In what ways are schizophrenic people more alert, focused, and attentive?

I've just recently learned that a schizophrenic person has an excess amount of the neurotransmitter dopamine, and if a person has a deficient amount of dopamine then they have Parkinson's disease. Dopamine causes you to feel alert, focused, and attentive. With that being the case does the schizophrenic person experience any of the positive effect of DA that a non schizophrenic person experiences. And furthermore if people with Parkinson's are characterized with being DA deficient then why can't we just give them more DA and take all their symptoms away?