The presence of coins improves social welfare, as it allows for more trades than barter would allow. Coin minting also provides income to the minting authority, as it can buy stuff with coins that have more value than their production cost. This is called seigniorage. This was also the case in medieval times, where "seigneurs" would mint gold or silver coins with somewhat less metal content than indicated and thus get income. One would thus think that these minters would be profit maximizing, and thus enhance welfare only as a by-product.
Angela Redish and Warren Weber say this is not quite true. They build a random matching model of commodity money, where the supply of silver is exogenous. They derive the welfare maximizing size and quantity of coins as a function of the quantity of silver and the probability of acceptance of cash. Using data from medieval Venice and England, they find that the model predictions follow remarkably well the historical record. This probably means that authorities were benevolent. I say probably because they may have acted in the same way out of selfishness, but that is not documented in the paper. Indeed, the model assumes than any holder of silver can mint, while in reality a limited number of people could do that.