Background
I just started an internship and while I'm enjoying myself I've spotted a few areas where efficiency and productivity could be improved. I am also not very busy (read: overqualified and bored) so it would be nice to see if I could develop a product to help solve it. Here's the hitch: I've just ended my first week and I'm only at the company for another 2 1/2 months. Then I'm back to university.
Facts
(Just since people are questioning implementation, I'm not too concerned about that bit myself. Just wondering about the ethics bit)
The product is somewhat innovative (towards Human-computer interaction). It is technically completely possible, but not quite a walk in the park to make and would involve a fair bit of effort. Mostly software, capital costs are very low.
This product however could potentially be used in many other industries. The company could probably sell it on.
The product would help to prevent damage/loss of my employer's sensitive products, I imagine potentially scales of two magnitude more than the cost of acquisition.
Team I work in is small and informal organized. Could be easily tested. They aren't expecting anything from me and I don't think they would question me doing it.
Dilemma
For a short internship, I'm wondering if it's worth the trouble to do the stuff just for this company and loosing ownership over it afterwards.
It's beyond expectation and I'm paid a fairly marginal salary. They don't hesitate to buy (even expensive) commercial products otherwise if it helps them. If I would I been there for a year I wouldn't have questioned it.
As an alternative, I could make it on my own and in my own time, but I'm concerned this is a conflict of interest with my employer. It will make me look bad.
Is it unethical to go with personal development of this idea and then to sell it back to them? (although perhaps give it to them for some time span for free perhaps or similar benefit, but I retain ownership over it)
Field: Engineering, Central Europe