Q.What are the Internal Economies of scale?

Constant Returns to Scale

The Everyday Intuition

Imagine you run a small bakery. You have one oven, one baker, and one counter. In one hour, you can bake 20 loaves of bread. Now suppose you decide to scale up — you buy a second oven, hire a second baker, and add another counter. You have doubled every input. What happens to your output?

If you now produce exactly 40 loaves per hour, you have experienced constant returns to scale. Output increased by the same proportion as inputs — double the inputs, double the output.

This is the simplest, most intuitive case of scaling a production process. It is the benchmark against which we compare other possibilities.

The Precise Definition

In economics, returns to scale describes what happens to output when all inputs are increased by the same proportion. Constant returns to scale (CRS) means:

If every input is multiplied by a factor $t$, output is multiplied by exactly $t$.

Let the production function be $Q = f(L, K)$, where $L$ is labour and $K$ is capital. Then constant returns to scale means:

This is the defining equation of CRS. It is a mathematical property of the production function, not a guess or an assumption — it either holds or it doesn't.

Where:

• $f(L, K)$ = output when using $L$ units of labour and $K$ units of capital
• $t$ = the scaling factor (e.g., $t = 2$ means doubling all inputs)
• $f(tL, tK)$ = output after scaling all inputs by $t$

Why It Matters

1. It is the dividing line between increasing and decreasing returns.

If output more than doubles when inputs double ($f(tL, tK) > t \cdot f(L, K)$), we have increasing returns to scale — often due to specialisation or indivisibilities (e.g., a bigger factory can use more efficient machinery). If output less than doubles ($f(tL, tK) < t \cdot f(L, K)$), we have decreasing returns to scale — often due to coordination problems or management difficulties.

CRS is the neutral case, the reference point.

2. It implies constant long-run average cost.

If inputs double and output doubles, total cost doubles. So average cost (cost per unit) stays the same. This is why CRS is associated with a flat long-run average cost curve — a horizontal line.

3. It is a common assumption in economic models.

Many foundational models (like the Solow growth model you will meet later) assume CRS for the aggregate production function. This simplifies analysis and matches certain real-world patterns — for example, if you replicate an entire economy (double all workers, all machines, all land), you would expect roughly double the output.

A Diagram in Words

Draw a graph with labour on the horizontal axis and capital on the vertical axis. Mark a point A with coordinates $(L_1, K_1)$. The output at A is $Q_1$. Now draw a ray from the origin through A. Any point on this ray has inputs in the same proportion as A — for example, point B at $(2L_1, 2K_1)$. …