Edit: the Mods kindly reached out to let me know that my post as it was mostly read as sort of a "your question sucks" reply, which was a product of bad writing rather than my intent, so this edit is an effort to redeem it.
The question of the way people attach value to things is a complex one, no less so when it is a person made through law into a thing that is being valued. To start my answer I should make it clear that enslavement is something that is by its nature dehumanising, and the discussion of it can easily follow the same trajectory, even via the process of description. Take this to every word of my reply: those forced through violence and coercion into labour, and who were traded as property, were people like you or I, and the decision to label them as property did nothing to change that.
In terms of my own background in this field, I come to it via histories of race and exploration, which has led me to read widely into Nineteenth Century abolitionist movements, as well as a fair bit of primary research in the Indian Ocean in that century (particularly Zanzibar). I also have a relatively decent understanding of Muslim history in general, but it orientates towards the general rather than the specific (though I've more specifically delved into the history, development and expression of Hanafi jurisprudence, the work of Ibn Khaldun, and the history of the Naqshbandi tariqa).
So to start addressing the question we need to look at its scope. You use the phrase "Islamic world" which is a starting point for exploring why the question of value is so complex. When it comes to markets (and given that you're asking about prices I am guessing we can exclude those bondage relationships that existed that did not initially involve markets, for example the system of wards amongst Tiv people in what is now Nigeria) it isn't just supply and demand that determines the nature of the price paid for something. Markets have pre-requisites for their existence and many of these relate to governance (the laws that manage trade, the currency in which trade occurs, the safety of trade itself etc.).
This is why the phrase "Islamic world" raises some revealing considerations. One of the interventions that came with the coming of Islam was that the religion essentially cut off many of the ways that a person could become a slave. David Graeber's book "Debt" cites an Egyptian sociologist named Ali 'Abd al-Walid Wafi (who he argues was the first to carry out a historical survey of the institution of slavery) with a list of the avenues into slavery:
Islamic law technically limited the avenues of entry into slavery to a single avenue: surrender or capture in war. This (and I repeat the "technically" because the practice was, as I'll discuss, different) meant that enslavement was in theory confined to the business of government and warfare. Muslim laws also made the enslaving of co-religionists impermissible, and in many cases (for example in Morocco through power of a royal fatwa) made the selling of enslaved people to Christians or other non-Muslims impermissible. Finally, a Quranic verse in Surah An-Nur made possible (with caveats) self-manumission:
And if any of those ˹bondspeople˺ in your possession desires a deed of emancipation, make it possible for them, if you find goodness in them. And give them some of Allah’s wealth which He has granted you.
The features of markets entailed a relationship between the law and the form of the trade, and in turn the value ascribed to trafficked people. This is clearly illustrated, for example, in Maliki legal texts from Sub-Saharan and Saharan Africa, that explore at length the possible factors in determining the value of an enslaved person, as well as the conditions of such a sale.
The nature of these legal texts also make it clear that regulation was required, as it was at least sometimes ignored (Islamic legal rulings often follow the format of a question and answer, one fatwa for example begins with the question "Is it permissible to sell a slave to another trader with the knowledge that they will in turn sell them to the Christians", a question that makes it clear that such a practice existed, even if the reply responded that it was not permissible - this fatwa was by Shaykh Sidi Abdallah ibn al-Hajj Ibrahim).
With that explanation in hand we turn to the framing of the "Islamic world", and to the fact that both the text of Muslim laws and Muslim practice in reality meant that the enslavement and trafficking of people by Muslims was by its nature interactive: it was never confined to Muslim lands. The factors that affected the price attached to slaves were intimately tied to regional and global trade and geopolitics. Further, even the existence of slavery itself in lands ruled or populated by Muslims was tied to those factors.
Two examples spring to mind:
In Egypt, because of a large population of rural workers, slavery was not really a part of the growth of cotton and the manufacture of textiles. This changed suddenly in the 1860s when the American Civil War led to a rush of demand for Egyptian textiles, which was met through the enslavement and trafficking of people to keep up with a global need.
In the Nineteenth Century the trade in enslaved people from West Africa to the Maghreb and then into the Middle East grew in relation to the slow collapse of the Atlantic slave trade. As the demand on the West African coast plummeted, while the systems for enslaving people for that trade remained, the price of enslaved peoples decreased, and this had a subsequent effect on the economic viability of trafficking across the Sahara and beyond.
We then come to the question of race, which I have avoided until now. You ask why "white slaves were more expensive than black slaves" and I think that deserves a bit of an exploration, namely to ask if that can be so definitively stated.
There are a few reasons that this is difficult to address.
The first and easiest to address is that value is not a static thing. The value of any type of item of exchange will vary wildly across time and distance, and even across individual items.
A salacious example is cocaine. A gram of cocaine purchased in Sydney is not going to be valued the same as a gram of cocaine purchased in Medellín. Even within Sydney the value will depend on who is buying, and who is selling. The value will also depend on regulations (or lack thereof) of the sale. It will also vary gram by gram, with purity and cut. Then even further it will depend on the time in which the sale occurs, fluctuating with police busts, global trade, conflict in regions of supply, cultural norms around consumption etc. etc.
This is then further complicated by the way that we measure value. Just as the value of that gram will vary from place to place, so will the value of the thing it is bought with will vary. The value of a Colombian peso in Medellín will not be the same as the value of an Australian dollar in Medellín, and vice versa. Both will not be the same in a few months, or years, or if they were both reduced to their constituent parts.
All of this makes it pretty hard to definitively establish a universal comparison of value, as similar issues apply to the slave trade.
Which doesn't mean that it isn't a revealing or bad question, but rather that examining the problems that the question raises is itself revealing!
So establishing comparative value is the first reason that it's a hard question to answer.