I totally agree with you, the gain is independent of C.

In your original post, you give a scenario where the cell-based meat enters the market in 100 years, while you seem to believe that an actual estimate would rather be ten years or less. I wondered if this was because you overestimated C, or underestimated F (both affect the timeline, but only F affects the gain)

I now understand that you overestimated C, so this doesn't affect your prediction about the gain

Thanks for clarifying!

Thanks for your response!

I think cell-based meat will enter the market within 10 years, so I don't expect C/F to be very big

This makes cell-based meat R&D actually less effective : without discount $gain=x\cdot \frac{U}{C}\cdot \frac{C}{F}$

In term of farm animal suffering, you estimation is $U=0.1\cdot {10}^{11}$, and C = ${10}^{10}$ . So for each euro invested, you'll avoid the suffering of $\frac{C}{F}$ farm animals. The smaller the time we have to wait before cell-based meat enters the market, the less we should donate.

(This is basically because if cell-based meat enters the market in 10 years, instead of 100, its neglectedness is 10 times smaller, therefore your donation is ten times less effective)

[EDIT]

It actually depends on why you think it will be 10 years instead of 100 : if you think it's because funding will be bigger, then the neglectedness is smaller. If, instead, you think that's because the cost is smaller (C = ${10}^9$), then, as previously stated, it doesn't impact the effectiveness of the donation

In the scenario where the level of funding F is the same every year, if you make a one time donation x, the outcome gets closer by $\frac{x}{F}$ years, therefore you've produced $U\cdot \frac{x}{F}$ utility.

The main assumption behind this result is that some utility U in the future is worth as much as some utility U right now. Therefore, when judging which of two projects is the best, since C only affects how long it will take to complete each project, it doesn't matter. The only quantities that matter are U of course, and the funding F.

What if you want to take into account the fact that no, some utility in the future is worth less than some utility right now, therefore completing quick projects first is better?

Warning : this part will involve math

One common way to do that is to assume that the utility decreases over time in a geometrical manner : 1 utility unit in 1 year is equivalent to $\tau$ utility units now, 1 unit in two years is equal to ${\tau }^2$ utility units now, with $\tau$ slightly smaller than 1. For example, if $\tau$ is equal to 0.99, then one utility point in one century is worth about one third of one now, and the closer $\tau$ is to 1, the more you adopt a longtermist point of view.

Ok so now we can compute the total utility of a project with cost C, annual funding F, and per year utility U :

$U_{total}=U\cdot \frac{1}{1-\tau }\cdot {\tau }^{\frac{C}{F}}$

Now, making a one-time donation x, is the same as decreasing the total cost C by x, thus the utility gain of this donation will be :

$gain=x\cdot \frac{-\partial U_{total}}{\partial C}=U\cdot \frac{-ln\left(\tau \right)}{1-\tau }\cdot {\tau }^{\frac{C}{F}}\cdot \frac{x}{F}=U\cdot {\tau }^{\frac{C}{F}}\cdot \frac{x}{F}$

So we have three factors : U, of course, $\frac{x}{F}$, which is how many years of funding you'll provide with your donation, and ${\tau }^{\frac{C}{F}}$ which represents how much this future utility is worth, compared to utility right now. Once again, if you think that utility in the future is equal to utility now, which means $\tau =1$, you get $gain=U\cdot \frac{x}{F}$, which is the original formula in the post. C matters only if utility in the future is not equal to utility in the present.

Now, we can re-write this formula with your notion of return on investment :

$gain=x\cdot \frac{U}{C}\cdot \frac{C}{F}{\tau }^{\frac{C}{F}}$

With this version, we see three factors influencing the gains : x, the bigger your donation, the better, $\frac{U}{C}$, the bigger the return on investment, the better, and finally $\frac{C}{F}{\tau }^{\frac{C}{F}}$, which is a function of $\frac{C}{F}$, the number of remaining years. This function is convex, it starts at 0, reaches a maximum, and its limit is 0 again when $\frac{C}{F}$ approches infinity.

#TODO : include a graph of this function, once I figure out how to do that

With this model, when $\frac{C}{F}$ is too small, it means that the project will soon be funded with or without you, thus you shouldn't invest in it. On the other extreme, if $\frac{C}{F}$ is too big, the benefits will take place too far in the future, and because utility points lose value when too far in the future, you shouldn't invest in it either. In the middle are the best projects.

Anyway, the main point is : the cost C matters only if you think that utility right now is worth more than utility in the future, otherwise only the funding F matters

As sparing 1 farm animal corresponds with reducing 0,1 ton CO2e, this one euro funding also means a reduction of 10 ton CO2e, the same order of magnitude as the emission by an average human in one year. Used as carbon offsetting, cell-based meat R&D has a price around 0,1 euro per ton CO2e averted. This is much lower than most other carbon offsetting mechanisms.

In your model, cell-based meat replaces animal-based meat in 100 years, thus each euro invested now will mean a reduction of 10 ton of CO2e in 100 years. I'd argue that one ton of CO2 now is worth way more than one ton of CO2 in 100 years.

How much more? One way to compare the two would be to imagine what would happen if, instead of spending your one euro now, you were to save it, and spend it in 100 years. With an annual interest rate of 5%, you would get 130 euros in 100 years, which you could then spend on the best carbon offsetting mechanism at the time.

My point is, in term of CO2 averted, it's probably more effective to save money and spend it in the future than to fund cell-based meat R&D

PS : To be fair, it's way better if many are willing to fund cell-based meat R&D too. If the funding goes from 10^8 up to 10^9, we only have to wait for ten years for the cell-based meat, and therefore the saving strategy isn't as good anymore.