When was inflation first talked about? I don't know if economics had a macro element to it in those times, like I don't know if the politics of taxation and money were the same in Ancient Rome.
However I've accepted as my definition of inflation, a phenomenon which results in the reduced buying power of the same amount of currency.
As in, short term price changes notwithstanding, when the entire Roman Empire no longer makes enough money to support itself and a revolution occurs.
Did they talk about the phenomenon of inflation in those days?
Yes, China had some understanding of the concept of inflation quite early. There were struggles with both inflation and deflation over time, people generally had some conception of what was happening.
The exact details of the economic organization of the earliest dynasties through Western Zhou are unclear, though it seems money didn't play an important role. The earliest records we have of markets suggest that the prices were just set by officials, so inflation didn't really matter, and the economy wasn't commercialized enough for this to cause too many distortions.
The Spring and Autumn period was when states grew both more powerful and commercialized, and was when the earliest discourse on monetary thought emerged. Coins in this time were generally bronze or copper, though gold and to a lesser extent silver were used, the latter two mostly for international trade. By the time of the Warring States, different coins had emerged in different states.
One of the first recorded piece of monetary theory came from Shan Qi in the 6th century BC. He assumed that pairs of copper coins, "mother" and "son" coins are in circulation, with the former being larger and the latter smaller. He argued against discarding the smaller coins in favor of some more of the larger ones, as the smaller coins were already in circulation, and it would thus impoverish the people. Instead, larger and smaller coins should be issued so that the demand for them is in balance. In arguing for a balance, he introduced terms that would come to characterize supply and demand for general goods, "heavy" and "light". A light coin, or good, has low demand or high supply, and is thus less valuable compared to a "heavy" coin. This doesn't have anything to do with the actual weight of the coin, which can be a little confusing.
There's a few things to note about his arguments. First, it was quite superficial: two coins, no real understanding of what drove movements in value of them beyond a ruler confiscating or banning one of them. Secondly, we aren't sure if this was completely his invention or not, something quite common in sources in this time period. It is too early and too much has been lost, so most of these authors can be thought of as representing an idea that may or may not have had previous development by one or multiple people, we just don't know. This applies to the following authors as well.
Building on this was Fan Li, prime minister of the state of Yue and after a very successful merchant. He proposed a theory of trade cycles in the 5th century BC, perhaps the earliest in the world to do so. In his vision, the basic underlying principal was to be found in a astrological system, where the movements of planets and stars effect harvests on earth. More grounded was what happens next: the success or failures of harvests drives the prices of foodstuffs, which in turn drives the prices of non foodstuffs. If food is plentiful, people will have more money available to buy goods, driving their price up, while if food is scarce, people will invest more in food, bidding it's price up, and leaving them less money for other goods.
Based off of this came one a brilliant idea. As a merchant, he would buy food and sell goods when food was cheap, and do the opposite when food was expensive. He realized that peasants must to the opposite because they need to eat, and cannot refuse to take the other side of that trade. When they had excess food, it would be wasted if they didn't sell it, as most peasants didn't have the storage facilities, and in bad harvest if they didn't buy food they would starve. Thus, the government could do what he did on a much larger scale to smooth fluctuations in the grain market, protect the peasantry and make a nice income. If a purchaser at the scale of the government bough massive amounts of grain when it was cheap, they could drive the price up, giving the peasantry a larger income, and then conversely drive the price down when it was expensive, alleviating the burden of purchasing food. The price of grain would still fluctuate, and the a latter price still higher than the former, so the government would make money, but the gap would be much smaller, so the peasantry would be better off too.
Famine relief had previously been part of the expected role of leaders, is a poem from Western Zhou where the King of Zhou exhorts his ministers to distribute relief during a drought. But these ideas represented a much more sophisticated approach. It is also a step closer to understanding-and alleviating-the effects of fluctuations in price and the value of money. This is a type of inflation and deflation found in agricultural societies where farming makes up the vast majority of economic activity: that fluctuations in the price of grain can drive prices of everything else.
This would be developed further and the role of money became better understood as well. Mohists pointed out that money and grain have the same relationship: when money is "light", that is common, grain will be cheaper, but when money is "heavy" it will be more expensive. They also thought short term fluctuations were generally driven by the grain market. It was a short step from there to a more full theory of foodstuffs, money, and other goods.