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What you seem to mean is the cost due to competition: Multiple miners trying the same block and the first one succeeding making all the work of the other mineres on this block worthless.
I meant the increase in difficulty for later blocks inherent in the algorithm.
One could - though I agree that it stretches the analogy - compare the first to gold miners competing in the same physical location - as has happened during the gold rush. This causes competition not exactly for the same gold veins but for the physical space and other resources around.
The second (algorithmical) increase can be compared to mines becoming sparser and sparser - you have to dig deeper.