Finding Price Elasticity through differentiation
Suppose the demand function for a particular graphing calculator is
D( p) = 1000 e - 0.02 p
a. Find the price elasticity of demand, the revenue function, and how revenue changes with price (dR/dp).
b. Determine the range of prices for which this demand function is elastic (, > 1) and inelastic (, < 1).
c. Determine how the elasticity of demand is related to the way that revenue responds to price increases (i.e., how does the sign of dR/dp relate to whether the function is elastic or inelastic?).