I'm going to repost the basic summary of Marx on scarcity from Chapter One of Das Kapital,
|The value of a commodity would therefore remain constant, if the labour time required for its production also remained constant. But the latter changes with every variation in the productiveness of labour. This productiveness is determined by various circumstances, amongst others, by the average amount of skill of the workmen, the state of science, and the degree of its practical application, the social organisation of production, the extent and capabilities of the means of production, and by physical conditions. For example, the same amount of labour in favourable seasons is embodied in 8 bushels of corn, and in unfavourable, only in four. The same labour extracts from rich mines more metal than from poor mines. Diamonds are of very rare occurrence on the earth’s surface, and hence their discovery costs, on an average, a great deal of labour time. Consequently much labour is represented in a small compass. Jacob doubts whether gold has ever been paid for at its full value. This applies still more to diamonds. According to Eschwege, the total produce of the Brazilian diamond mines for the eighty years, ending in 1823, had not realised the price of one-and-a-half years’ average produce of the sugar and coffee plantations of the same country, although the diamonds cost much more labour, and therefore represented more value. With richer mines, the same quantity of labour would embody itself in more diamonds, and their value would fall. If we could succeed at a small expenditure of labour, in converting carbon into diamonds, their value might fall below that of bricks. In general, the greater the productiveness of labour, the less is the labour time required for the production of an article, the less is the amount of labour crystallised in that article, and the less is its value; and vice versâ, the less the productiveness of labour, the greater is the labour time required for the production of an article, and the greater is its value. The value of a commodity, therefore, varies directly as the quantity, and inversely as the productiveness, of the labour incorporated in it.|
Now, on to your question,
|In essence rarity does play a role since considerable labor time is required to extract it, then it gets further work in polishing and setting in rings, etc., which is more labor time. Yes, I understand labor time and its importance in determining cost while it take the seller to set the price. The seller is the capitalist. Is it the labor that mades a diamond valuable or it's use value? What was its use value in Marx's day. I still tend to believe that it's rarity made it valuable rather than it usefullness|
First, diamond has potential value, as many natural resources and untreated raw materials.
Remember the duality of a commodity. It has a use value, which satisfies a need and an exchange value.
As long as diamond remains buried deep in a mine, it is useless. It first must be located, then extracted and transported for use.
Remembering the duality of a commodity, the diamond must have a use value. It, has no utility remaining deep inside of the mine.
If it has no utility then it has no exchange value.
then V is 0 as well.
Use value adds nothing to the value of an object. No matter how many bourgeois economists want you to believe, you can not calculate use value.
An object either has use value or it doesn't. So the use value will either be 1 if an object has utility or 0 if it does not. If a object has no use value, it has no value.
As Marx says in that passage quoted,
|The value of a commodity, therefore, varies directly as the quantity, and inversely as the productiveness, of the labour incorporated in it|
You also later asked,
|Good point about leaving it for a later study. Diamonds are a good example. Why did they have value in Marx's days? Were they used in industry or was the value based mostly on beauty and rarity?|
The use value of diamonds and Marx's day, is the same as it is in this day. Either 1 or 0. Since diamonds have been purchased endlessly since the the 1800s, the use value of diamonds has continued to be 1 for those who found utility in them.
I hope i made things clear. To reiterate.
* A commodity has to have utility in order to have a(n) (exchange) value.
* Utility, whether an object has a use value, is is mathematically represented as a 1 if it proves useful and 0 if it has no usefulness. If a commodity's utility is 0, so is it's value.