Applications in Economics

I am currently taking an Economics course. Unfortunately, the teacher is not very well qualified for this course, so basically we as students have to spend time to teach ourselves by looking through a very boring book --> No mathematics.

However, when it reached the Elasticity part, it mentioned some elementary concepts of Elasticity of Demand and Supply:

E(d) = % Δd / % Δ p

E(s) = % Δs / % Δ p

where s, d, and p are Supply, Demand, and Price respectively.

Those deltas reminded me a fundamental Calculus concept: Derivatives and Integrals.

So, with much curiosity, I have been cogitating on this matter and came up with the following relations, please feel free to correct my mistakes:

E(s) = Derivative of Supply function with respect to variable Price.

E(d) = Derivative of Demand function with respect to variable Price.

∫ E(s) dP = Δs

∫ E(d) dP = Δd

∫ E(s) dD = Δs * E(d) --> because % ΔP = % ΔD / E(d), so E(s) = % Δs / % Δ p = (% Δ s / % ΔD) * E(d)

∫ E(d) dS = Δd * E(s)

Feel free to share any extra Economics using Calculus as an approach with me, or correcting my mistakes, thanks.

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