elasticity

Economics 1A COECA1-22 Eduvos (Pty) Ltd

• Institution Information:
    - Eduvos (Pty) Ltd, formerly known as Pearson Institute of Higher Education.
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Week 2: Lesson 2 - Elasticity

• Learning Objectives:
    - Define price elasticity of demand and supply.
    - Calculate and interpret the following:
      - Price Elasticity of Demand (PED)
      - Cross Elasticity of Demand (XED)
      - Income Elasticity of Demand (YED)
      - Price Elasticity of Supply (PES)

Lesson Coverage

• Topics to be covered in this lesson:
    - Calculation of Price Elasticity of Demand.
    - Calculation of Cross Elasticity of Demand.
    - Calculation of Income Elasticity of Demand.
    - Calculation of Price Elasticity of Supply.
    - Interpret and explain results of the above calculations.

Elasticity (Responsiveness)

• The Law of Demand:
    - States that as the price decreases, the quantity demanded increases.

• Inquiry:
    - What happens when a supplier increases the price?
    - What factors influence the extent of quantity demanded changes?

• Price Elasticity of Demand (PED):
    - Definition: A measurement of responsiveness of quantity demanded to a change in price (ceteris paribus).
    - Significance: It shows the extent to which demand changes in reaction to price changes.
    - Formula for calculating PED:
      $\text{Price Elasticity of Demand (PED)} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

Calculation of Price Elasticity of Demand

• Formula Representation:
      \text{PED} = \frac{%\Delta Qd}{%\Delta P}

Interpreting Price Elasticity of Demand (PED)

• Two Key Aspects:
    1. The Sign
       - Generally negative due to the law of demand (increase in price leads to a decrease in quantity demanded).
    2. The Size
       - Determines the elasticity characteristics:
          - Inelastic Demand:
            - 0 < PED < 1           - $$         - Perfectly Inelastic Demand:           - $PED = 0$         - Unit Elastic Demand:           - $PED = 1$           - $$         - Elastic Demand:           - 1 < PED < \infty           - $$
          - Perfectly Elastic Demand:
            - $PED = \infty$
            - $$

Example Calculation of Price Elasticity of Demand

• Scenario:
    - Price of cola increased from R5 to R10, leading to quantity demanded declining from 30 cans to 20 cans per week.

• Calculation of Price Elasticity of Demand:
    - Calculate Percentage Change in Quantity Demanded:
      $\%\Delta Q_d = \frac{(20 - 30)}{(20 + 30)/2} = -0.333$
    - Calculate Percentage Change in Price:
      $\%\Delta P = \frac{(10 - 5)}{(10 + 5)/2} = 0.333$
    - Thus:
      $PED = \frac{-0.333}{0.333} = -1.0$
    - Since PED is < 1, demand is inelastic.

Pricing Example for Apples

• Data Summary:
    - Price per kilo of apples (cents): 30, 20, 10
    - Quantity of apples per week (kilograms): 3, 5
    - Question posed:
      - Calculate PED as price increases from 10 to 20 cents.

Cross Elasticity of Demand

• Definition:
    - Cross Elasticity of Demand (XED) measures the responsiveness of the demand for a good to a change in the price of another good.

• Formula:
      XED = \frac{% \Delta Q_d (Good 1)}{% \Delta P (Good 2)}

Interpreting Cross Elasticity of Demand

• Significance of the Sign:
    1. Positive XED indicates substitute goods.
       - Example: If price of one good increases, the demand for its substitute increases.
    2. Negative XED indicates complementary goods.
       - Example: If price of one good increases, the demand for its complement decreases.

Example Calculation of Cross Elasticity of Demand

• Scenario:
    - Airlines A and B each charge R1000, both have 200 tickets demanded. Airline A raises its price to R1050, resulting in airline A's quantity demanded dropping to 0 and airline B's tickets increasing to 400.

• Calculation:
    - XED = \frac{(% \Delta Q_d (B))}{(% \Delta P (A))}
    - Inputs:
      - $\%\Delta Q_d (B) = \frac{(400-200)}{(400+200)/2} = 1.0$
      - $\%\Delta P (A) = \frac{(1050-1000)}{(1050+1000)/2} = 0.095$
    - Thus:
      $XED = \frac{1.0}{0.095} \approx 10.53$

Income Elasticity of Demand

• Definition:
    - Income Elasticity of Demand (YED) measures the responsiveness of quantity demanded to a change in income.

• Formula:
      YED = \frac{% \Delta Q_d}{% \Delta Y}

• Income Elasticity Categories:
    - Greater than 1: Normal good, income elastic.
    - Positive but < 1: Normal good, income inelastic.
    - Negative: Inferior good.

Example Calculation of Income Elasticity of Demand

• Scenario:
    - If income rises by 20% and quantity of food demanded decreases by 10%.

• Calculation:
    - $YED = \frac{-10}{20} = -0.5$
    - Since YED is negative, food is considered an inferior good.

Elasticity of Supply

• Definition:
    - Elasticity of Supply measures the responsiveness of quantity supplied to a change in price.

• Formula:
      PES = \frac{% \Delta Q_s}{% \Delta P}

• Influential Factors:
    - Resource substitution possibilities.
    - Time frame for the supply decision.

Total Revenue and Elasticity

• Total Revenue Formula:
    - $R = P \times Q$

• Relationship Implications:
    - If demand is elastic:
      - A 1% price cut results in an increase in quantity sold greater than 1%, total revenue INCREASES.
    - If demand is inelastic:
      - A 1% price cut results in an increase in quantity sold less than 1%, total revenue DECREASES.
    - If demand is unit elastic:
      - A 1% price cut results in an increase in quantity sold by exactly 1%, total revenue STAYS THE SAME.