# Monopoly single-price: marginal revenue & elasticity #### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. #### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. #### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! ##### 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
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 $\,$$\,$ MR = 0
• In a Monopoly, Demand is always Elastic
##### Examples
###### Lessons
1. Use the following table to:
 Price (p) Quantity (q) 6 0 5 3 4 6 3 9 2 12 1 15 0 18
1. Create a table of values for the total revenue curve
2. Graph the total revenue curve.
2. Use the following table to:
 Price (p) Quantity (q) 6 0 5 4 4 8 3 12 2 16 1 20 0 24
1. Create a table of values for the total revenue curve
2. Graph the total revenue curve.
3. Finding the Marginal Revenue & Demand Curve
Use the table of values of the total revenue curve to:
 Price (p) Total Revenue (R) 0 0 5 25 10 40 15 45 20 40 25 25 30 0
1. Calculate the marginal revenue
2. Graph the marginal revenue curve
4. Suppose the demand curve is p = 6 - 2q
1. Graph the demand curve
2. Determine function of the marginal revenue curve.
3. Graph the marginal revenue curve.
5. Suppose the demand curve is p = 10 - 5q
1. Graph the demand curve
2. Determine function of the marginal revenue curve.
3. Graph the marginal revenue curve.
6. Learning the Relationship Between Elasticity & Marginal Revenue
Fill in the blanks
1. Elasticity $\,$$\,$ 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
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.