In: Economics
Alienware and Foxconn are two multinational electronics company
operating in a homogeneous computer hardware market. The
engineering department at Alienware has been steadily working on
developing a patented technology that has enabled the firm to
reduce its marginal cost and emerge as a leader in the
market.
The inverse demand function for the market is P = 1200
- 6Q
Alienware's costs are TC = 60QA and Foxconn's costs
are TC = 120QF.
The current output for Alienware is QA = 100 while
Foxconn produces QF = 50. The current price is P =
300.
Ignoring antitrust possibilities, suppose Alienware makes an offer to Foxconn and they are in the process of negotiating a merger.
What is the potential price of the product after the merger?
Please give rating it will be appreciable, thank you
the solution of the above question is,
Merger or Cartels are same as Multiplant Monopoly,
Inverse Demand Function
P= 1200 - 6Q where Q = QA + QF
the two multinational electronic firms cost curves are
Alienware's costs curve - TCA = 60QA
Foxconn's costs curve - TCF = 120QF
The merger will aim to maximise the Total Joint Profit
Profit (π) = Profit of Alienware's(πA)+ Profit of Foxconn's(πF)
Profit (π) = P*Q - TCA -TCF
Profit (π) = (1200 - 6Q)*Q - 60QA - 120QF = 1200Q - 6Q2 - 60QA - 120QF
Profit (π) = 1200(QA + QF) - 6(QA + QF)2 - 60QA - 120QF = 1200QA + 1200QF - 6(QA2 + QF2+ QA QF) -60QA - 120QF
Profit (π) = 1200QA + 1200QF - 6QA2 - 6QF2- 6QA QF) -60QA - 120QF
Profit (π) = 1140QA + 1080QF - 6QA2 - 6QF2- 6QA QF
Apply Profit Maximisation
Langarazian Function
∂π / ∂QA = ∂[1140QA + 1080QF - 6QA2 - 6QF2- 6QA QF]/∂QA
∂π / ∂QA = 1140 - 12QA - 6QF = 0
1140 - 12QA = 6QF
QF =(1140 - 12QA )/6 = 190 - 2QA Equation I
∂π / ∂QF = ∂[1140QA + 1080QF - 6QA2 - 6QF2- 6QA QF]/∂QF
∂π / ∂QF = 1080 - 12QF - 6QA = 0
1080 - 6QA = 12QF
QF =(1080 - 6QA )/12 Equation II
By Equation I and II
190 - 2QA = 90 - 0.5QA
190 - 90 = 2QA -0.5QA
100 = 1.5QA
QA = 100/1.5
QA = 66.6667
Put Above Value of QA into Equantion II
QF =(1080 - 6QA )/12 = (1080 - 6(66.666)/12 =(1080 - 400)/12 = 680/12 = 56.6667
QA = 66.66667
QF = 56.66667
P = 1200 - 6Q = 1200 - 6(QA + QF)
P = 1200 - 6(66.66667 + 56.66667) = 1200 - 6(123.3333)
P = 1200 - 740 = 460
the Potential Price is 460