here's no gain here. 50k spent to get a 30k increase in property value is a 20k LOSS.

oops sorry, my mistake, i meant to say: there is a *capital gain* of 30k, so the property value increases by 80k

Let's say Bob and Jon each invest 10k to buy a property. So jointly they have invested 20k, and owe 50% of the property each.

Suppose Bob then invests 50k on improvements, and suppose as a result the property value increases by 30k.

The total amount invested is therefore 70k and the total gain 30k, making the new property value 100k.

How could this value be allocated equitably?

Is 60/70 of the gain attributed to Bob, and 10/70 to Jon i.e. 85.7k to Bob and 14.3k to Jon ?