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Unformatted text preview: Elasticity and Revenue Maximization with Exponential Functions David J. Bryce There are some mathematical results that you may find interesting or want to be aware of with respect to exponential demand functions. Exponential functions have some very nice properties for computing elasticities and revenue maximizing prices. Price Elasticity of Demand To begin, let’s compute the own-price elasticity of a general exponential function of the form e p Q β α = , where , α β are constants and 0. β < Q and p are quantity and price, respectively. Recall that price elasticity of demand is given by dQ P dP Q η = ⋅ . Step 1, differentiate with respect to p . 1 e p dQ dp β βα = (1) Step 2, multiply the result by P/Q. e e p p p β β η βα α = ⋅ (2) Step 3, cancel, yielding . p η β = (3) In other words, the price elasticity of an exponential function is simply the exponent multiplied by the price ! This number is always negative (demand slopes down) so its absolute value should be utilized for standard elasticity interpretation.absolute value should be utilized for standard elasticity interpretation....
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