Wäre dankbar für jede Hilfe :-)
Aufgabe:
Consider an initially symmetric Cournot oligopoly with 3 firms and an inverse demand function of the form p(Q) = 1 - Q. Each firm has constant marginal costs of c E {0, 1/2}. Suppose now that two of the firms merge. This time there is a cost synergy, such that the merged firm's marginal costs reduce to αc, with α E (0, 1).
1. Derive the symmetric Cournot equilibrium in which one firm has marginal costs of αc and the other firm has marginal costs of c. Why is this relevant? Moreover, verify that under the given assumptions, both firms will always be active in equilibrium.
2. Provide the conditions on c and α such that the profits of the outsider (the firm which did not partake in the merger) increase. Hint: You have to distinguish two cases. For a sufficiently small c (which one?), this holds for all α E (0, 1). For a larger c, this will only hold if α is sufficiently large (how large?).
3. Provide the conditions on c and α such that the joint profits of the insiders (the firms which engaged in the merger) increase. Hint: This can only hold if c is sufficiently large (how large?) and α is sufficiently small (how small?).
4. Can you find a parameter constellation (c and α) such that both the joint profits of the insiders as well as the profit of the outsiders increase?
Nachtrag: Der Kurs in der Uni ist auf Englisch deshalb auch die Fragen. Antworten auf Deutsch verstehe ich.
