If the conversion per unit capital invested were linear, regardless of amount, then you'd spend all that you can. However, it's not linear by any stretch of the imagination, at some point you will saturate and not generate any new conversions for the unit capital spent. So, you might approach the problem by asking how large your target market is, and then how much of that market is exposed to your product with a measured block of advertising. After all, once someone has seen your message 2-3 times, they're either going to investigate further or ignore it.
Once you've mapped exposure to your spend, you can then try to match that against what you think your growth rate should be. Put simply, if you had the ability to drive all of your potential market to your application all at once, would you? No, you'd ramp it up so that you can test all of the scaling assumptions on real, live users. So based on your technical load testing so far, you know how large the initial user pool should be. Use that number to back into the exposure level you need (based on the hypothetical conversion rate above) and finally back to how much you should spend. This number should be way below the "spend all the money" scenario. That should be your initial quarter budget for advertising.
The next point is very important: MEASURE. You come into this with the assertion that the revenue generated by converted users is greater than the amount spent on advertising. However, you don't just spend on advertising right? Theres the rest of the business to pay for as well. Use the initial spend to measure your actual yield for dollar spent, and then get your marginal costs for adding each additional user and do a sanity check on the pricing and cost structure. If scaling is in your favor, that marginal number will get smaller as you grow your user base, but in the nasty case where it doesn't, you've got a heads-up before you grow a huge user base that is costing you money to support.
Once that initial phase is done, then you can base your spend rates on measured yields and desired growth rates figured from your technical and strategic plan.