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I've recently been ready about the labor theory of value used in classical and Marxian economics. I haven't studied it very long, but I think it basically has to do with calculating the embodied labor time of commodities. This isn't just the labor time directly put into creating a commodity. It also takes into account the embodied labor time of machines used during production. For example, if a machine has an embodied labor time of 1000 hours and can produce 1000 widgets over its lifetime (a very small amount, but whatever,) each widget's embodied labor time will be 1 hour beyond the labor directly put into its production, accounting for the depletion of the machine.

The Wood Economy

I tried applying the theory to a hypothetical economy in Minetest. This economy involves wooden axes, sticks, wooden plank nodes, and tree trunk nodes. The economy can be represented by a system of equations:

    A = 3W + 2S (An axe contains the embodied labor of 3 wooden plank nodes and 2 sticks)
    S = W/4 (A stick is made from a quarter of a wooden plank node)
    W = T/4 (A wooden plank node is made from a quarter of a tree trunk node)
    T = 1.6 + A/30 (A tree trunk node takes 1.6 seconds of direct labor to break, and a wooden axe has 30 uses, meaning 1/30 is used per tree trunk node)

Solving this system of equations gave me these results:

    A wooden axe has 1.442 seconds of embodied labor time.
    A stick has 0.103 seconds of embodied labor time.
    A wooden plank node has 0.412 seconds of embodied labor time.
    A tree trunk node has 1.648 seconds of embodied labor time.

The Stone Economy

For comparison, I also calculated an economy where stone axes and picks are used. Here is the system of equations:

    P = 3C + 2S (A stone pick takes 3 cobblestone and 2 sticks)
    A = 3C + 2S (Same with the axe)
    C = 1 + P/60 (Mining a cobblestone node takes 1 second and 1/60 of a stone pick)
    S = W/4 (Same as in the previous economy)
    W = T/4 (Same as in the previous economy)
    T = 1.3 + A/60 (Mining a tree trunk node takes 1.3 seconds and 1/60 of a stone axe)

The results are as follows:

    The stone pick and axe both have 3.336 seconds of embodied labor time.
    A cobblestone node has 1.056 seconds of embodied labor time.
    A stick has 0.084 seconds of embodied labor time.
    A wooden plank node has 0.339 seconds of embodied labor time.
    A tree trunk node has 1.356 seconds of embodied labor time.

As you can see from the embodied labor time of the tree trunk node, the more advanced stone economy is more efficient than the wood economy.

Conclusion

These calculations are hypothetical. For accuracy, you would need to measure the input and output of actual activities such as woodcutting. However, my results are still interesting to me.

Please tell me if I've made a mistake in my calculations.