-Person A supplies an idea for an app.
-Person B builds the app.
-In percentage terms, how much is the idea worth in the marketplace?
-What percentages should A and B receive, respectively?
It is worth zero. A lot of ideas exist. Market adoption the generates real revenue is the only determination of value.
Generally speaking, person B receives 100% and person A receives an honorable mention in the "About" page :-)
That being said, it depends on what constitutes an idea.
If A comes to B and says something like: "I have an idea for an app that is like Instagram, except instead of sharing selfies people share drawings of their children". Such an idea is worth zero. Not because nothing will come out of it (this actually might work, who knows), but because it contributes nothing of value.
On the other hand, if A is an expert in, say, import-export, and has been a successful consultant in that field for many years, has many clients, and over the years has developed a fool-proof algorithm, so that any idiot (or a machine) who just follows this algorithm can be a decent consultant. So, he comes up with an idea of making an app that will automate his work, and provide a service to the millions importers and exporters in the world (true story, by the way). In this case, B supplies not just a generic concept, but a complete algorithm, content, and interface down to the smallest details, deep knowledge of the market, and the early adopters (his existing clients). That's worth a lot, probably around 50% of the startup, and if he takes upon himself the marketing operation, then he can definitely get even more than 50%.
It's way to easy to think that bringing an idea is worth 0!
All is about involvement. Bringing an idea doesn't bring value in itself unless person A is an expert in something.
But bringing the idea, the team to build it, the plan to market it, the contacts to be approached etc. could be very interesting.
Besides, if by idea you mean "designed idea" with an example of situation, it could also be very interesting: here is what I was thinking of developing, and we could use it this way, with those people, which is much better than the 10 competitors I already studied, and we could market it this way.
B- <1% / 99%.
Ideas are a dime a dozen. It's sweat equity & progress that means something, & in your example only Person B has done that. Person A should be doing customer development, marketing, support, secondary testing, finances, design, strategy, & more.
It all comes down to who pays for the whole shebang? If time-equity (as I read the question) we go one step down:
How is the idea communicated? In the form of a working prototype? With micro-interactions in the front and architecture for the back? Who does the marketing, user acquisition, etc. After all factors have been considered and weighted you can come up with a fair percentage.
I respect all humans equally, having said that I'd like to add a counter view.
People who say ideas are worth "0%" use a technocratic point of view with "0%" barring. Ideas are worth "100%" if communicated and understood in the right way. It all comes down to how well thought thru, illustrated and explained the idea is.
Here's an example for reference (percentage for illustrative purpose only):
Delivery of idea
"An app that offers a free SMS alternative" <- Worth "0-0.1%"
Above + simple wireframes for core-interactions <- Worth "0.1-0.2%"
Above + fully fleshed out prototype with all assets <- Worth "10-15%"
Above + disruptive backend architecture that greatly reduces cost <- Worth "30-40%"
Above + Re-framed as a service (not app) with business patterns, behavior hooks, channel strategy and a unique and proven funnel strategy for user acquisition <- Worth "80-90%".
Warning! without an actual service on the market, the whole thing is creating 0% real world value and could be considered to be worth 0% money.
Pro tip! Developing an app is not the "problem". Developing, deploying and improving an experience (product or service) that customers needs and wants to come back to time and again is the problem.
What percentage A and B receive is something totally up to them and should be negotiated up front, and pay for a lawyer to write up the agreement, even if it's something as simple as a Memorandum of Understanding. However, an agreement between two parties should also consider issues of liability, growth, break up, etc. Again, talk to a lawyer about what the basics are.
How much an idea is worth in the marketplace is vague. While most people have said "nothing!" here, consider companies like Facebook, whose stock is valued based on the "idea" of its value, often with little regard to its actual value (especially for companies whose "product" is based on revenue from advertising clicks!)
That said, consider an idea to be like a boulder sitting on top of a mountain. It may have a lot of "potential" worth, and once given an adequate shove, becomes "actual" worth in its momentum. Obviously, if people didn't think ideas had worth, we wouldn't have VC's investing in ideas! What the VC wants to see happen is for the boulder to move from potential to actual value.