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Finding profit in pre and post merger scenario

The market for a standard-sized cardboard container consists of two firms: BooBox and Flimflax. As manager of BooBox you enjoy patented technology that permits your company to produce boxes faster and at lower cost than Flimflax. You use this advantage to be first to choose profit-maximizing output level in the market.

The inverse demand function for boxes is P = 800 - 4Q, BooBox's costs are TCb = 40Qb ( where TCb BooBox's costs, Qb, BooBox's Q), and Flimflax's costs are TCf = 80Qf (where TCf Flimflax's costs, Qf , Flimflax's Q). Ignoring antitrust considerations, would it be profitable for your firm to merger with Flimflax and act as one firm? If not, explain why not.

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Solution:

Total Output Q=Qb+Qf

For Boobox's total revenue is

TRb = (800-4(Qb+Qf))* Qb
TRb=800-4Qb^2-Qf*Qb
MRb=d(TRb)/dQb=800-4*Qf-8*Qb
For profit maximization equate MR=MC
MCb = d(TCb)/dQb=40
Put MC=MR
800-4*Qf-8*Qb =40
4Qf+8Qb=760
Qf+2Qb=190
Qf=190-2Qb ...

Solution Summary

Solution describes the steps to find out whether two given firms should merge or not?

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