Consider a situation where N consumers interact with a monopolist in a market. Half of these consumers (γ 0.5) have low demand, θ1-100 for the monopolist's product, while the other half have high demand, θ2-150. Consumer i receives consumer surplus according to the following function (0, - p)2 2 for i-1,2 q-- p. Total costs for the firm which implies that the demand function for consumer i is q are c(a) - q2 and if this market behaved as if in a perfectly competitive setting, p and qC, for i -1,42
1-) Suppose that the monopolist could identify which group each consumer belonged to and wanted to implement a two-part pricing scheme. Find the size of the access fee charged to each group and calculate the per unit price.
2-) Suppose now that the monopolist could not prevent arbitrage. What will happen in this case?
3-) Suppose now that the monopolist could prevent arbitrage, but could not identify which group each consumer belonged to. If the monopolist were to implement a two-part tariff, find the price they would charge as an access fee and calculate the peir unit price. (It might be helpful to know that aggregate demand is Q(p) - N 125-p)