Overview
This lecture explains how to calculate and interpret marginal revenue for a monopolist, using algebraic methods and graphical analysis, without calculus.
Marginal Revenue Concept
- Marginal revenue (MR) is the change in total revenue from selling one more unit of a good.
- When quantity is 0, total revenue is 0.
- MR can be approximated by dividing the change in total revenue by the change in quantity for very small increases.
Calculating Marginal Revenue (Without Calculus)
- For Q = 0 to Q = 0.001, MR ≈ 6 (using the equation TR = -Q² + 6Q).
- The smaller the change in Q, the more accurate the approximation (approaches calculus’ derivative).
- For Q = 1, MR ≈ $4 per unit (using slope between Q = 0 and Q = 2).
- For Q = 2, MR ≈ $2 per unit (using slope between Q = 1 and Q = 3).
- At Q = 3, MR = 0, meaning total revenue is maximized.
- For Q > 3, MR becomes negative.
Characteristics of Marginal Revenue Curve
- MR curve is a straight line with twice the negative slope of the demand curve if demand is linear.
- Example: If demand curve’s slope is -1, MR curve’s slope is -2.
- MR curve falls faster than the demand curve.
Relationship to Demand and Profit
- Demand curve shows price and quantity combinations the market will buy.
- MR tells how much additional revenue selling one more unit yields at a specific quantity.
- Continue increasing production as long as MR > marginal cost for profit maximization.
Key Terms & Definitions
- Total Revenue (TR) — the total amount of money received from sales (TR = Price × Quantity).
- Marginal Revenue (MR) — the additional revenue generated from selling one extra unit.
- Demand Curve — a graph showing the relationship between price and quantity demanded.
- Slope — the rate of change; here, how much price or revenue changes as quantity changes.
Action Items / Next Steps
- Review how marginal cost interacts with marginal revenue for profit optimization.
- Prepare to analyze profit maximization for a monopolist in the next lesson.