How to Calculate Returns to Scale
Returns to scale compares the output multiplier with the input multiplier: scale every input by t, and output rising by more than t times means increasing returns.
The Returns to Scale formula
Calculator
Enter inputs and output before and after scaling up to get both multipliers and the returns to scale verdict.
Workers used at the starting scale.
Machines used at the starting scale.
What those inputs produce.
Workers once the firm scales up.
Machines at the larger scale. Every input must grow in the same proportion.
What the scaled-up inputs produce.
Output ended up 1.8 times its old level.
- Input multiplier (t)
- 2
- Output if returns were constant
- 400
- Elasticity of scale
- 0.85
- Returns to scale
- Decreasing returns to scale
Every input grew by the same factor of 2, which is what makes this a returns to scale question.
Constant returns would have produced 400 units, so compare the actual figure against that benchmark.
A 1% rise in every input lifts output by about 0.85%, and that figure sits above 1 only under increasing returns.
Output multiplied by 1.8 while inputs multiplied by 2, and the gap between those two numbers is the whole answer.
How to calculate Returns to Scale, step by step
- 1Scale every input by the same factor. Returns to scale is a long-run idea, so labor, capital and every other input have to grow in the same proportion t.
- 2Check the input multipliers match. Divide each input after by the same input before. If labor doubles while capital triples, you are changing the input mix rather than the scale.
- 3Find the output multiplier. Divide the new output by the old output to see how many times larger production became.
- 4Compare the two multipliers. Output growing faster than t is increasing returns to scale, growing exactly with t is constant returns, and lagging t is decreasing returns.
- 5Turn it into one number if you want. Elasticity of scale = ln(output multiplier) ÷ ln(t), which reads above 1 under increasing returns and below 1 under decreasing returns.
Worked example: Returns to Scale
A workshop uses 10 workers and 5 machines to turn out 200 chairs. Doubling both inputs to 20 workers and 10 machines lifts output to 360 chairs. Every input was multiplied by 2, so t = 2, while output multiplied by only 360 ÷ 200 = 1.8. Constant returns would have delivered 2 × 200 = 400 chairs, and 360 falls short of that, so the workshop faces decreasing returns to scale. As a single figure, the elasticity of scale is ln(1.8) ÷ ln(2), which is about 0.85, so a 1% rise in every input lifts output by roughly 0.85%.
Returns to Scale questions
What is the difference between returns to scale and diminishing marginal returns?
Returns to scale is a long-run idea where every input grows together. Diminishing marginal returns is a short-run idea where one input grows while the rest stay fixed, which is why a firm can face both at once.
What causes decreasing returns to scale?
Coordination costs. A larger firm needs more layers of management and more communication between them, so each proportional rise in inputs delivers a smaller proportional rise in output.
How do returns to scale show up on the long-run average cost curve?
Increasing returns pull long-run average cost down, which is the economies of scale stretch. Constant returns leave the curve flat, and decreasing returns push it back up into diseconomies of scale.
Can you read returns to scale straight off a production function?
Yes, when the function has the form Q = A × K^α × L^β. Exponents summing above 1 give increasing returns, exactly 1 gives constant returns and below 1 gives decreasing returns, with no need to scale the inputs by hand.
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated