Monopoly single-price: marginal revenue & elasticity

Monopoly single-price: marginal revenue & elasticity

Lessons

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 = TRq\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 \,

  3. 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.

  4. Inelastic \, \, MR < 0 \, \, R \, \downarrow \,

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

  6. 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.
  • Introduction
    Monopoly Single-Price: Marginal Revenue & Elasticity Overview:
    a)
    Total Revenue & Demand Curve
    • Total Revenue: p × q
    • Deriving Total Revenue from Demand
    • Total Revenue curve
    • Quadratic function

    b)
    Marginal Revenue & Demand Curve
    • Finding Marginal Revenue from Total Revenue
    • Formula to Calculate Marginal Revenue
    • Graphing Marginal Revenue

    c)
    Elasticity & Marginal Revenue
    • Elastic Demand \, \, MR > 0
    • Inelastic Demand \, \, MR < 0
    • Unit Elastic Demand \, \, MR = 0
    • In a Monopoly, Demand is always Elastic