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Monopoly single-price: marginal revenue & elasticity

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Intros
Lessons
  1. Monopoly Single-Price: Marginal Revenue & Elasticity Overview:
  2. Total Revenue & Demand Curve
    • Total Revenue: p × q
    • Deriving Total Revenue from Demand
    • Total Revenue curve
    • Quadratic function
  3. Marginal Revenue & Demand Curve
    • Finding Marginal Revenue from Total Revenue
    • Formula to Calculate Marginal Revenue
    • Graphing Marginal Revenue
  4. Elasticity & Marginal Revenue
    • Elastic Demand  \, →  \, MR > 0
    • Inelastic Demand  \, →  \, MR < 0
    • Unit Elastic Demand  \, →  \, MR = 0
    • In a Monopoly, Demand is always Elastic
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Examples
Lessons
  1. Use the following table to:

    Price (p)

    Quantity (q)

    6

    0

    5

    3

    4

    6

    3

    9

    2

    12

    1

    15

    0

    18
    1. Create a table of values for the total revenue curve
    2. Graph the total revenue curve.
  2. Use the following table to:

    Price (p)

    Quantity (q)

    6

    0

    5

    4

    4

    8

    3

    12

    2

    16

    1

    20

    0

    24
    1. Create a table of values for the total revenue curve
    2. Graph the total revenue curve.
  3. Finding the Marginal Revenue & Demand Curve
    Use the table of values of the total revenue curve to:

    Price (p)

    Total Revenue (R)

    0

    0

    5

    25

    10

    40

    15

    45

    20

    40

    25

    25

    30

    0
    1. Calculate the marginal revenue
    2. Graph the marginal revenue curve
  4. Suppose the demand curve is p = 6 - 2q
    1. Graph the demand curve
    2. Determine function of the marginal revenue curve.
    3. Graph the marginal revenue curve.
  5. Suppose the demand curve is p = 10 - 5q
    1. Graph the demand curve
    2. Determine function of the marginal revenue curve.
    3. Graph the marginal revenue curve.
  6. Learning the Relationship Between Elasticity & Marginal Revenue
    Fill in the blanks
    1. Elasticity   \, →  \, MR ______ 0   \, →  \, price cut   \, →  \, R_______.
    2. Inelasticity   \, →  \, MR ______ 0   \, →  \, price cut   \, →  \, R_______.
    3. Unit Elasticity   \, →  \, MR ______ 0   \, →  \, price cut   \, →  \, R_______.
  7. If a company is producing a good where the demand is elastic, then the owner should
    1. Decrease the price of the good.
    2. Keep the price the same.
    3. Increase the price of the good.
    4. Not enough information to determine what to do.
  8. If a company is producing a good where the demand is inelastic, then the owner should
    1. Decrease the price of the good.
    2. Keep the price the same.
    3. Increase the price of the good.
    4. Not enough information to determine what to do.
Topic Notes
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Total Revenue & Demand Curve


Since there is only one firm in a monopoly, the demand curve for the single firm is the market demand.

Total revenue & demand curve

Using the demand curve, we can calculate the total revenue curve.

Total Revenue: is the price multiplied by the quantity sold.

Total Revenue: price multiplied by quantity sold


Note: The total revenue curve is a quadratic function.

Marginal Revenue & Demand Curve

Using the total revenue, we can also find and graph the marginal revenue curve for single-price monopoly.

To calculate marginal revenue, we use the formula:

MR = △TR△q\large \frac{\triangle TR}{\triangle q}

Marginal revenue curve for single-price monopoly

Plotting the points with the demand curve together gives us the following graph:

Marginal revenue curve for single-price monopoly


Note: The MR curve can also be derived algebraically by multiplying the coefficient of the demand curve by 2.

Elasticity & Marginal Revenue

Marginal revenue is related to the elasticity of demand.

Marginal revenue is related to the elasticity of demand
  1. If demand is elastic, then 1% price cut increases the quantity sold by more than 1%. This causes marginal revenue is positive, and revenue will increase.

    2. Elastic  \, →  \, MR > 0  \, →  \, R  ↑ \, \uparrow \,

  2. If demand is inelastic, then 1% price cut increases the quantity sold by less than 1%. This causes marginal revenue is negative, and revenue will decrease.

    3. Inelastic  \, →  \, MR < 0  \, →  \, R  ↓ \, \downarrow \,

  3. If demand is unit elastic, then 1% price cut increase the quantity sold by 1%. This does not change the revenue. 

    4. Unit Elastic  \, →  \, MR = 0  \, →  \, R unchanged

Note: In a monopoly, the demand will always be elastic. The firm will never produce a huge quantity to sell at a low price. Instead, they would increase their price, and sell less quantities to increase profit.