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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?

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What I believe you mean is that a production function has Constant Returns to 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!

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  • $\begingroup$ Should I? $\endgroup$ – Giskard Jan 16 '18 at 5:44
  • $\begingroup$ 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. $\endgroup$ – elfinorr Jan 16 '18 at 7:23
  • $\begingroup$ @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) $\endgroup$ – FreakconFrank Jan 16 '18 at 18:12
  • $\begingroup$ @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. $\endgroup$ – Giskard Jan 16 '18 at 18:16
  • $\begingroup$ @denesp so you think, this question is off-topic, am I right? Why so? $\endgroup$ – elfinorr Jan 16 '18 at 19:55

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