How is calculus used in economics and finance?

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black scholes used trajectory calculus (yeaaaah rocket science) to allow pricing of options

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Remember A Beautiful Mind? John Forbes Nash Jr was a mathematician who won the Nobel prize in economics for his mathematical work. You may think of finance as being spreadsheets, but as an example any time you use mathematical modeling in economics you might be using calculus. Differential equations based on rate of change is one example.