Have you considered having a pay per search plan in addition to the subscription.
For eg: For 10$, you give 700 free searches and beyond that you charge exactly what it costs for a search.
I think, instead of changing the subscription amount, keeping it at 10$ and playing around with how many free searches you can provide will be better. As more people join and scaling lets you reduce cost per search, the amount of free searches can be increased.
10$/month most people who want an alternate to Google/Bing ..etc would be willing to pay. With this model, your risks are reduced. You make a profit when people use it for less than 800 searches per month and whenever they use more the cost per search pays for that
