Marginal, average and total revenue curves

Welcome to the World of Revenue!

In this chapter, we are going to look at the "money in" side of a business. Whether it’s a small lemonade stand or a giant tech company, every firm needs to understand its revenue—the total amount of money it receives from selling goods or services.

Don't worry if graphs and formulas seem a bit scary at first. We will break everything down into small, manageable steps. By the end of these notes, you’ll understand how price, sales, and revenue all fit together like pieces of a puzzle!

1. The Three Types of Revenue

To understand how a firm performs, we look at revenue in three different ways: Total, Average, and Marginal.

Total Revenue (TR)

This is the simplest one. It is the total amount of money a firm receives from selling its output.

The Formula:
\( TR = P \times Q \)
(Where P = Price and Q = Quantity sold)

Example: If you sell 10 cupcakes for £2 each, your Total Revenue is \( 10 \times 2 = £20 \).

Average Revenue (AR)

This is the revenue a firm receives per unit sold.

The Formula:
\( AR = \frac{TR}{Q} \)

Important Trick: In almost all cases, Average Revenue is exactly the same as the Price (P). Think about it: if your total revenue from 10 cupcakes is £20, the "average" you got for each one is £2... which was the price!

Marginal Revenue (MR)

This is the extra revenue a firm earns from selling one additional unit of output.

The Formula:
\( MR = \frac{\Delta TR}{\Delta Q} \)
(The change in Total Revenue divided by the change in Quantity)

Quick Review:
• Total Revenue: The whole "pot" of money.
• Average Revenue: The money per item (The Price).
• Marginal Revenue: The money from the next item sold.

2. The Average Revenue Curve and Demand

In Economics, the Average Revenue (AR) curve is also the firm’s demand curve.

Why? Because the AR curve shows the price that must be charged for each level of output. If a customer is willing to buy 100 units at £5, the firm's Average Revenue for those 100 units is £5. Therefore, the price consumers are willing to pay (Demand) is the same as the revenue the firm receives per unit (AR).

Did you know?
When you look at a graph and see a line labeled "D" for Demand, you can also label it "AR"! They are two sides of the same coin.

3. Revenue Curves: Two Main Scenarios

The way these curves look on a graph depends on whether the firm can control its price or not. The syllabus highlights two main situations:

Scenario A: The Firm is a "Price Taker" (Perfect Competition)

In some markets, there are so many competitors that a single firm has no choice but to sell at the market price. If they raise the price even by 1 cent, everyone goes to the shop next door.

• Price is Constant: No matter how many you sell, the price stays the same.
• The Curves: Because the price never changes, the AR and MR are the same horizontal line.
• The TR Curve: Total Revenue will be a straight diagonal line pointing upwards (like a 45-degree angle).

Scenario B: The Firm has "Market Power" (Monopoly Power)

If a firm is a Monopoly or has Monopoly Power, it faces a downward-sloping demand curve. To sell more units, the firm must lower its price for all units.

The "Falling Price" Rule:
1. The AR curve slopes downwards (the Demand curve).
2. The MR curve also slopes downwards, but it falls twice as fast as AR. This is because to sell one more unit, you have to lower the price on all previous units you were selling!
3. The TR curve looks like an upside-down "U" (a hill). It rises at first, hits a peak, and then starts to fall.

Key Takeaway:
If a firm has to lower its price to sell more, its Marginal Revenue will eventually become zero and then negative. When \( MR = 0 \), the Total Revenue is at its maximum point.

4. Calculating Profit

The syllabus reminds us that revenue is not the same as profit. Revenue is just the money coming in; Profit is what you keep after paying your bills.

The Formula:
\( Profit = Total \ Revenue (TR) - Total \ Costs (TC) \)

If TR is higher than TC, the firm makes a profit. If TC is higher than TR, the firm makes a loss.

5. Step-by-Step Calculation Guide

Let's look at how the numbers change when a firm has to lower its price to sell more:

1. Quantity (Q): 1 unit, Price (P): £10 → \( TR = £10 \), \( AR = £10 \)
2. Quantity (Q): 2 units, Price (P): £9 → \( TR = £18 \), \( AR = £9 \), \( MR = £8 \) (The TR went from 10 to 18)
3. Quantity (Q): 3 units, Price (P): £8 → \( TR = £24 \), \( AR = £8 \), \( MR = £6 \) (The TR went from 18 to 24)

Notice how MR is falling faster than the price (AR)!

6. Common Mistakes to Avoid

• Confusing Revenue and Profit: Always remember that revenue does not account for costs. You can have millions in revenue but still be losing money if your costs are even higher!
• Forgetting \( AR = P \): This is the most useful shortcut in Economics. If you know the Price, you know the Average Revenue.
• MR and TR Relationship: Students often think TR keeps rising as long as you sell more. But if you have to lower the price too much to sell that extra unit, your TR might actually go down! (This happens when MR becomes negative).

Quick Summary Box

• Total Revenue (TR): \( P \times Q \).
• Average Revenue (AR): \( TR / Q \) (Always equals Price).
• Marginal Revenue (MR): The extra money from selling one more.
• Maximum TR: Happens when \( MR = 0 \).
• Profit: \( TR - TC \).