How much of the Napoleonic wars were paid by the sale of Louisiana?
score:9
Not much. According to the Wiki:
By the terms of the Anglo-Russian agreement of 1803, Britain paid a subsidy of ₤1.5 million pounds for every 100,000 Russian soldiers in the field...
The whole cost of the war [for Britain] came to £831 million. By contrast the French financial system was inadequate and Napoleon’s forces had to rely in part on requisitions from conquered lands.
Assuming the cost was comparable to both sides, and taking 1 pound to be 20 francs, Louisiana Purchase was 68M francs ~ 3M pounds - at most 1% of war cost.
The sale of Louisiana to the US was a strategic move (the only good strategic move that Napoleon, the great tactician, has ever made) as opposed to a financial one; in that respect it is similar to the Alaska Purchase. Napoleon could not defend Louisiana against either Britain or US, and by selling it to the US he ensured, that when the US was deciding who to fight in 1812 (both Britain and France were nasty), there was little to gain from fighting France, so the US declared war on Britain.
PS. It has been argued in the comments that war was cheaper for France than for Britain. While the French 2.5M-strong army was conscripted, the 250k British army was volunteer. A British private was paid 7s/week, which amounts to 7s/week*52week/year*20years*250000men/20s/£ = £91M - about 11% of the total cost. Even if we assume that the war costs half as much for the French as for the British, still Louisiana purchase was only 6% of the war cost.
PPS. There are many side issues here: Britain subsidized other countries' armies, maintained a navy, fought on the perimeter, incurring higher transportation costs. France had a larger army (which had to be fed and clothed, and early industrial Britain got guns and clothes cheaper), and fought more countries. However, the central point remains that the value of Louisiana was two orders of magnitude lower than the cost of the wars. Even if creative accounting reduces the difference to a single order of magnitude, that is enough to see Louisiana purchase for what it was - a political and strategic move, rather than a financial one.
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