Linear Homogeneous Production function is another name for _______.
(A) Law of variable proportion
(B) Constant returns to scale
(C) Increasing returns to scale
(D) Decreasing returns to scale

Question

Accepted Answer

> [!TLDR]
> "Linear homogeneous" = homogeneous of degree 1 = output scales exactly with inputs = constant returns to scale.

### Step 1 — Meaning of homogeneous of degree 1
A production function $Q=f(L,K)$ is homogeneous of degree $n$ if $f(kL,kK)=k^{n}f(L,K)$. "Linear homogeneous" means $n=1$:

$$f(kL,kK)=k^{1}\,f(L,K)=k\,Q$$

### Step 2 — Interpret
Multiply all inputs by $k$ and output is multiplied by the SAME $k$ — a proportionate, one-for-one response. By definition that is **constant returns to scale** (the Cobb-Douglas $Q=AL^{a}K^{b}$ with $a+b=1$ is the classic example).

### Why the other options are wrong
- **(A)** Law of variable proportions is a short-run law (one factor varied) — unrelated to homogeneity of the whole function.
- **(C)** Increasing returns to scale ⇒ homogeneous of degree $n>1$. …

Returns to Scale

How it works

The three cases

Quick example

Step 1 — Meaning of homogeneous of degree 1

Step 2 — Interpret

Why the other options are wrong

Step 1 — Meaning of homogeneous of degree 1

Step 2 — Interpret

Why the other options are wrong

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