Please answer the following question. 4, Cost reduction and the Herfindahl and L
ID: 1111329 • Letter: P
Question
Please answer the following question.
4, Cost reduction and the Herfindahl and Lerner Indexes. Consider a duopoly where firms compete in output levels (Cournot competition). In an initial equilibrium, both firms have the same marginal cost, c40. Then Firm 1, by investing heavily in R&D;, manages to reduce its marginal cost to = 28; a new equilibrium takes place. Market demand for the products is P = 100-Q (a) What is the value of H (the Herfindahl index) and L (the Lerner index) before the innovation? (b) What impact does the innovation have on the values of H and L? (Find actual values of H and L before and after the innovation.) (c) What impact does the innovation have on consumer welfare? What does this imply about L as a performance measure for a market?Explanation / Answer
a). Solution :- Equating P and MC, (P = Price and MC = Marginal cost).
100 - Q = 40 (P = 100 - Q)
60 = Q
Q = 60 units.
P = 100 - 60 = $ 40
Market share of two firms = 100 % (50 % of each firm)
Herfindahl index (H) before the innovation = (50)2 + (50)2
= 2500 + 2500
= 5000.
Lerner index (L) before the innovation = (Price - Marginal cost) / Price
= (40 - 40) / 40
= 0 / 40
= 0
Conclusion :-
b). Answer :- The value for Herfindahl index (H) will remain same as earlier i.e., 2500 (after the innovation). The value of lerner index (after the innovation) will be calculated as follows :-
= (40 - 28) / 40
= 12 / 40
= 0.30
Conclusion :-
Herfindahl index (H) before the innovation 2500 Lerner index (L) before the innovation 0