Imagine you have two causes where you believe their cost-effectiveness trajectories cross at some point. Cause A does more good per unit resources than cause B at the start but hits diminishing marginal returns faster than B. Suppose you have enough resources to get to the crossover point. What do you do? Well, you fund A up to that point, then switch to B. Hey presto, you’re doing the most good by diversifying.
It might be helpful to draw a dashed horizontal line at the maximum value for B, since you would fund A at least until the intersection of that and the curve for A, and start funding B from there (but possibly switching thereafter, and maybe back and forth). Basically, you want to start funding B once the marginal returns from A are lower than the marginal returns for B. It doesn’t actually matter for whether you fund B at all that B hits diminishing marginal returns more slowly, only that A’s marginal returns are eventually lower than B’s initial marginal returns before you exhaust your budget.
If you’re including more than just A and B, and A’s marginal expected returns are eventually lower than B’s initial marginal expected returns before you would exhaust your budget on A, then we can still at least say it wouldn’t be optimal to exhaust your budget on A (possibly you would exhaust it on B, if B also started with better marginal returns, or some completely different option(s)).
It isn’t clear what you meant by crossover point. I assumed it was where the curves intersect, but if you did mean where A’s curve reaches the maximum value of B’s, then it’s fine.
It might be helpful to draw a dashed horizontal line at the maximum value for B, since you would fund A at least until the intersection of that and the curve for A, and start funding B from there (but possibly switching thereafter, and maybe back and forth). Basically, you want to start funding B once the marginal returns from A are lower than the marginal returns for B. It doesn’t actually matter for whether you fund B at all that B hits diminishing marginal returns more slowly, only that A’s marginal returns are eventually lower than B’s initial marginal returns before you exhaust your budget.
If you’re including more than just A and B, and A’s marginal expected returns are eventually lower than B’s initial marginal expected returns before you would exhaust your budget on A, then we can still at least say it wouldn’t be optimal to exhaust your budget on A (possibly you would exhaust it on B, if B also started with better marginal returns, or some completely different option(s)).
I’m not sure if you’re disagreeing with my toy examples, or elaborating on the details—I think the latter.
It isn’t clear what you meant by crossover point. I assumed it was where the curves intersect, but if you did mean where A’s curve reaches the maximum value of B’s, then it’s fine.