<p>For quasi-linear production of <span class="math-container">$F(K,L)= \sqrt{K}+L $</span>. I know for the optimal efficiency to exist <span class="math-container">$q \geq \frac{w}{2r}$</span> where w is the cost labour and r is the cost of capital. <br />
My question is what happened when the firm chooses to produce in <span class="math-container">$ q \leq \frac{w}{2r}$</span> condition? Would such a situation covert the production function into substitution function?</p>

CC BY-SA 4.0
2021-02-08T14:41:32.027Z
What does "optimal efficiency" mean? And how did you get $q\ge \frac{w}{2r}$ as a condition for that?
Herr K.
CC BY-SA 4.0
2021-02-08T20:43:16.207Z
Use a basic cost function $C(K,L)=wK+rL$. The cost minimising occurs at $\sqrt{K}=\frac{w}{2r}$. If you operate in $q < \frac{w}{2r}$ then you to get negative unit of Labour value which does not make sense in reality. So I assumed the firm operate at $\sqrt{K}=\frac{w}{2r}$ and L=0, which is different then the cost minimising input thus implies inefficiency. But something tell me my intuition might be wrong.
Finality
<production-function>
Quasi-Linear Production and Inefficiency
Finality
# Quasi-Linear Production and Inefficiency

(Asked by: username_0 on 2021-02-08)

For quasi-linear production of $F(K,L)= \sqrt{K}+L $. I know for the optimal efficiency to exist $q \geq \frac{w}{2r}$ where w is the cost labour and r is the cost of capital.   
My question is what happened when the firm chooses to produce in $ q \leq \frac{w}{2r}$ condition? Would such a situation covert the production function into substitution function?

**Tags:** production-function

> **Comments:**
> **username_1**: What does "optimal efficiency" mean? And how did you get $q\ge \frac{w}{2r}$ as a condition for that?  
> **username_0**: Use a basic cost function $C(K,L)=wK+rL$. The cost minimising occurs at $\sqrt{K}=\frac{w}{2r}$. If you operate in $q < \frac{w}{2r}$ then you to get negative unit of Labour value which does not make sense in reality. So I assumed the firm operate at $\sqrt{K}=\frac{w}{2r}$ and L=0, which is different then the cost minimising input thus implies inefficiency. But something tell me my intuition might be wrong.  

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## 0 answers

