1. People start out in real life with random endowments of “stuff” (no one picks where and in which family they are born), some of which they don’t want and trade for stuff they do want, and
2. You are right that if the “optimum” (which I presume you define as the maximum of all possible aggregate welfare values) happens, it is purely out of luck. But then again, the idea is not to attain some idealized optimum but just to show that trade can, in principle, make everyone better off in our stylized economy (and brings us closer to the idealized optimum by so doing).

Redistribution is an entirely different ball game which my students don’t get to hear about until the second required econ course they take at the Sanford School, which centers around public economics.

Before the next round of trade I had them wrote down their willingness to pay for their good (we learned WTP in a previous class, not WTA), and added up aggregate WTP for each group. Then I had them trade again, but changed the rules to let one group dictate the terms of trade; members of the other group had to accept whatever deal was proposed. After this round of “trade” they wrote down their new utilities, and their new WTP. The aggregate utility for one group was much lower than the other, of course, and the decrease for the plundered was about the same as the increase for the plunderers. But the increase in aggregate WTP for the plunderers was much greater than the decrease in aggregate WTP for the plundered! This outcome was a nice surprise because it demonstrated a potential Pareto improvement. This result led into to a good discussion on efficiency, equity, and ethics, which are underlying themes for the class. They seemed to really like the game- even those that lost the good trinkets. Thanks again for the idea.

I would suspect that equality had also increased, as more people have been left with the goods they wanted (and will assign a higher value to) over goods they valued lowly.

Using the game’s rules, we see that nobody’s welfare will decrease (because a trade cannot happen if it does), and the total welfare will go up. But if we try to make a more realistic rule, you will see that while the total welfare may go up, it’s no longer guaranteed that everybody will be better off. Imagine that one of the students decides that instead of getting a trinket he wants, he trades for a trinket he thinks other people likes, but he didn’t like. So he will first make a trade that, on a strict level, decreases his welfare, with the expectation to earn it back later. Even if he’s right, it is no longer true that the welfare always increases after every trade. The reason that this scenario is more realistic, because no one in the society makes things strictly for his own consumption. Everyone makes things expecting to trade with other people. And when the expectations are off, people lose. American manufacturers made investments expecting to trade with American consumers. Workers made investments in skills expecting to trade with American manufacturers. When the American consumers chose to trade with Chinese manufacturers, some people are worse off from this trade. People don’t have a choice whether to be exposed to these risks, they have to be exposed to some kind of risk. Most often, the winners and losers are chosen randomly, as no one can foresee the future. The free market principle ignores this, and ignores that sometimes people lose due to nothing but luck. The case for progressivism would be for the government to step in and mitigate that risk. Regardless of whether you agree, it’s important to note that the answer is not simple.