Dear professor Wolff, Suppose that a self-employed shoemaker works 4 hours a day and produces 1 pair of shoes. Now I invent a tool that enables him to produce 1 pair in two hours. How many pairs of shoes is my tool worth?
In value theory, the value of a tool is determined by the amount of socially necessary labor (SNL) it takes in an economy to produce that tool. In an economy where exchange of products occurs - i.e. where products of labor go through a market exchange process in passing from producer to consumer - produces become "commodities" and thus acquire a value in exchange (or exchange value): for example, a tool equals so and so many pairs of shoes, etc. If the exchange vale is the same as the labor embodied value (which may or may not be the case depending on the economic conditions specific to time and place), then the exchange value of a tool would depend on how many SNL hours were embodied in the tool relative to the SNL embodied in the pairs of shoes.