Based only on the knowledge that the pre-merger market share of two firms proposing to merge was 20 percent each, an economist working for the Justice Department was able to determine that, if approved, the post-merger HHI would increase by 800. How was the economist able to draw this conclusion without knowledge of the other firms market shares? From this information, can you devise a general rule explaining how the Herfindahl-Hirschman index is affected when exactly two firms in the market merge? (Hint: compare a2 + b2 with (a + b) 2)