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11.5. Merger and the Herfindahl index. Consider an industry with demand Q=ap where 3 identical
firms that compete a la Cournot. Each firm's cost function is given by C=F+cq. Suppose two of the
firms merge and that the merged firm's cost function is given by C=F+cq, where F<F<2F. (a)
Determine each firm's market share before and after the merger (b) Suppose that a=10 and c=3.
Determine the Herfindahl index after the merger takes place when (i) d=2 and (ii) d=1. Compare
this to the post-merger Herfindahl index calculated based on pre-merger market shares. Why do
these values differ?

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