Question

Consider an industry with demand Q a -p where 3 identical firms that compete a la Problem 4. Cournot. Each fim'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' + dq, where F<F' < 2F. (a) Determine each firm's market share before and after the merger Check: https://www.justice.gov/atr/15-concentration-and-market-shares 2 (b) Suppose that a = 10 and c 3. Determine the Herfindahl index after the merger takes place when (i) 2 and (i) = 1. Compare this to the post-merger Herfindahl index caleulated based on pre-merger market shares.

Answer 1

Solulion The demand function 1s iven by a) Befo1e the meiger cach Hirm's cost -funelibo is given by CFIC the pYofit -function of -the 15t -fiym f5: liPla)qi Ci Smtlarly fo1 fiim 2& 3 a C--2 3 gel oudtancously Sloving equation 2&3 Simul The market share of cach -fiym IS qi Thus the maYket share of the 3firms aie ' ymmetvc structere)

The post merger -fiym is menged Cost -function ol the C The piolil fundlions aye (a-p)qF-C fiym&3 as 'q' denoting the -0. aC- a aC' - 91 the simultancously sloving うe-フ+ク= 2 G a-c-c' 32 The maket share of -iym i = Cs) a aa-c-c The maTket Shaie of the merged -firm (2 3)= Sq Syu 2a-C-c 1ot - G 15 ayio-3-a

ot3-4 o.6 6o'/. - t5 y0 60- 5200 - 16 a0-1-3 500 Sylot 3-3 2o-1-3 lio0 16 ННД1 50 0 90l1/T 5103 The post merger HHT based on the pre merger Shares fs given Ьy - Sy . dHt 5556 - wohen ma1gunal losi Jleduction due to merger is not very Substantlal-lhe n the Ht based oo pre merger marKet Shares likely to ovevestimate the post merger Value of t* . this is merger maket shares we do not becац5 e, usina the pTe

consider for he fact lhal the meiging -ftms pToduce a tola) Octlput thal is less than the Sum of outlput of the individua Hp H Significart On the Contrary ff marqinal Cost Teduction Cc'= )then the post merger estimate of H based on Pre Itkely merge market shares 16 to underestimate the Post (Hp L H This because the total oulpel Meiger value of H merging fitims is ndividual outpuls qrcale ta-the Sum of thei1 the Thus maginal cost 0leduction, makes the merger efficient by Taising oulpet