How to define the adequate cash prize sizing for hosting a Kaggle or similar compeition?
This is a generic question that may need more than just cash prize.

1) Organizational Reputation 
2) Dataset Size
3) Defining Problem statements with Domain knowledge
4) Time period
5) Computation required for the contest.
6) How curated/clean is the dataset
and much more.

If the problem statement is huge and the reward is in single digits, its not worth anyones time and at the same time, if the problem statement is mediocre and huge money is rewarded, it does not serve the purpose of the Kaggle competition at all.

even though Kaggle provides GPU and 16GB ram with CPU's, sometime the Kernel crashes and there is no work around unless you spend some money on AWS/Azure instances.

I hope this gives few pointers