# 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.

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

Total Revenue: is the price multiplied by the 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 = $\large \frac{\triangle TR}{\triangle q}$

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

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.

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

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