Applications_Differentiation

Applications_Differentiation - Vineet Goyal Derivative...

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Chapters 12 and 13 1 Vineet Goyal Derivative Rules Log., Exp. Functions Implicit, Log. Differentiation Higher-order derivatives Extrema Quantitative Skills Review Program Differentiation Chapters 12 and 13

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Chapters 12 and 13 2 Vineet Goyal Derivative Rules Log., Exp. Functions Implicit, Log. Differentiation Higher-order derivatives Extrema Section 12.3: Elasticity of demand Measure of how change in price of product affects the quantity demanded Economics η = (% change in qty. / % change in price) = (p/q) / (dp/dq) (point elasticity) (Remember p = f(q)) Example from notes
Chapters 12 and 13 3 Vineet Goyal Derivative Rules Log., Exp. Functions Implicit, Log. Differentiation Higher-order derivatives Extrema Elasticity of Demand Three possibilities If |η| > 1, demand is elastic (luxury goods) If |η| = 1, demand has unit elasticity If |η| < 1, demand is inelastic (gas, electricity) REMEMBER ! η is negative ! Why?

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Chapters 12 and 13 4 Vineet Goyal Derivative Rules Log., Exp. Functions Implicit, Log. Differentiation Higher-order derivatives Extrema Elasticity & Revenue If p = f(q) and r = pq dr/dq = p(1+1/η) Implications Elastic demand Inelastic demand Example 12.3 (27)
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