Economics (9640) | The law of diminishing returns and returns to scale

Welcome to Costs, Production, and Efficiency!

Hi there! This chapter might seem technical, but it’s actually one of the most practical parts of microeconomics. It answers a fundamental business question: How much "stuff" (output) do we get when we add more "ingredients" (inputs)?

Understanding the difference between the Law of Diminishing Returns (short run) and Returns to Scale (long run) is essential because these concepts directly determine the costs a firm faces, and ultimately, how big and efficient a company can become. Let's break it down!

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1. Measuring Productivity: Total, Average, and Marginal Returns

Before we discuss the "laws," we need to understand how economists measure the output generated by inputs (factors of production: Land, Labour, Capital, Enterprise).

Key Concepts of Returns (Output)

• Total Product (TP): This is the total quantity of output produced by a firm over a given time period using all its factors of production.
• Average Product (AP): This is the output produced per unit of the variable factor (usually labour). It tells us the average productivity of each worker.
  Formula: \(AP = \frac{TP}{Quantity \ of \ Variable \ Input}\)
• Marginal Product (MP): This is the crucial one! It is the extra output produced by adding one more unit of the variable factor (e.g., hiring one more worker).

Formula: \(MP = \frac{\Delta TP}{\Delta Quantity \ of \ Variable \ Input}\)

Analogy: The Student and Study Time

Imagine you are studying for an exam (output). If you study 5 hours, you get 80 marks (TP). If you study 6 hours, you get 85 marks (TP). The extra hour of study (the marginal input) resulted in 5 extra marks (MP).

Quick Takeaway: Marginal Product is the extra bang you get for your buck (or the extra output you get from your last added input).

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2. The Law of Diminishing Returns (The Short Run)

The Law of Diminishing Returns is strictly a short-run concept. Don't worry if this seems tricky; remember the kitchen analogy!

What is the Short Run?

In economics, the short run is a time period where at least one factor of production is fixed (e.g., the size of the factory, the amount of machinery).

The Law of Diminishing Returns

The law states that when successive equal units of a variable factor (e.g., labour) are added to a fixed factor (e.g., land or capital), eventually the marginal product (MP) and then the average product (AP) will begin to decrease.

Simple explanation: If you keep adding workers to a factory of a fixed size, those new workers will eventually have less space, fewer tools, or just start getting in each other’s way, meaning the additional output they create starts shrinking.

Stages of Production and Diminishing Returns

When a firm increases its labour force, output goes through three phases:

1. Stage 1: Increasing Marginal Returns

   What happens: MP is rising. Output increases significantly with each new worker. This is often due to specialisation and the division of labour.

2. Stage 2: Diminishing Marginal Returns (The Law Kicks In)

   What happens: MP starts to fall (it's still positive, so total output is still rising, but at a slower rate). This occurs because the fixed factor (the factory or machinery) starts to become congested or overworked.

3. Stage 3: Negative Marginal Returns

   What happens: MP becomes negative. Hiring more workers actually causes Total Product (TP) to fall. The firm is now grossly inefficient (the workers are literally blocking each other from operating the machines).

Common Mistake Alert: Students often think 'diminishing returns' means output is falling. It doesn't! It means the *rate* of increase in output is slowing down (MP is falling, but is still positive).

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3. Returns to Scale (The Long Run)

In the long run, a firm can change all of its factors of production. Returns to Scale deals with what happens to output when a firm increases its scale of operations by increasing all inputs simultaneously and proportionally.

For example, if a firm doubles its labour AND doubles its capital, what happens to total output?

The Three Types of Returns to Scale

We compare the percentage change in output to the percentage change in inputs.

1. Increasing Returns to Scale (IRS)

   The Situation: If you double all your inputs, output more than doubles.
   Example: Inputs increase by 10%, Output increases by 15%.
   Why this happens: Usually due to economies of scale (benefits of being larger), such as better specialisation of management or using larger, more efficient machinery.

2. Constant Returns to Scale (CRS)

   The Situation: If you double all your inputs, output exactly doubles.
   Example: Inputs increase by 10%, Output increases by 10%.
   Why this happens: The firm has reached its optimal size, and proportional growth yields proportional output.

3. Decreasing Returns to Scale (DRS)

   The Situation: If you double all your inputs, output less than doubles.
   Example: Inputs increase by 10%, Output increases by only 5%.
   Why this happens: Usually due to diseconomies of scale (disadvantages of being too large), such as bureaucratic inefficiencies, slow communication, or complex management structures.

Did you know? Returns to Scale is the long-run equivalent of looking at productivity, whereas Diminishing Returns is the short-run view.

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4. The Crucial Link: Production Relationships and Costs

The syllabus requires you to understand how these production laws influence the shape of a firm's cost curves.

The relationship between production (returns/product) and costs is inverse:

In the Short Run: Diminishing Returns and the U-Shaped Cost Curve

When studying short-run costs (like Average Variable Cost and Marginal Cost), you will notice they are typically U-shaped. This U-shape is a direct result of the Law of Diminishing Returns.

• When Marginal Product (MP) is rising (Stage 1): Adding new workers is highly effective, meaning the cost of producing that extra unit of output (Marginal Cost) is falling.
• When Diminishing Returns set in (Stage 2): Each new worker adds less and less output. Since the firm is paying the worker the same wage but getting less output, the cost of producing that extra unit of output (Marginal Cost) must rise.

The takeaway: When productivity falls, costs rise. The U-shape of the short-run cost curves is fundamentally caused by diminishing returns.

In the Long Run: Returns to Scale and the Long-Run Average Cost (LRAC) Curve

The shape of the LRAC curve is determined entirely by returns to scale:

• Increasing Returns to Scale (IRS) means output grows faster than costs. Therefore, the LRAC curve is falling.
• Constant Returns to Scale (CRS) means costs and output grow proportionally. Therefore, the LRAC curve is flat/constant.
• Decreasing Returns to Scale (DRS) means output grows slower than costs. Therefore, the LRAC curve is rising.

The LRAC curve is often drawn as a shallow 'U' or 'L' shape, demonstrating the shift from IRS (falling costs) to CRS/DRS (constant or rising costs) as the firm expands.