No it wouldn’t if initial endowments are different.

As I said at the beginning, someone may value a product more (in the sense of the utility they gain) but their “willingness to pay” may be lower because they have a lower level of wealth than other people in society – implying that their opportunity cost from buying the product is higher (as they have less resources and so would have to sacrifice buying something that they value at an even higher rate).

An easier way to state this is that if we had two people with the same utility function (and no altruistic values) but different initial endowments (in terms of utility value), the person with the greater endowment would end up better off through free market trade – even though it would be welfare maximising to have an equilibrium where they both consume exactly the same amount (given our assumption about the individuals utility functions). Note the equilibrium would be pareto efficient – but it’s not welfare maximising given our normative judgment and the full set of potential pareto efficient equilibrium.

Fundamentally, this is one of the differences between willingness to pay and the marginal utility that someone receives. (Prices captures the impact of relative marginal utility (as the price ratio equals the marginal rate of substitution), but it doesn’t necessarily capture the absolute value between market participants.

Given different endowment structures we receive different pareto efficient equilibrium (assuming that we achieve uniqueness – which in itself is unlikely). Now as they are pareto efficient we can’t objectively rank them.

However, if we have a set of value judgments we can apply them to rank the equilibria and decide what the optimal initial endowment of resources would be – give these assumptions.

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I am not trying to defend transfers – as you can see we need to discuss why we believe someone “values” the product more in the first place. However, even if we were incredibly left-wing and wanted to redistribute to hell, we should still leave prices to the market and redistribute the initial endowment to get where we want.

“take some resources from those that receive a low value on the additional dollar of spending and give it to those who receive a higher value”

were pareto efficient then it would be in the process of happening now.