It is my understanding that Rome had no economists, despite having a very advanced economy and many "advanced" professions ranging from historians to astronomers to botanists and architects. Why is this? Surely Romans saw the effects that basic economic principles had on their daily lives and understood finance?
Although the Romans were advanced, and I'd argue (beer and pretzel's argument, not scholarly argument) that they were the first modern economy, they had no notion of economics. (remember they also had no word for Volcano)
Economics is generally dated to the Wealth of Nations in 1776 (arguably mercantilism was a precursor economics, but that's another beer & pretzels discussion.)
The publication of Adam Smith's The Wealth of Nations in 1776, has been described as "the effective birth of economics as a separate discipline. Wikipedia
The notion of supply and demand first occurs in the 14th century, so Rome wouldn't have had the concept.
According to Hamid S. Hosseini, the power of supply and demand was understood to some extent by several early Muslim scholars, such as fourteenth-century Syrian scholar Ibn Taymiyyah, who wrote: "If desire for goods increases while its availability decreases, its price rises. On the other hand, if availability of the good increases and the desire for it decreases, the price comes down." Wikipedia
Again arguably, Rome had a macroeconomic policy, which was roughly, "Take (peaceably if possible, by force if necessary)from those who are not Roman to enrich the Romans.", but they neither had the concepts to articulate their macroeconomic policy, nor the basics of microeconomics.
My mother would be utterly unable to articulate the theory that underpins the medical devices that sustain her life - but she can use them just fine. Similarly, I'm confident that canny Roman merchants used the principles of supply and demand, but they didn't have the theory of supply and demand.
If you want further proof that the Romans had no economists, examine the monetary policy of Diocletian (disclaimer - the Mises institute has a bit of an agenda about monetary policy. I happen to agree with them, but I'm citing them because they're relatively terse and accessible, not because they are objective.) Roman coinage was regularly debased, and I've found figures of up to 90% debasement.
There are plenty more examples of boneheaded Roman macroeconomic policies, but you seem to really be asking about microeconomic strategies and activities. Policy tends to leave more explicit records; microeconomic activity leaves traces, but it takes significant effort to assemble evidence of price and supply curves in a period for which we have only partial records.
Consider their slavery policy - They imported enough slaves to significantly devalue their labor supply and had to implement the dole to prevent riots and preserve the government.
Consider their luxuries - things like citruswood, which is intrinsically scarce. Again, they had an instinctive understanding that rare and exotic items were valuable, but they didn't have a theory to explain it, or to predict what impact an increase in supply would have on prices.
Some rudimentary development of economic theories did occur in Greece (before it was conquered by Rome). At that time, economics did not yet separate itself from philosophy (the same is the case with other branches of science, with very few exceptions, like mathematics). You can find a reasonably detailed treatment of Greco-Roman economic thought in Chapter II (Ancient and Medieval Economics, by S. Todd Lowry) of "A Companion to the History of Economic Thought", Edited by: Warren J. Samuels, Jeff E. Biddle and John B. Davis.
Interestingly, ancient Greeks already coined the term "economics". Here is a fragment from Todd Lowry's article:
The best record of the tradition of training in administrative economics is found in Xenophon’s treatise, the Oeconomicus, written in the mid-fourth century B.C. (Pomeroy, 1994). He also draws on the Babylonian and Persian tradition in his biography of Cyrus the Great, the Cyropaedia, that emphasizes the training of Cyrus for administration and military leadership. Xenophon’s Hiero contains discussions of the administrative stimulus of private production and technology through public recognition and prizes. His Ways and Means was a treatise on economic development, emphasizing economies of scale, programming, and promotion. The Oeconomicus is a systematic treatment of the organization and administration of the agricultural estate, emphasizing human capital and organizational efficiency (Lowry, 1965; 1987, ch. 3). The family farm was the backbone of the economy and booty from military operations was the prime source of surplus for farm and city (Hanson, 1995).
Read more there on economic thoughts by Aristotle and others.
Accepting that theoretical economics at the time was a part of the general philosophy, the question becomes why Roman civilization never produced a philosopher comparable to, say, Plato and Aristotle. (Same for mathematics: Nobody comparable to Euclid or Archimedes, although Diophantus comes close.) I do not have a good answer for that, I am not sure anybody has. While Romans adopted much of Greek culture, science and religion, theirs was a very different society. Maybe the Classical Greek science was just a remarkable historic accident, an ancient marvel.