19.5 One way of measuring the size distribution of firms is through the use of the Herfindahl Index, which is defined as H

2 i,

where i is the share of firm i in total industry revenues. Show that if all firms in the industry have constant returns-to-scale production functions and follow Cournot output decisions (Equation 19.10), the ratio of total industry profits to total revenue will equal the Herfindahl Index divided by the price elasticity of demand. What does this result imply about the relationship between industry concentration and industry profitability?