[More musings. I started writing this post arguing that they are joint inputs. Now I'm not so sure. So I changed the title into a question.]
We need both land and labour to produce wheat, but land and labour are not "joint inputs", because we can combine them in variable proportions. The marginal product of land is the extra wheat per extra land, holding labour constant; the marginal product of labour is the extra wheat per extra worker, holding land constant. Both are well-defined under variable proportions. If we are combining land and labour optimally (to minimise costs of producing a given amount of wheat), the envelope theorem (IIRC) tells us that the marginal cost of an extra ton of wheat will be the same whether we produce that extra ton by: adding extra land to labour; adding extra labour to land; or adding both extra land and extra labour.
But suppose we could only produce wheat by combining labour and land in fixed proportions: one acre of land plus one (full-time) worker produce one ton of wheat. Two workers and one acre produce one ton; two acres and one worker produce one ton. The marginal product of land is either: zero (if there is more land than labour); one (if there is less land than labour); or undefined (if there is equal quantities of land and labour). The same for the marginal product of labour. Land and labour would then be "joint inputs". We could only talk about the marginal product of the composite input land+labour (one acre of land plus one full-time worker have a combined marginal product of one ton of wheat); and the marginal cost of wheat would be the cost of the extra land+labour needed to produce an extra ton of wheat.
The above assumes that all land is identical and all labour is identical. It gets more complicated if there are two types of land and/or two types of labour.
The above was all just by way of introduction, to explain what "joint inputs" means, and why it matters.
Forget about land. Assume labour produces haircuts, but the amount of haircuts produced per worker per year (productivity) depends on that worker's technology (or knowledge).
It (sometimes) takes resources to invent a new technology ("R&D"). That is a fixed cost for the economy as a whole, that is independent of the number of workers that use that technology. And it's a sunk cost because that R&D only needs to be done once for each new technology (provided it's not forgotten).
It (sometimes) takes resources to learn a new technology ("learning"). That is a variable cost for the economy as a whole, that is increasing in the number of workers that learn that new technology. And it's a sunk cost for each individual worker, but not a sunk cost for the economy as a whole, if workers have finite lives, so each new generation must learn it anew.
This post is about the costs of learning, not about the costs of invention. This is empirically important, because most people spend much more time learning existing ideas than inventing new ideas. Assuming costly learning seems to be at least as important as assuming costly R&D.
Just like I assumed identical land and labour above, let's assume that all workers are identical, that each new technology is equally hard to learn, and that each new technology increases productivity by the same amount. (So if learning one new technology increases productivity by one haircut per worker per year, then learning two new technologies increases productivity by two haircuts per worker per year, though all I'm really doing here is defining units for "technology".)
Are new technologies, and learning those new technologies, joint inputs?
It seems to me that they are joint inputs. And if they are joint inputs, that can only be combined in fixed proportions, we are forced to define a composite input, and talk about the marginal product of that composite input.
What is the marginal product of adding a new technology, holding time spent learning constant? That is only well-defined if it can be learned in zero time. Otherwise, the only way workers could learn a new technology is if they either increase total learning time, or else leave some other technology unlearned. But if all technologies and workers are identical, in the sense defined above, leaving some other technology unlearned would mean zero net increase in productivity. (Just like if labour and land are joint inputs, then employing one extra acre of new land, holding employment of labour constant, simply means leaving another acre of identical land unemployed, with no change in the total output of wheat).
But maybe I'm wrong about technology and learning being joint inputs. Maybe they are complements, but not strict complements, so we can have variable proportions. The students learn one more idea, in the same total time, but learn each idea less intensively. (Just like the same number of farmers cultivate an additional acre of land, but farm less intensively.)
We have to recognise learning time as important. If one person invents a new idea it won't just appear in every producer's head by magic, even if the inventor does give them permission to use it.
To make the same point more metaphysically: if one inventor creates an idea, and 100 producers need to use their time to learn that idea, can we talk about the marginal product of one idea, or can we only talk about the marginal product of 100 ideas plus the time spent to learn them?
Or maybe we shouldn't be too persnickety about this; maybe it makes sense to model technology and learning as joint inputs, if it's a close enough approximation to reality.
[This post can be read as it is, or as a belated response to Paul Romer. Sometimes it takes time to think about things.]