📘 Profit as a Function of Quantity Sold

1️⃣ Basic Definition of Profit

By definition:

Profit = Revenue – Cost

This means:

👉 A company makes profit when the money it earns is greater than the money it spends.

2️⃣ What is Revenue?

Revenue = Price × Quantity

Where:

• P = price per unit

• Q = number of units sold

So if you sell more units, revenue increases.

3️⃣ What is Cost?

Cost has two parts:

🔹 Fixed Costs

These do NOT change with production.

Examples:

• Rent

• Salaries

• Insurance

• Depreciation

Even if the company produces zero units, fixed costs still exist.

🔹 Variable Costs

These change depending on production.

Examples:

• Raw materials

• Packaging

• Sales commissions

• Electricity for machines

The more you produce, the higher the variable cost.

So total cost is:

Cost = Fixed Cost + (Variable Cost × Q)

4️⃣ Combining Everything

We substitute Revenue and Cost into the Profit formula:

This means:

👉 Profit depends on how many units you sell (Q).

It is a linear function.

📊 Example

Let’s imagine a company that sells notebooks.

Given:

• Price per notebook (P) = €20

• Variable cost per notebook = €8

• Fixed costs = €6,000

🎯 What You Should Understand

1. Profit depends on quantity sold.

2. There is a break-even quantity.

3. Fixed costs create the initial loss.

4. After break-even, profit increases linearly.

Given:

• Price (P) = €20

• Variable Cost per unit = €8

• Fixed Cost = €6,000

• Contribution per unit (k) = 20 − 8 = €12

Profit function:

Profit=12Q−6000

📊 Profit Table for Different Quantities