GDP isn't about units of work, it's about the final product. So using two units of work instead of one to produce the same thing shouldn't affect GDP. But perhaps you are implying GDP is not correctly calculated?
That depends on how you're calculating GDP. If you are summing up all expenditures or incomes, the paid work done by each AI would be counted. If you're counting production, meaning the value added, it probably wouldn't count since digging a hole only to fill it back in created no value.
GDP calculates the market value delivered. In this case of the labour. If someone is paying for the labour, GDP will be affected by the value of that labour. If the net output in terms of a product at the end is zero, then that does not erase the labour.
The only case where digging and filling a hole does not increase GDP is if the labour is not paid for.
EDIT: Basically, the two methods you list are the income or expenditure ways of calculating GDP, but in both cases consumption by employers is a factor, and so the payment for the labour increases the GDP irrespective of whether they also increase the final output.
I'm not so sure calculating GDP by production would capture this. It should, mind you, as all GDP calculations should get the same answer, but a silly/stupid example of two LLMs digging and filling in a hole may not fit in a production calculation.
> the production approach estimates the total value of economic output and deducts the cost of intermediate goods that are consumed in the process (like those of materials and services)[1]
This is a very rough definition of it, but role with it. There is no economic value since the hole was dug only to be filled back in. There was a service paid for on each end of the project, but those are services that could fall into the category of intermediate goods consumed that is actually deducted. The transaction could actually have a negative GDP when using the production calculation approach.
[1] the production approach estimates the total value of economic output and deducts the cost of intermediate goods that are consumed in the process (like those of materials and services)
GDP is about products or services. If someone is paid for digging a hole, then that a finished, delivered service. Filling it the same.
If you dig and fill a hole without anyone paying you for either, sure it won't affect GDP, but if someone pays you, that the net result is no change does not alter the fact that you have been paid to dig a hole and to fill a hole.
The method used to calculate the investment can affect whether the income produced increase the GDP or whether only the consumption generated by that increased income is counted, but in a real-world scenario either alternative will increase the GDP.
> But perhaps you are implying GDP is not correctly calculated?
That GDP doesn't accurately reflect productive, useful effort for this reason has been a core part of the criticism of GDP since it was first formulated.
Does it raise GDP, though? I would have thought a more accurate thing to say is it raises the global temperature.