I am trying to understand how marginal product of capital net of depreciation is the following:

enter image description here

Given that the production function is quite standard

enter image description here

I understand the first term of the marginal product, but I am asking about the depreciation part.

  • $\begingroup$ I think there is an error in the formula. As far as I know the net MPK is simply $MP_K - \delta$. If you google "net marginal product of capital" or so you get that definition everytime. For example, in Mankiw's book here. Your definition does not nest with the simpler case of $\delta=0$. There is an extra 1 floting around. $\endgroup$ – luchonacho Oct 12 '17 at 9:15
  • $\begingroup$ Thank you. That is exactly why I am confused (about the extra "1"), but I don't think it is a mistake as it is from a published peer-reviewed paper. $\endgroup$ – Bird_1991 Oct 12 '17 at 10:31
  • $\begingroup$ Can you provide the link to the paper please? $\endgroup$ – luchonacho Oct 12 '17 at 10:54
  • $\begingroup$ Eq. (2) and (3): nber.org/papers/w13602.pdf $\endgroup$ – Bird_1991 Oct 12 '17 at 11:03
  • $\begingroup$ Notice that NBER papers are not peer-reviewed (beyond informal commentary from seminars and conferences). $\endgroup$ – luchonacho Oct 12 '17 at 13:10

This is a misuse of terms.

The marginal product of capital net of depreciation is indeed $MP_k - \delta$, there is no doubt about it.

What the authors mean is that

$$R = 1 + (MP_k - \delta) $$

is the "gross return on capital" factor. In fact a few lines below the equation they call it exactly that, which is the correct term. Here "gross" reflects the inclusion of $1$.

| improve this answer | |
  • $\begingroup$ Is this a common thing? Calling $1+X$ the gross return of an asset paying $X$? For instance, it the interest rate of a loan is 3%, is 1.03 the "gross" return on loans? Looks very odd to me. $\endgroup$ – luchonacho Oct 12 '17 at 11:56
  • $\begingroup$ @luchonacho The proper term is the "gross return factor" and not the "gross return rate". $\endgroup$ – Alecos Papadopoulos Oct 12 '17 at 12:25
  • $\begingroup$ That is an odd term. Google returns only ten results! $\endgroup$ – luchonacho Oct 12 '17 at 13:00
  • $\begingroup$ @luchonacho Indeed. It returns twenty thousand for "gross return on capital". The problem with this last one, is that it is sometimes used to mean $R$ as above, and sometimes is used to mean "gross interest rate" (i.e. prior to subtract depreciation). Using the word "factor" helps avoid the confusion. $\endgroup$ – Alecos Papadopoulos Oct 12 '17 at 21:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.