<p>What I believe you mean is that a production function has <a href="https://www.economicshelp.org/blog/glossary/constant-returns-scale/" rel="nofollow noreferrer">Constant Returns to Scale</a>.</p>

<p>i.e. $$f(\lambda K, \lambda L)= \lambda f(K, L) $$</p>

<p>Where $\lambda \ge 0$ </p>

<p>Thus in your case where $K=3$ and $L=6$</p>

<p>$$f(3,6)=3 \times f(1,2)$$ </p>

<p>and since ${f_{max}(1,2)=4}$  (i.e. $f(1,2) \le4$) the <em>maximum product</em> a firm can produce using $K=3$ and $L=6$ would be</p>

<p>$$3 \times f(1,2)= 3 \times 4 =12$$</p>

<p>Hope this helps!</p>

CC BY-SA 3.0
2018-01-16T05:44:24.450Z
[Should I](https://economics.meta.stackexchange.com/questions/1662/should-i-downvote-valid-answers-to-off-topic-questions)?
Giskard
CC BY-SA 3.0
2018-01-16T07:23:35.720Z
You solution is just fine, but I meant exactly Increasing Returns to Scale, i double and triple checked the task.
I guess the answer is like 'we can't say anything about fmax', but I'm not sure.
elfinorr
CC BY-SA 3.0
2018-01-16T18:12:04.650Z
@denesp you are then just simply resorting to punishment tactics which gives a false impression that the answer is not correct. Which in this case it is (for the most part)
Bensstats
CC BY-SA 3.0
2018-01-16T18:16:53.827Z
@FreakconFrank All this has been considered and the according to the current consensus downvoting is the lesser of two evils. Please read the meta debate I have linked.
Giskard
CC BY-SA 3.0
2018-01-16T19:55:16.090Z
@denesp so you think, this question is off-topic, am I right? Why so?
elfinorr
CC BY-SA 3.0
2018-01-16T22:09:58.720Z
@elfinorr Because of the [meta guidance on homework questions](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions).
Giskard
CC BY-SA 3.0
2018-01-16T22:47:24.323Z
so, "demonstrate some evidence of having attempted to answer the question independently" - haven't i done it?; "if your question contains numbers that are not essential to your particular problem, it is most likely too specific to be of general use"-it is controversial, ofc i could replace that numbers with parameters, but would anyone feel any better after that? And what is more important, i can't understand, why @FreakconFrank's solution, which is not for the task(i mentioned increasing return) is considered to be valid?(But still, FreakconFrand, thank you very much for response!)
elfinorr
CC BY-SA 3.0
2018-01-16T05:07:53.493Z
2018-01-16T05:07:53.493Z
Bensstats
<p>Let $f=f(K,L)$ - production function.
Let $f(1,2) \le4 $ and a production function is defined to have increasing returns to scale.
What maximum product can the firm produce using K=3 and L=6?</p>

<p>So we know that $f(3,6) = f(3*1, 3*2) &gt; 3*f(1,2)$ and $f(1,2)\le4$</p>

<p>But what should I do next?</p>

<microeconomics>
Increasing returns to scale
elfinorr
# Increasing returns to scale

(Asked by: username_0 on 2018-01-15)

Let $f=f(K,L)$ - production function.
Let $f(1,2) \le4 $ and a production function is defined to have increasing returns to scale.
What maximum product can the firm produce using K=3 and L=6?

So we know that $f(3,6) = f(3\*1, 3\*2) > 3\*f(1,2)$ and $f(1,2)\le4$

But what should I do next?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2018-01-16. Score: 1

What I believe you mean is that a production function has [Constant Returns to Scale](https://www.economicshelp.org/blog/glossary/constant-returns-scale/).

i.e. $$f(\lambda K, \lambda L)= \lambda f(K, L) $$

Where $\lambda \ge 0$

Thus in your case where $K=3$ and $L=6$

$$f(3,6)=3 \times f(1,2)$$

and since ${f\_{max}(1,2)=4}$ (i.e. $f(1,2) \le4$) the *maximum product* a firm can produce using $K=3$ and $L=6$ would be

$$3 \times f(1,2)= 3 \times 4 =12$$

Hope this helps!

> **Comments:**
> **username_2**: [Should I](https://economics.meta.stackexchange.com/questions/1662/should-i-downvote-valid-answers-to-off-topic-questions)?  
> **username_0**: You solution is just fine, but I meant exactly Increasing Returns to Scale, i double and triple checked the task. I guess the answer is like 'we can't say anything about fmax', but I'm not sure.  
> **username_1**: @denesp you are then just simply resorting to punishment tactics which gives a false impression that the answer is not correct. Which in this case it is (for the most part)  
> **username_2**: @FreakconFrank All this has been considered and the according to the current consensus downvoting is the lesser of two evils. Please read the meta debate I have linked.  
> **username_0**: @denesp so you think, this question is off-topic, am I right? Why so?  
> **username_2**: @elfinorr Because of the [meta guidance on homework questions](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions).  
> **username_0**: so, "demonstrate some evidence of having attempted to answer the question independently" - haven't i done it?; "if your question contains numbers that are not essential to your particular problem, it is most likely too specific to be of general use"-it is controversial, ofc i could replace that numbers with parameters, but would anyone feel any better after that? And what is more important, i can't understand, why @FreakconFrank's solution, which is not for the task(i mentioned increasing return) is considered to be valid?(But still, FreakconFrand, thank you very much for response!)  

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