# Questions regarding Marginal Rate of Technological Substitution

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 ?

## 1 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.

• MRS and MRTS are different. – Giskard Aug 29 '20 at 6:32
• I'm not familiar with Calculus – asdfghjkl Aug 29 '20 at 10:52
• @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. – Armenthus Aug 29 '20 at 15:19