What did parchment and papyrus cost in the Roman Empire?

TL;DR: There is no good answer to this question, because (1) we are missing reliable sources, (2) because there was no market price for any certain commodity, not for one and the same time and certainly not across four centuries. Evidence points to a price between 2 drachmae and 5 drachmae per roll (seems to be 10000 cm²) of papyrus, whatever that may mean. In any case parchment takes longer to produce and was most likely almost always more expensive.

Ancient economies were different from those today:

• Everything was subject to huge fluctuations in supply and to massive transportation costs. Prices fluctuated wildly.

• There were no market prices like on a modern stock exchange. The entire concept did not exist yet. You could expect prices to be different not just between different parts of the empire but also between different cities in the same province. What is more, there would probably have been price discrimination by status, at least in retail trade. The idea that a senator, a slave, an a foreigner would be made the same offer at the same price would not have seemed obvious at the time. This may have been different in wholesale trade over long distances.

• Much of the economy would have been a barter economy and a gift economy with commodities being exchanged for other commodities instead of for money; especially in rural areas.

• Various currencies were used in parallel, some intended for local use. Those currencies were managed decentrally and there is no reason to assume that there were constant exchange rates. (I am not certain if there were even official exchange rates.) The official currency was bi-metallic (gold aurei and silver denarii with an initial value of 1 aureus = 25 denarii) and was gradually debased (the precious metal content reduced) over time. Knowing what coin was worth how much, let alone agreeing on this with a trading partner, must have been a huge mess.

Pliny on papyrus and parchment

People in Roman times did not regularly record prices for commodities. They were more concerned with the deeds of gods and men than with such mundane issues as the economy. Luckily for us, they did occasionally write sales receipts and letters about mundane issues so that we can infer a bit. Also, Pliny the Elder (23-79 CE) had the idea to write an opus about how the world works - in 37 volumes no less - his Naturalis Historia. And he lets us in on a few of his insights on papyrus, mostly in book XIII.

Pliny specifically details how papyrus is made etc. and, more interestingly for us,

1. that there were many different qualities of papyrus (standardized with names such as "Augustus paper", "Livia paper", "hieratic paper", etc. (book XIII.23)

2. that the papyrus supply was sometimes (or maybe even always from the 1st century BCE) controlled by the government: Under emperor Tiberius (14-37 CE) there was a papyrus shortage that threatened to disrupt public life in Rome ("...as early as the principate of Tiberius a shortage of paper led to the appointment from the senate of umpires to supervise its distribution, as otherwise life was completely upset." book XIII.27)

Pliny even recounts that Ptolemy (the original one, 367-283 BCE) outlawed exporting papyrus for similar reasons and that his rival in Anatolia, Eumenes (362-316 BCE) therefore had parchment invented as a replacement (book XIII.21). This particular episode indicates at least that Pliny and his contemporaries were aware that

1. papyrus and parchment are substitutes

2. parchment would only be used if papyrus is not readily available even as an import good. (So papyrus is either much cheaper or of better quality; considering that parchment is very sturdy and has quite a few desirable qualities it is probably that papyrus is cheaper.)

However, even though the episode has attracted a lot of interest from historians (summarized and exemplified here: Richard R. Johnsn, "Ancient and Medieval Accounts of the 'Invention' of Parchment", California Studies in Classical Antiquity, Vol. 3 (1970), pp. 115-122, paper is behind a paywall, sorry.) the details of this episode should not be taken serious since this chapter (book XIII.21) also contains a ridiculous amount of bullshit that we know to be false. (He claims that Alexander the Great (356-323 BCE) invented papyrus, that Eumenes invented parchment, that Egypt did not yet exist in Homer's lifetime etc. etc.)

Letters and other sources

Skeat (T.C. Skeat, "Was papyrus regarded as 'cheap' or 'expensive' in the ancient world?", Aegyptus, Anno 75, No. 1/2 (gennaio-dicembre 1995), pp. 75-93, paper is behind a paywall, sorry.) has a very insightful chapter on the price of papyrus.

• He quotes a different source in German (HJ. Drexhage, "Preise, Mieten/Pachten, Kosten im römischen Ägypten bis zum Regierungsantritt Diokletians", 1991, p 384-7.) as listing a large number of prices that have been recorded in letters etc.

• He points out that information about the price alone is not useful if details on quality and quantity are missing. He tries to resolve this and arrives at the following standard quantities:

• A roll of papyrus being about 340cm x 29.5 cm (the width seems suspiciously close to A4), hence about 10000 cm², a roll being composed of 20 sheets, i.e. a sheet would have been about 17cm x 29.5cm.

• The price of a roll being between 2 drachmae and 5 drachmae in the first centuries CE. Drachmae at the time were local currencies in Greece and Egypt.

• In letters it was common to request more papyrus to be able to write more or to refer to empty papyrus sheets enclosed with the letter to enable the recipient to reply. While this would suggest that papyrus was extremely expensice, Skeat dismisses this on the basis of his computation laid out above and suggests that it is more a figure of speech or a gesture to indicate impatience or so. ("Dear mum, I am sorry I was not able to write sooner. This is definitely not because I attended so many orgies, but because ... um ... I did not have any papyrus." - "Dear son, will you finally reply again? Here's a sheet of papyrus for you in case you're out again.")

Implications for later historical periods

According to Fravia, Europe switched to parchment after the Muslim kalifat's conquest of Egypt as papyrus had become unavailable. Writing on parchment is apparently easier to erase than on papyrus (because parchment is sturdier). This is, according to Fravia, one of the reasons why we know so little about the early European middle ages: Whatever they wrote was later erased and the parchment reused for silly stuff in the late middle age or early modern age. (The identity of Fravia is afaik not entirely clear, but he appears to have been trained in medieval history among other subjects like computer science and linguistics.)