Please Show all step-by-step work

1. Consider the market for internet providers and assume that you can observe ten companies competing in this market. You are the CEO of one of the companies and are thinking that you should establish a cartel to maximize our revenue. Each of the companies is subject to the following Cost function: C=50+2Q. Demand across the industry equals Q_D= 100-P.

a. Which characteristics of the market for internet providers would support your endeavor? Explain why it might be a good idea for internet providers to establish a cartel and who could be opposed to the idea.

b. Indicate the profit maximization the cartel would have to solve to maximize profits.

c. Calculate total profits for the cartel and the associated prices and quantities in the market. Assuming that the market gets equally divided, calculate the profits each firm is realizing when it is a member of the cartel.

d. If the cartel is not in place, all companies are subject to market mechanisms that lead to perfect competition. Calculate prices and quantities in the market in this situation. Compare the profits made in perfect competition with profits in the cartel setting.

e. Given your results in D, do you think that the cartel will work and stay in place in the long run? Show what could impact the stability of the cartel 2. The market demand for personalized key chains is given by P = 150 - Q_D. Suppose that there are only two firms in this market; firm 1's cost function is given by C₁ = 5Q₁² and firm 2's cost function is given by C₂= 0.3Q₂

a. Show the profit function of both companies.

b. Calculate the reaction function for both companies if they are competing in a Cournot duopoly.

c. Indicates prices, quantities, and profits for the reaction functions derived in b)

d. Describe the situation in a Bertrand setting. Which results would you expect? How do those results differ from the Cournot world?

e. Which scenario would the companies prefer? Which customers?

f. Draw a diagram to show the change in consumer surplus between the two scenarios graphically. Please pay attention to clearly labeling your graph.