Is there a biological limit for "amount" of happiness? I have heard about neurotransmitters like dopamin and serotonin that are supposed to play a role in our feeling of happiness. I don't know how these chemicals works in our brain, but I am thinking that if happiness is dependent on chemical reactions in our brains there must be some physical limit to how happy we can be.

If I own a 10 million dollar yacht, and upgrade to a 100 million dollar yacht could it be that my happiness is already at its maximum and I am throwing away 90 million dollars?

Does the chemistry of the brain impose a limit on how happy it is possible to feel?
My knowledge of the neurobiology of pleasure (aka, hedonia, hedonic happiness, happiness, "liking", reward, etc.) is admittedly lacking, but I'd contend that this is mostly true because we actually know very little about how pleasure is instantiated in the brain.  So the answer to your question is that we don't know!

First of all, mesolimbic dopamine seems to be more involved in the motivational component of reward (what Berridge and Kringelbach would call "wanting"; e.g., Kringelbach &amp; Berridge, 2009; see also Salamone &amp; Correa, 2012). 

On the other hand, opioid and cannabinoid neurotransmitter signals (and others) seem to mediate the hedonic component (i.e., the "liking"). Even then, stimulation only to certain parts of the brain (i.e., "hotspots") produce hedonia (e.g., in parts of the nucleus accumbens; Pecina, Smith, &amp; Berridge, 2006).  And even then, as the context changes, these hotspots will stop producing the expected output or will change valence.  And even then, these findings from non-human animals may not be comparable to the more complex experiences of pleasure that humans have!

And only very recently have we been able to map out which brain regions correspond to positive or negative affect (Lindquist et al., 2015).  And it seems that no brain region or voxel uniquely represents positive or negative affect (see degeneracy). (But there are preferences. And there may be confusion between which regions cause pleasure and which code pleasure; Kringelbach &amp; Berridge, 2009).

Not to mention, happiness encompasses a broad range of potentially heterogeneous experiences and feelings.  Happiness evoked by one experience might feel very different and look very different in the brain compared to some other happy experience (see C. Wilson-Mendenhall's work).  So how do we compare?

And this is just the broader view.  How the biochemistry of the brain produces the subjective experience of pleasure is completely unknown, so it's more or less impossible to know (at present) whether there's a biological limit to the intensity of happiness.