As in the other areas, there are two significantly divergent types of history done in economic history of the Renaissance. The one, and perhaps older, addresses large issues and seeks to characterize the Renaissance as a time of economic expansion or as a time of economic recession and crisis.
Economics turns out to be closely related to the whole question of the Renaissance because of the role played by the merchant classes as patrons of the humanists and artists. If the Renaissance (especially the 14th and early 15th centuries) was a time of economic contraction, then the Renaissance in a sense happened in spite of economic factors. If, on the other hand, the theme is economic expansion, then it becomes easy to tie the fortunes of the artists to the fortunes of the merchants.
The other school, or methodology, ignores such large questions, or at least defers them, in favor of more specific questions. These look for the origins and growth of banks, of insurance, of business methods, and so on. They look at agriculture and especially at the movement of merchants out of trade and into land-owning. In short, these studies focus of specific issues and usually on quite specific places and times.
Hay makes some good points about the rather different nature of economic life from our own times. I'll try to add and expand on these.
Economics is the study of wealth, and in pre-modern Europe all true wealth was in the land. To a lesser extent it was also in bullion, but even that could be unreliable at times. The one solid foundation of wealth, and all estates agreed on this, was land - specifically, cultivated land. Appreciating this fact takes more work than it might first appear, but it is the basis for understanding much of the economy of Europe prior to industrialization.
Money, on the other hand, was not omnipresent as it is in our society. Most Europeans never had more than pennies, largely because there literally was not much for them to buy, restricted as they were to the local village market and wandering peddlers.
Money was risky, as were the means of getting it. Employment was risky -- certainly riskier than own land or even being a peasant or serf -- for employment could be terminated. Investment was even riskier, though the rewards were greater. It's not surprising to me that merchant families turned fairly quickly to the land, seeking the titles that were the necessary accoutrement of landed wealth. Staying in business meant continuing to expose oneself to the stress and risk of investment and trade. Far better to own a few villas!
Cities were the great concentrations and concentrators of money. Indeed, the first gold coins were struck by cities, in the 13th century. Here, too, were located manufacturing and trade. Those who understood money, or at least who were willing or desperate enough to run its risks, naturally gravitated to the cities.
While there were some technological innovations during this period, as there is in any era covering 250 years, in general the Renaissance is not known for many accomplishments in the economic realm. The great innovations in business techniques belong to the 13th century or even earlier: banking, coinage, double-entry bookkeeping, contracts, insurance. Other innovations belong to the 17th century: joint-stock companies, money markets, stock exchanges.
No Economic Renaissance
The Renaissance saw, however, a great acceleration of the trends of the 13th century. The first banks may belong to the Middle Ages, but the first banks of note belong to the 14th. The other innovations of capitalism likewise may have sprouted in earlier times but they came to fruition in the Renaissance. Think of this time as an era of adoption and elaboration. You should note, too, that there is little evidence of merchants attempting to imitate the ancients in matters of trade and manufacture; in this sense, there was no such thing as a Renaissance of business.
Our era marks the beginning of the definitive split between eastern and western Europe in matters of landholding. Even as serfs were becoming peasants in the west, the free peasants of the Slavic lands were being turned into serfs. The reasons for this, and the dynamics of the process, are complex as you might expect; I point out here only the fact itself.
ExplorationThe greatest economic innovation of this time at first looks more like technology than economics. In the 15th century the Europeans learned to make long ocean voyages . . . for profit. While other civilizations had built navies and sailed wide oceans, they either sailed for political purposes or else did not maintain their efforts for very long.
It takes sophisticated naval technology to sail in open waters for weeks at a time, and even more skill to do so and make money at it. It also requires an economic system back home able to absorb and reward the risks; in other words, it takes merchants as well as sailors.
This was the great economic advance of the Renaissance: the creation of the means to exploit vast new markets. It was one of the key developments that demarcate the Middle Ages from modern times, for not only did exploration open new markets, it opened up paths of colonization and conquest as well, with lasting effect on a global scale.