How costly was space travel in the world of Dune?

Question

It is clear that spice was costly and that the Guild Navigators used large quantities of it:

Herbert notes in Children of Dune that the geriatric properties of melange had been "first noted by Yanshuph Ashkoko, royal chemist in reign of Shakkad the Wise." By the events of Dune, the spice is used all over the universe and is a sign of wealth; Duke Leto Atreides notes that of every valuable commodity known to mankind, "all fades before melange. A handful of spice will buy a home on Tupile." Due to the rarity and value of melange and its necessity as a catalyst for interstellar travel¹...
¹Source

The spice being so costly, and by being such huge consumers of the spice can we gauge what the Guild charged for space transportation in return?

Can we say how costly was Guild based space travel?
Or is there an example of what space travel cost in the books?

_{The cost to someone in terms of spice or solari for transporting a described good or object. Obviously an exact number like an airfare is impossible. I'm looking for some indication from the novels, or even the movies.}

Answer 1

There is a clear empirical answer (at the least an estimate) of the enormous cost of such travel.

The Baron sighed. "I give you different instructions about Arrakis this time, Nephew. When last you ruled this place, I held you in strong rein. This time, I have only one requirement."
"M'Lord?"
"Income."
"Income?"
"Have you any idea, Rabban, how much we spent to bring such military force to bear on the Atreides? Do you have even the first inkling of how much the Guild charges for military transport?"
"Expensive, eh?"
"Expensive!"
The Baron shot a fat arm toward Rabban. "If you squeeze Arrakis for every cent it can give us for sixty years, you'll just barely repay us!"
Rabban opened his mouth, closed it without speaking.
"Expensive," the Baron sneered. "The damnable Guild monopoly on space would've ruined us if I hadn't planned for this expense long ago. You should know, Rabban, that we bore the entire brunt of it. We even paid for transport of the Sardaukar."
_{Dune pg. 237}

First note the use of the common term cent above, Mr. Herbert appears to have carried this into the Dune-universe. There is another piece of evidence in Heretics of Dune to get a gauge of the worth of a solari, consider the conversation between Lucilla and Sirafa.

"That is not a concern. You must never act as though you recognize such distinctions. Your first concern is to make sure of your pay. You, I think, should ask fifty solari."
...
Sirafa produced a small pouch from her bodice and passed it to Lucilla, who hefted it in one hand. "That contains two hundred and eighty-three solari. If someone identifying himself as a divine... You remember that? Divine?"
...
"Very well. If a divine interrupts, I return one hundred solari to Skar and -" "Fifty!" "I think not, Sirafa." Lucilla shook her head slowly from side to side. "After being entertained by me, the divine will know that fifty solari is too small a sum."

This analysis gives the rough estimate 1 solari = 1 USD (at least in 1960-70's currency) when the books were written.

Let us couple this with the fact that Melange is easily the most expensive commodity in history. And the fact that, that commodity has to be harvested for sixty years to repay the cost of a single military expedition.
Further than this we will be in speculation. But if we know the GDP of Arrakis in USD circa 1970's it's simple arithmetic to estimate the cost of that one ill-fated expedition to Arrakis. Let

Global GDP (1970) rounded down = $12 trillion multiply by 60 = $720 trillion (solari).

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There is a subtle flaw in this argument, it assume a constant linear GDP of $12 trillion over the entire 60 year period. This is typically not the case, assuming a nominal 1% annual GDP increase leads to the horrendous cost of $4,069 trillion that's four quadrillion solari. _{(I used an Excel sheet and multiplied successive cells by 1.01)}
On the surface this would seem a error on Mr. Herbert's part, perhaps he simply picked sixty out of thin air, except for two things.

1. Piter describing the computational ability of the Barron:

   "They were toys compared to me," Piter snarled. "You yourself, Baron, could outperform those machines."
   _{Dune pg. 18}

2. Mr. Herbert describes his very careful sentence construction:

   Well, this was done deliberately to control that oral pace by the length of sentence, by the variety of sentence, by the words in the sentence, whether long convoluted words or short chopping words…
   _{Frank Herbert and his wife, Beverly (3 February 1969) interview with Professor Willis E. McNelly}

Answer 2

There are two relevant quotes:

"The Harkonnens took ten billion solaris out of here every three hundred and thirty Standard days."

plus

"If you squeeze Arrakis for every cent it can give us for sixty years, you'll just barely repay us!"

This lets us establish lower bound of 600b for the invasion, likely more given the "squeeze for every cent" part. Similarly, Hawat thought:

"The entire spice income of Arrakis for fifty years might just cover the cost of such a venture. It might."

This puts the estimate of costs at 500b+, in line with the previous estimate.

On the other hand, we also know Harkonnens ruled the planet for 80 years. Assuming same 10b/year and saving this complete money stream for this invasion, the upper bound is 800b.

In total, we are looking at several hundred billions for the whole invasion, both the lower and the upper bound are fairly close actually. It is heavily implied that the invasion costs are dominated by the transport costs, but I don't know breakdown - therefore I guess transport costs are between 50% and 100%. This was for 10 legions + more than 2000 ships (Hawat's estimation from the same part as the quote above).

Therefore, I estimate that a ship plus approximately 150 people (1/200 of a legion) costs somewhere between 150M and 400M for transport costs.

There are some assumptions, the obvious one is that nobody lies or is completely mistaken. Then 330 days vs 1 year isn't sure to be the same, even though it looks plausible to be at least close. Finally, Harkonnens had another planet to extract money from. However, 10b/year sounds a very high number to people listening to the exchange. Therefore, other planets seem to bring less, or the number wouldn't seem nearly as impressive. I guess the total upper bound including home planet might be on the order of 1500b at most, while ~1000b is more likely.