = P \text{ (price)} \times Q \text{ (quantity)}$
Sellers can adjust their selling price depending on the price elasticity of demand for their product.
DD is elastic: Change in Q > change in P, therefore TR follows the direction of Q.
DD is inelastic: Change in Q < change in P. Therefore, TR follows the direction of P.
DD is Unitary elastic

Examples

Elastic demand: Change in Q > change in P, therefore TR follow the direction of Q
- $P0$ = 5, $Q0$ = 20, $TR$ = 100
- $P1$ = 6, $Q1$ = 10, $TR$ = 60
Inelastic Demand: Change in Q < change in P. Therefore, TR follows the direction of P.
- $P0$ = 5, $Q0$ = 10, $TR$ = 50
- $P1$ = 8, $Q1$ = 8, $TR$ = 64
Unitary elastic
- $P0$ = 3, $Q0$ = 4, $TR$ = 12
- $P1$ = 4, $Q1$ = 3, $TR$ = 12

Elasticity

Chapter 4: Elasticity

Chapter Objectives

Definition of Elasticity

Elasticity of Demand

Price Elasticity of Demand (εd\varepsilon_dεd​)

Degree of Price Elasticity

5 Degrees of Price Elasticity of Demand

Income Elasticity of Demand (εY\varepsilon_YεY​)

Responses of Income Elasticity

Income Elasticity of Demand (εY\varepsilon_YεY​) - Examples

Cross Elasticity of Demand

Responses of Cross Elasticity

Cross Elasticity of Demand - Interpretation

Price Elasticity of Supply (εs\varepsilon_sεs​)

Degree of Price Elasticity of Supply

Degrees of Price Elasticity of Supply

Determinants of Price Elasticity of Demand

Determinants of Price Elasticity of Supply

Price Elasticity of Demand (EdE_dEd​) & Relation to Total Revenue (TR)

Examples

Price Elasticity of Demand ( $\varepsilon_d$ )

Income Elasticity of Demand ( $\varepsilon_Y$ )

Income Elasticity of Demand ( $\varepsilon_Y$ ) - Examples

Price Elasticity of Supply ( $\varepsilon_s$ )

Price Elasticity of Demand ( $E_d$ ) & Relation to Total Revenue (TR)