<p>To answer your first question it is helpful to rewrite the MRS as a ratio of the partial derivatives. What you are looking at is the slope of the Isoquant. If you plug in &quot;real changes&quot; of Q and L you will move along a linear approximation of the (usual) convex curve.
<span class="math-container">\begin{equation}
MRS=\frac{\frac{\delta Q}{\delta L}}{\frac{\delta Q}{\delta K}} \approx \frac{\Delta Q}{\Delta L}
\end{equation}</span>
Regarding your second question it is some kind of definition problem. I assume MRS KL means MRS from K to L. Or in other words how much capital is needed to compensate the loss of labor. If you change the denominator and nominator of the fraction you would than need to change the notation to MRS L to K instead of K to L.</p>

CC BY-SA 4.0
2020-08-29T06:32:08.633Z
MRS and MRTS are different.
Giskard
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2020-08-29T10:52:07.643Z
I'm not familiar with Calculus
Alumi
CC BY-SA 4.0
2020-08-29T15:19:41.227Z
@Giskard thanks for pointing this out. MRS and MRTS are pretty similar, in fact they are both marginal rates of subsitution. MRS is the generic term, MRTS soley looks at the MRS in the production technology of the firm.
Levittstyle
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2020-08-28T21:16:12.603Z
2020-08-29T15:20:14.560Z
2020-08-29T15:20:14.560Z
Levittstyle
<p>Definition of MRTS is: keeping constant the total output, how much input 1 has to decrease if input 2 increases by one extra unit. How then is MRTS_KL = MP_L / MP_K if MP_L = ΔQ/ΔL and MP_K = ΔQ/ΔK. Isn't the quantity not constant then?
Also why is it MRTS_KL = MP_L / MP_K and not MRTS_KL = MP_K / MP_L ?</p>

<microeconomics>
Questions regarding Marginal Rate of Technological Substitution
Alumi
# Questions regarding Marginal Rate of Technological Substitution

(Asked by: username_0 on 2020-08-28)

Definition of MRTS is: keeping constant the total output, how much input 1 has to decrease if input 2 increases by one extra unit. How then is MRTS\_KL = MP\_L / MP\_K if MP\_L = ΔQ/ΔL and MP\_K = ΔQ/ΔK. Isn't the quantity not constant then?
Also why is it MRTS\_KL = MP\_L / MP\_K and not MRTS\_KL = MP\_K / MP\_L ?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2020-08-28. Score: 1 | Accepted answer

To answer your first question it is helpful to rewrite the MRS as a ratio of the partial derivatives. What you are looking at is the slope of the Isoquant. If you plug in "real changes" of Q and L you will move along a linear approximation of the (usual) convex curve.
\begin{equation}
MRS=\frac{\frac{\delta Q}{\delta L}}{\frac{\delta Q}{\delta K}} \approx \frac{\Delta Q}{\Delta L}
\end{equation}
Regarding your second question it is some kind of definition problem. I assume MRS KL means MRS from K to L. Or in other words how much capital is needed to compensate the loss of labor. If you change the denominator and nominator of the fraction you would than need to change the notation to MRS L to K instead of K to L.

> **Comments:**
> **username_2**: MRS and MRTS are different.  
> **username_0**: I'm not familiar with Calculus  
> **username_1**: @Giskard thanks for pointing this out. MRS and MRTS are pretty similar, in fact they are both marginal rates of subsitution. MRS is the generic term, MRTS soley looks at the MRS in the production technology of the firm.  

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