A beta version probably should be free due to it being a non-finished product.
On my current project (https://report4me.com) we're trying the free beta model not only to get beta testers but also to determine a price point.
We give away the product to beta users for the foreseeable future, with the intent to ask them outright what they feel the product would be worth. The idea is that since they can feel comfortable that they won't actually have to pay the price they mention they might actually be more honest about it.
On my current project (https://report4me.com) we're trying the free beta model not only to get beta testers but also to determine a price point.
We give away the product to beta users for the foreseeable future, with the intent to ask them outright what they feel the product would be worth. The idea is that since they can feel comfortable that they won't actually have to pay the price they mention they might actually be more honest about it.