We are, though, required to attempt to form our conscience in accordance with Church teaching. The idea that just because a Pope has not spoken ex cathedra on the matter that one is free to believe whatever one wishes on the topic is simply wrong. The Papal encyclicals are among the most serious teaching instruments that the magisterium has at its disposal; on this particular topic the Papacy has released numerous, consistent statements over the last century and a half through its encyclicals. Dissent is, of course possible, but it ought to be a tragic conclusion at which one arrives after struggling to understand and bring one’s conscience into accordance with the teaching office and finding it impossible to do so. [on the importance of encyclicals and the level of assent that is demanded to them, see, e.g., Pius XII, Humani Generis]
The mathematics here is secondary, as someone else already pointed out. The mathematical models of any economic theory already presuppose basic dispositions regarding what it is to be human, how we relate to others and the goals of human personal interactions (even if the presupposition is, in some cases, merely indifference to the nature of the human end).
Economy, which takes its name from the household and its organization (oikonomia), is an attempt to describe a large and very important sphere of personal interactions; it is an account of personal relationships between people (or groups of people) in a particular region of life. Thus it has to be organized in a manner that accords with justice and charity and promotes the good. Any organization of society that fails in this regard does violence to persons and families and destroys community.
The social encyclicals have made repeatedly clear that liberal economics and socialism both fail in precisely those respects. I highly recommend Leo XIII, Pius XI, JP2 et al. for further reading.