Let's say you're at the $400 level (you tossed 9 heads in 9 tries). Should you toss again? If you do, you have a 50-50 chance getting the $1400 or nothing, so your expected return is 0.5*($0) + 0.5*($1400) = $700, which is greater than $400, so the odds say to flip the coin. I suppose the real answer depends on how many tries you have and how much of a gambler you are, but all we can do here is calculate the expected return.
Now suppose you have tossed 8 heads in 8 tries. If you toss again, you either get $0 or you're into the situation in the previous paragraph, which we decided has an expected return of $700. So you should toss again, because your expected return is $350 and you only get $200 if you don't toss.
I think you can calculate the rest.
Let us know if you're still stuck.