The price that your competitors charge is only one of many signals that you should consider when setting a price. I think it's good that you're focusing on the value that you're bringing your customers. As other have pointed out, that can be hard to quantify, but it's still very important.
I'd say there are five important factors that determine any startup's price:
1. Cover the costs of production. This includes the salaries of your engineers and your average cost of customer acquisition, including marketing and sales costs. At minimum, your price should cover these costs.
2. Charge for the value you're brining to customers. This is something a lot of startups ignore. If you're offering a product or service that bring substantial value to your customers, make sure you charge for that. Consider using a pricing structure that lets you extract more values from customers as they get more benefit out of your product, like charging for each additional user/login on a corporate account.
3. Consider what your competitors are charging. This can help, but it can also hurt. If you're going to be charging substantially more than your competitors, you need to know why. And you need to be able to explain why to your custom when they inevitably ask during the sales process. Plan ahead for this.
4. Consider economic signals. As others have mentioned, high prices can indicate high quality. I've heard stories of several startups who were more successful after raising prices -- without substantially improving their product. If what you're offering is a premium service, you should compete on quality, not prices. And in most cases, higher price points imply higher quality. Use that to your advantage.
5. Make the price relatable. The only way you'll ever make a sale is if you can convince your potential customers that the value of your product is higher than the cost you're charging. Humans can be surprisingly irrational when it comes to judging value. Put the cost of your product in terms that are relatable to them.
A great example of this was JibJab raising their price from $9.99 per year to $12 per year and seeing their conversions go up -- now their product was "only a dollar a month!" which seemed like a better deal since the price was more relatable.
I wrote about most of these factors in this blog post:
I'd encourage you to do some experimenting to see what works best for your company in your industry. It's a very specific and sensitive issue for any business and it's hard to offer one-size-fits-all advice.