<p>Yes:
<span class="math-container">$$
f(x_1,x_2)=-x_1x_2
$$</span>
has constant marginal return in both inputs and decreasing return to scale by your definition.</p>
<hr />
<p>EDIT: Answer above assumes OP meant &quot;constant&quot; as constant w.r.t. the input whose marginal product we are talking about. For totally constant, see the the <a href="https://economics.stackexchange.com/questions/39860/returns-to-scale-microeconomics">answer to the duplicate question</a>.</p>

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2021-09-21T16:05:35.417Z
2021-09-22T07:28:36.083Z
2021-09-22T07:28:36.083Z
Giskard
<p>Marginal product of input xi=
<span class="math-container">\begin{equation}
\frac{\partial f }{\partial x _{i}} 
\end{equation}</span></p>
<p>Decreasing return to scale:
f(tx,ty) &lt; t f(x,y) for t&gt;1</p>

<microeconomics><production-function>
If I have a production function f where the marginal product of all the input is constant, can f exhibit decreasing returns to scale?
dilemma
# If I have a production function f where the marginal product of all the input is constant, can f exhibit decreasing returns to scale?

(Asked by: username_0 on 2021-09-21)

Marginal product of input xi=
\begin{equation}
\frac{\partial f }{\partial x \_{i}}
\end{equation}

Decreasing return to scale:
f(tx,ty) < t f(x,y) for t>1

**Tags:** microeconomics, production-function


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## 1 answers

### Answer by username_1 on 2021-09-21. Score: 2

Yes:
$$
f(x\_1,x\_2)=-x\_1x\_2
$$
has constant marginal return in both inputs and decreasing return to scale by your definition.

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EDIT: Answer above assumes OP meant "constant" as constant w.r.t. the input whose marginal product we are talking about. For totally constant, see the the [answer to the duplicate question](https://economics.stackexchange.com/questions/39860/returns-to-scale-microeconomics).


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