Allocative efficiency -- correlation between MB and p in populace with wealth inequality
My textbook asserts that a competitive market would produce an efficient allocation of resources. Resources would be moved from less profitable products to more profitable ones, and this would necessarily increase the monetary value to consumers of the total products sold.


The textbook is correct (provided the assumptions behind "competitive market" and other implicit ones hold).

First, assume the distribution of wealth is given. Then, based on their budget constraint, consumers will have a certain demand for goods. Firms will compete for such demand, offering the lowest price that earn them an economic profit. In competitive markets, such profits are zero. Resources are allocated such that consumers are maximising their utility at the given prices. The allocation is Pareto Optimal.

This result is summarised in the First Welfare Theorem.

Second, through some form of lump-sum taxation, we could redistribute wealth in order to change that allocation. A competitive market will make the equilibrium Pareto Optimal too. This is the Second welfare theorem (see link above).

So, your intuition that the wealth/income distribution affects prices and the final allocation is correct. But the key to allocative efficiency is in the mechanism (market), not in what is being allocated.

I hope I am answering your questions.