Don't worry about the tone, opportunity cost is that hinterland where it is too complicated to explain to someone who doesn't get it in one sentence, but too fundamental not to need to talk about so it is very difficult to judge tone when you're not sure whether you can assume familiarity with economic concepts.

It sounds to me like we basically agree - the cost of switching search engine is ten minutes (assumption) and this pays off about 50 cents a day for forever (assumption). This makes cutting off the analysis at one year arbitrary, which I agree with. You also have to compare the effort you put into searching with anything else you could do with that time, (even if you would have been doing those searches 'naturally') for the purpose of correctly calculating opportunity cost.

I think we disagree on the final step - if this is to be ineffective you need to be able to find an activity which is a better use of my time than conducting those daily searches. Since my primary contribution to charitable causes is from my salary, and I use a lot of Google in my job (I would be fired if I didn't do internet searches because I would be totally ineffective) I can't think what else I should be doing - what is a better use of my time than doing those searches? Assume we're only interested in maximising my total charitable giving.