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> if the government prints money to build infrastructure, where does the value they've added come from?

Increased real productivity. Imagine a toy town where only two goods are produced on opposite sides of a river. To trade them, risky river crossings risking product and person must be attempted.

A bridge removes that risk and cost. The town will become wealthier for having the bridge despite its cost. (Same for e.g. ancient Mesopotamian, Mesoamerican and Hohokam canals.)

> the government makes some money

If the government prints money to fund its deficit then inflation “taxes” everyone. It is analogous to a company selling stock to do something useful. The share count went up but the aggregate value (hopefully) will too.



Increased real productivity might occur due to public spending, but its less likely that it was in the 1800s, if the Govt "bet" on that bridge does not payoff, then is each dollar printed to bet on it is diluting the value. I wouldn't trust the public sector to correctly allocate the resources to increase the real economic output over the private sector, for self evident historical lessons. And now that the low fruit has been taken, they might be tempted to build bridges to nowhere https://www.alaska.org/detail/bridge-to-nowhere




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