Usually, people tell that prices are set by demand versus supply. But, on a stable society, without large disruptive technologies or special events that might prevent stockpile and so make demand overtake supply, price is set by the total ammount of work needed to produce a certain object. This comes from the theory of value that comes from Adam Smith ("Richness of the nations.").
If distribution in your society still works as a market based one, and you still have labour as part of your production chain, price is the comparision of how much labour is needed to produce a certain commodity versus each other. Its a strange prospect to be so far in the future and still have a labour intensive economy to justify the existence of slaves. Robots replace slaves in most futuristic settings.
In our society the most important aspect of production is labour and capital, with energy and raw materials as the second most important things. When your society reachs a certain level of automatization of production, your source of value will shift towards energy and raw materials.
So, to have a society where raw material shortage is so big as to justify why go all the lengths to reach other planets, this is not very compatible with slave labour.
But, if your society has slave labour, this does not mean that production has no measure ("value"). Your value will be the total output of your labour pool, per time period, multiplied by the capacity of the machinery to increase productivity. People make the usual mistake of taking the prices of things as the limit of production. But, this is not usually true. Price is an arbitrary number that holds no meaning by itself. It can only have meaning when compared to other prices and salaries.
So, what you should measure is the ammount of man-hours spent to produce something. This is your price.
To verify if something is economically feasible, you should take the ammount of men-hours needed to produce that thing. If its too big, bigger than your labour pool can produce, then its impossible. Even then, you might produce things on the long run. If you give a project enought time to mature, you can overcome labour limitations. If, for one, your society cannot build a spaceship in a single generation, this does not prevent it from doing so in multiple generations. But, economy is the management of scarcity. So, we usually wont do what would take too much time to return the work spent, except in special cases.
A good rule of thumb is to take the time that a spaceship takes to reach another planet and verify if the same ammount of raw resources could be mined here on earth instead. If, going that length produces more raw resources than applying the same ammount of work on earth would produce, then we have a profit, and so, we might do the trip. This means that the price for that spaceship is relative. You can set your story in a way that raw resources on earth are already depleted, so that exploring mines on earth takes a lot of resources, while taking the trip to Tau Ceti takes only a certain ammount of energy that might be extracted from both our sun and Tau Ceti sun's.
Technology plays a role in productivity. If your society is able to directly convert energy to matter and vice versa. You might have a way to store enough energy to do the trip. Technology increases the value of work, because it allows a single man to produce more by each man-hour he spends working. In energy, technology means more advanced forms of energy that stores more energy per volume or weight.
Chemical energy is what we use to launch space rockets today. Its energy density is small compared to the ammount of energy that is needed to launch a space ship to Tau Ceti. Ion thrusters are a way to convert electrical energy into impulse. But it need xenon gas to work, and this has a low density. Nuclear fission is a lot more compact than chemical energy forms. Nuclear fusion is even more powerfull than fusion, and as the technology is almost within reach, it might be interesting. Anti-matter anihilation has even more capacity to do work per volume than fusion. Direct matter to energy conversion is the ultimate source of energy in our universe, and means that ordinary matter can be used as energy source. This decreases the ammount of human work that must be done to launch a space ship, and so on. At each step, the human work to gather the energy is multiplied by the technology used. If takes some man-hours to gather petroleum and turn it into gas, the same ammount of man-hours would produce much more joules if used to gather matter to be used in direct energy conversion process.
And there is where things become complicated. If you can convert energy directly to matter, and you can convert matter directly to energy, you can create ordinary matter however you want. Eliminating scarcity.
If you take matter from soil, and turn into energy, to fly into Tau Ceti to get ordinary matter from Tau Ceti, you are wasting matter for nothing. The matter spent to reach Tau Ceti might very well be converted into other forms of matter here on earth.
Something that might change this, however, is if you setup a large fleet of ships between earth and Tau Ceti. The total ammount of energy spent in the trip, is proportional to how close to the speed of light you go. How close to the speed of light you go, is proportional how much energy you put on the ship to make it accelerate. If you do the trib at small values compared to C, you might very well spend a small ammount of energy in the process. But, at the same time, you lenghten the time that takes to reach there.
This means the following. Take a large fleet of ships that are roboticly commanded, setup a chain of ships, where each ship leaves earth after the previous, with a certain time between then. Keep launching ships until the first ship sent arrives. Now you have a circle of ships going and comming back to earth. The time between each ship should be choosen so that you have enough time to build another ship between each launch. The only drawback of that strategy is that the slower you go, the more time it takes to have a return in your investment.
Now you can feasibly explore the richness of other planets.
Keyword here is how fast you need your ships to return.