Question 1: Consider the market for a single network good as discusse…

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions