Overview
This lecture explains how a monopolist can maximize profit by analyzing total revenue (TR) and introducing the concept of marginal revenue using a monopoly on oranges as an example.
Total Revenue Calculation
- Total revenue (TR) is calculated by multiplying price by quantity sold (TR = price × quantity).
- If quantity is 0, TR is $0.
- Selling 1,000 pounds at $5/pound earns $5,000 in TR.
- Selling 2,000 pounds at $4/pound earns $8,000 in TR.
- Selling 3,000 pounds at $3/pound earns $9,000 in TR.
- Selling 4,000 pounds at $2/pound earns $8,000 in TR.
- Selling 5,000 pounds at $1/pound earns $5,000 in TR.
- Selling 6,000 pounds at $0/pound earns $0 in TR (no revenue if given away for free).
- The TR curve is a downward-facing parabola because higher quantity requires lower prices, reducing revenue beyond a certain point.
Demand Curve and Algebraic Representation
- The demand curve shows the relationship between price and quantity demanded.
- Algebraically, price as a function of quantity is p = 6 – q.
- TR as a function of quantity: TR = (–q + 6) × q = –q² + 6q.
- This quadratic equation creates a downward-opening parabola for TR.
Introduction to Marginal Revenue
- Marginal revenue (MR) is the change in total revenue divided by the change in quantity (MR = ΔTR / ΔQ).
- MR at a specific quantity is the slope of the tangent line to the TR curve at that point.
- Calculating MR can require calculus, but can be approximated using algebra.
Key Terms & Definitions
- Total Revenue (TR) — The total money received from selling a product (TR = price × quantity).
- Marginal Revenue (MR) — The additional revenue earned from selling one more unit (MR = ΔTR / ΔQ).
- Demand Curve — A graph showing the relationship between price and quantity demanded.
- Monopoly — A market structure with only one seller for a product or service.
Action Items / Next Steps
- Review the formula for total revenue and how it is graphed.
- Prepare to calculate marginal revenue for different quantities in the next lesson.