# Marginal product of capital net of depreciation

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

Given that the production function is quite standard

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

• 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. – luchonacho Oct 12 '17 at 9:15
• 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. – Bird_1991 Oct 12 '17 at 10:31
• Can you provide the link to the paper please? – luchonacho Oct 12 '17 at 10:54
• Eq. (2) and (3): nber.org/papers/w13602.pdf – Bird_1991 Oct 12 '17 at 11:03
• Notice that NBER papers are not peer-reviewed (beyond informal commentary from seminars and conferences). – 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 $1$.

• 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. – luchonacho Oct 12 '17 at 11:56
• @luchonacho The proper term is the "gross return factor" and not the "gross return rate". – Alecos Papadopoulos Oct 12 '17 at 12:25
• That is an odd term. Google returns only ten results! – luchonacho Oct 12 '17 at 13:00
• @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. – Alecos Papadopoulos Oct 12 '17 at 21:43