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I recently read (Citizens by Simon Schama) that France had a per capita debt of two-thirds of the annual income of a carpenter or tailor in 1714. By 1738 France had managed to balance the budget (more-or-less) despite the failure of John Laws' bank managed loan system. Given the failure of Banque Generale, what were the other strategies or predicaments that lead to France balancing the budget by 1738?

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Balancing the Budget is very different from eliminating the National Debt. A Balanced Budget simply means that a country made a decrease, no matter how small, in the National Debt over the specified time period (usually a year).

Given the horrendous expense of running Louis XIV's court, it is easy to see how the Budget might have improved simply in consequence of his death in 1715. According to Wikipedia's article on Louis XV it was sufficient to stabilize the French currency in order to complete the process of balancing the budget by 1738. However, no mention is made of eliminating the French National Debt.

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