Suppose there is a cable company that has the ability to provide internet service over its cable lines. Assume that the marginal cost of the service is zero.
A key feature is that the more users on the system the slower it is, and so the less valuable the service. Suppose that there is a unit mass of consumers with taste parameter θ uniformly distributed where 0 < θ < 1. If a fraction μ of the population uses cable modems and the price is p then a user of type θ has utility (1 - μ)(1 - θ) - p, that is I like the service best when I am the only user and μ = 0. A consumer who does not obtain the service receives utility of 0.
b) Derive the demand function for this market.