redistribution of wealth is a tricky thing. You can't just magically transfer money from the bank accounts of the rich to the poor. What needs to happen to redistribute wealth is an increase in taxes on the wealthy and a decrease in taxes/increased spending on the poor. If you made that adjustment through say an income tax you depend on the wealthy to continue labor at the same rate as before which we know that isn't the case since the "cost of lesiuire" has gone down due to their smaller wage. This of course depends where you are on the Laffer Curve as such a redistribution may not even be possible. Ignoring those factors, it is hard to say that an increase in wealth by the poor would effect aggregate demand as that would depend on the Marginal Propensity to Consumer of the poor compared to the Marginal Propensity to Consume of the rich for the additional dollars that the poor would acquire. You might also say that a loss in income would shift down the MPC of the rich which could further hinder aggregate demand. This should get you started on a couple of ideas that can be worked into a hypothesis on what could happen in that situation. Take this for what it's worth, Macro was never my strong point, I was much more of a Micro person. I intentionally didn't give you answer, hell, there probably isn't a correct answer to this question anyways.
PS. If you are looking at this from more of a Micro perspective, think of utility of people based on a bundle of private income and a public good. Efficient Allocation is a powerful micro tool that can be used to answer a lot of macro questions.
PPS. What is your textbook definition of equity? You seem to be using it in a different way then I know it to be. From the context of your post, It seems that you are using it to mean that all people will be equal.