<p>A closed form solution does not exist. Unless the value for lambda and gamma is specified. Cost minimisation is not possible.</p>

CC BY-SA 4.0
2024-09-16T15:25:08.673Z
This answer is not correct.
Herr K.
CC BY-SA 4.0
2024-09-16T07:11:42.643Z
2024-09-16T07:11:42.643Z
PoopyPoops
<p>For the function: <span class="math-container">$f(L,K) = L^\lambda + K^\gamma $</span>. The value for <span class="math-container">$\lambda$</span> and <span class="math-container">$\gamma$</span> is not given.</p>
<ol>
<li>What type of production function is this (quasi-linear, CES)?</li>
<li>Is it true for there to be diminishing MRTS, <span class="math-container">$\lambda$</span> and <span class="math-container">$\gamma$</span> has to be between 0 and 1?</li>
<li>I am trying to minimise the cost for inputs L and K to produce q quantity of output, is it possible to do so with this function via lagrangian multiplier? I have tried to do so but the derivations ended up being too complicated.</li>
</ol>

CC BY-SA 4.0
2024-09-16T15:26:03.130Z
Welcome to Economics SE! Please note that we do have a [policy on homework questions](https://economics.meta.stackexchange.com/questions/1465/) that requires you to demonstrate reasonable effort, which includes your own attempt(s) at a solution as well as properly formatting the post using [Markdown](https://stackoverflow.com/editing-help) and [MathJax](https://economics.meta.stackexchange.com/questions/1417).
Herr K.
<microeconomics><optimization>
Cost minimisation for the production function $f(L,K) = L^\lambda + K^\gamma$
PoopyPoops
# Cost minimisation for the production function $f(L,K) = L^\lambda + K^\gamma$

(Asked by: username_0 on 2024-09-16)

For the function: $f(L,K) = L^\lambda + K^\gamma $. The value for $\lambda$ and $\gamma$ is not given.

1. What type of production function is this (quasi-linear, CES)?
2. Is it true for there to be diminishing MRTS, $\lambda$ and $\gamma$ has to be between 0 and 1?
3. I am trying to minimise the cost for inputs L and K to produce q quantity of output, is it possible to do so with this function via lagrangian multiplier? I have tried to do so but the derivations ended up being too complicated.

**Tags:** microeconomics, optimization

> **Comments:**
> **username_1**: Welcome to Economics SE! Please note that we do have a [policy on homework questions](https://economics.meta.stackexchange.com/questions/1465/) that requires you to demonstrate reasonable effort, which includes your own attempt(s) at a solution as well as properly formatting the post using [Markdown](https://stackoverflow.com/editing-help) and [MathJax](https://economics.meta.stackexchange.com/questions/1417).  

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## 1 answers

### Answer by username_0 on 2024-09-16. Score: -1

A closed form solution does not exist. Unless the value for lambda and gamma is specified. Cost minimisation is not possible.

> **Comments:**
> **username_1**: This answer is not correct.  

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