price elasticity / consumer surpluus

Dube and Misra ("Personalized Pricing and Customer Welfare" ) charge random prices to estimate the demand curve of consumers of a service. It turns out the average consumer of this service has a demand curve that can be expressed as q = 0.3476 exp(-0.003p), where q E (0, 1] denotes quantity (each individual consumer either purchases the service or not, so you can think of q as the probability of purchasing the service). 1. (8 points) The firm was originally charging $99 for their service. What is the price-elasticity of the average consumer at p =$99? 2. (8 points) What is the average consumer surplus when the company charges $99? Hint: you will have to solve a definite integral of the average demand curve. It might be helpful to draw a sketch of the demand curve and the fixed price of $99 before integrating. You may use a calculator to get your final result in dollars