Welcome to Costs, Revenue, and Profits!

Hi there! This chapter is all about how firms make money—the "Revenue" side of the business equation. Understanding revenue is critical because it tells us how a firm's pricing decisions relate to its total income and, ultimately, its profits.

Don't worry if the concepts seem mathematical; we will break down Total Revenue (TR), Average Revenue (AR), and Marginal Revenue (MR) into simple, easy-to-understand terms. Once you master these three concepts, you'll be able to predict how a firm will behave in any market!

1. Total Revenue (TR): The Big Picture

Total Revenue (TR) is simply the entire amount of money a firm receives from selling its goods or services in a specific period.

Calculation of Total Revenue

This is the easiest formula to remember:

\(TR = Price (P) \times Quantity (Q)\)

Example: If a bakery sells 100 loaves of bread at \$3 each, its Total Revenue is \(100 \times \$3 = \$300\).

Key Takeaway for TR

Total Revenue shows the overall income generated. To increase TR, a firm needs to carefully consider if it should raise the price (hoping Q doesn't fall too much) or lower the price (hoping Q rises a lot). This relationship is where Marginal Revenue becomes crucial!

2. Average Revenue (AR): The Price per Unit

Average Revenue (AR) is the revenue earned per unit sold. It tells us, on average, how much money the firm gets for each item it sells.

Calculation of Average Revenue

The formula is:

\(AR = \frac{Total Revenue (TR)}{Quantity (Q)}\)

Let's use the TR formula inside the AR formula:

$$AR = \frac{P \times Q}{Q}$$

The Q's cancel out, which means:

\(AR = Price (P)\)

The Average Revenue Curve is the Demand Curve

This is a fundamental concept for A-Level Economics (Syllabus 3.1.3.5):

  • Since AR is always equal to the price, the Average Revenue curve (AR) shows the relationship between the price charged (AR) and the quantity demanded (Q).
  • By definition, the curve showing the relationship between Price and Quantity Demanded is the firm’s Demand Curve.

Important Connection: When drawing diagrams, remember that the AR curve and the Demand curve are the exact same line for the firm.

Did you know? If a firm has a downward-sloping demand curve (like most firms in the real world), it means to sell more output, it must lower its price. Therefore, the AR curve slopes downwards!

3. Marginal Revenue (MR): The Revenue of the 'Last Unit'

Marginal Revenue (MR) is the additional revenue generated from selling one more unit of output.

Calculation of Marginal Revenue

The formula focuses on the change:

\(MR = \frac{Change \ in \ Total \ Revenue (\Delta TR)}{Change \ in \ Quantity (\Delta Q)}\)

Why MR is Usually Less Than AR (Price)

This is the part that often confuses students, so pay close attention!

In most markets (known as imperfectly competitive markets, like monopolistic competition or monopoly, where the firm has some control over price), if a firm wants to sell an extra unit, it must lower the price not just for that extra unit, but for all previous units too.

Step-by-Step Example:

  1. You sell 4 burgers at \$10 each. TR = \$40. (AR = \$10)
  2. To sell the 5th burger, you must drop the price to \$9.
  3. New TR = 5 burgers \(\times\) \$9 = \$45.
  4. The Marginal Revenue from the 5th unit is \( \$45 - \$40 = \$5\).

Notice that the price (AR) of the 5th burger was \$9, but the Marginal Revenue (MR) was only \$5. Why? Because the firm lost \$1 on each of the four previous burgers it could have sold at \$10.

Key Principle: When the demand curve (AR) slopes downwards, the MR curve will lie below the AR curve and will be steeper.

Analogy: The Class Average

Think of AR as the average grade in your class, and MR as your grade on the latest test:

  • If your latest test grade (MR) is lower than the current class average (AR), your new average (AR) will fall.
  • Since the firm's MR (revenue from the new unit) is always less than the price (AR) it charges for that unit, the average revenue (AR/Price) is constantly pulled down by the marginal revenue (MR).
Quick Review Box: The Curves

AR Curve: The firm's Demand Curve. Shows the Price (P). Downward sloping in most real markets.

MR Curve: Shows the addition to TR. It lies below and is steeper than the AR curve (when AR is downward sloping).

4. The Critical Relationship Between TR, MR, and PED

The connections between Marginal Revenue, Total Revenue, and the Price Elasticity of Demand (PED) are vital for analyzing pricing decisions (Syllabus 3.3.2.4).

PED measures how sensitive the quantity demanded is to a change in price.

We can use the MR curve to perfectly predict when TR will rise, fall, or hit its maximum.

Case 1: Price Elastic Demand (\(|PED| > 1\))
  • Meaning: Consumers are sensitive to price changes. A small drop in price leads to a proportionately larger increase in quantity sold.
  • MR Status: MR is positive (\(MR > 0\)). Since the gain in sales volume outweighs the loss in price per unit, the total revenue continues to rise.
  • TR Curve: TR is rising.
  • Strategy: If demand is elastic, lowering the price will increase Total Revenue.
Case 2: Unit Elastic Demand (\(|PED| = 1\))
  • Meaning: The change in quantity sold exactly offsets the change in price.
  • MR Status: MR is zero (\(MR = 0\)). Selling one more unit adds zero net revenue, as the revenue gained from the new unit is exactly offset by the price reduction on all previous units.
  • TR Curve: TR is at its maximum point (the peak).
  • Memory Aid: TR is Maximum when MR is Zero.
Case 3: Price Inelastic Demand (\(|PED| < 1\))
  • Meaning: Consumers are insensitive to price changes. A drop in price leads to only a proportionately smaller increase in quantity sold.
  • MR Status: MR is negative (\(MR < 0\)). The loss in revenue from lowering the price on all units outweighs the gain from selling the extra small quantity.
  • TR Curve: TR is falling.
  • Strategy: If demand is inelastic, lowering the price will decrease Total Revenue. A firm should raise the price to increase TR when operating in this region.

5. Visualizing the Revenue Curves

When you are asked to draw and interpret revenue curves, you are usually expected to draw the relationship for a firm with market power (i.e., a firm facing a downward sloping demand/AR curve).

Drawing Tips for Downward Sloping AR/MR Curves
  • Start Point: AR and MR must start at the same point on the vertical axis (at Q=0, the AR/Price is the highest, and the revenue from the very first unit (MR) is equal to that price).
  • Slope: The MR curve must be steeper than the AR curve. If the AR curve is a straight line, the MR curve falls at twice the rate.
  • The TR Peak: The MR curve hits zero (\(MR=0\)) exactly when the TR curve reaches its maximum point.
  • Negative MR: The MR curve continues into the negative axis. When MR is negative, the TR curve begins to fall.
Common Mistake to Avoid

Do not confuse the AR curve with the MR curve. Students sometimes assume they are the same because they are accustomed to the perfect competition model. Remember: If AR is falling, MR must be lower than AR!

Final Key Takeaways

  • AR = P: Average Revenue is the firm's Demand Curve.
  • MR's Position: When AR slopes down (imperfect market), MR lies below AR.
  • Profit Maximization vs. Revenue Maximization: Revenue maximization occurs where \(MR = 0\) (and TR is highest). Profit maximization occurs where \(MR = MC\) (which is covered in later chapters!).

Well done! You now understand the revenue components that dictate a firm's pricing strategy. Use these concepts to tackle questions about elasticity and market structure!