I'm started to work on this exercise but I don't know to continue. Here is the excercise, I'm not sure if i should use log function or just simple equation. Consider a trade set up in which a company sells ice cream to its customers. Producing ice cream is costly: it costs $^2 − \frac 14$ to produce units of ice cream, () = $^2 − \frac 14$ Consumers have a different valuations for ice cream: type 1 consumers moderately like ice cream and have valuation v1(x) =$^2√$, where x is the quantity of ice cream consumed, while type 2 consumers absolutely love ice cream and have valuation v2(x) = √. If consumers get no ice cream, both types receive the same utility v1(0) = v2(0) = 0.
- Assume the firm has full information on customer types. Depending on customer types, what price does the firm choose to maximize its profits? What quantity does the firm produce to maximize its profits? Find the optimal prices and the profit of the firm. Thank you a lot for helping me.