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A cigarette industry consists of 4 firms, each producing a differentiated product. As common in the...

A cigarette industry consists of 4 firms, each producing a differentiated product. As common in the tobacco industries, the prices of the differentiated products are the same atP= 2. The demandsQ1,Q2,Q3,Q4for firms 1,2,3,4 are given byQ1= 7−P2,Q2= 6−2P,Q3= 2−P/2, andQ4= 12−P3.

(a) What is the market share of each of the four firms?

(b) What is the 3-largest-firm concentration?

(c) What is the HHI?

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Answer #1

when P = 2:

Q1 = 7 - P2 = 3

Q2 = 6 - 2 x 2 = 2

Q3 = 2 - 2/2 = 1

Q4 = 12 - P3 = 4

a) Market share of firm 1 = 3/(3 + 2 + 1 + 4) x 100 = 30%

Market share of firm 2 = 20%

Market share of firm 3 = 10%

Market share of firm 4 = 40%

b) 3 largest firm concentration = 40% + 30% + 20% = 90%

c) HHI = 40%2 + 30%2 +  20%2 +  10%2 = 0.3 or 3000

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