Question

Amazon is the dominant firm in the online shopping service industry, which has a total market demand given by Q = 100 – 2 P. Amazon has competition from a fringe of four small firms that produce where their individual marginal costs equal the market price. The fringe firms each have total costs given by TC_i = 10 Q_i +  Q ²_i. If Amazon’s total costs are given by TC_A = 10 + 10 Q_A, what price should Amazon establish for online shopping service?

Answer 1

There are fringe of 4 small firms. Each small firm has a total cost given by TCi = 10Qi + Qi²

=> MCi = ΔTCi / ΔQi

=> MCi= 10 + 2Qi

P = MCi is the individual small firm supply function.

=> P = 10 + 2Qi

=> Qi = (P-10) /2

=> Qi = 0.5P - 5

There are 4 small firms with identitical features.

Market supply by fringe firms: Qs = 4Qi

=> Qs = 4(0.5P -5)

=> Qs = 2P - 20 (Market supply of fringe firms)

Q = 100 - 2P (Market demand curve equation)

Demand curve of dominant firm; Q_A = Q - Qs

=> Q_A = (100 - 2P) - (2P -20)

=> Q_A = 100 - 2P - 2P + 20

=> Q_A = 120 - 4P (Demand curve faced by the dominant firm i.e., Amazon)

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Dominant firm maximize profit at MR_A = MC_A

Q_A = 120 - 4P

=> P = (120 - Q_A)/4

=> P = 30 - 0.25Q_A

TR_A= Q_A*P

=> TR_A= (30 - 0.25Q_A) Q_A

=> TR_A= 30Q_A - 0.25Q_A²

=> MR_A= ΔTR_A /ΔQ_A

=> MR_A = 30 - 0.5Q_A

--

TC_A = 10 + 10Q_A

=> MC_A = ΔTCA / ΔQ_A

=> MC_A = 10

--

Set MR_A = MC_A

=> 30 - 0.5Q_A = 10

=> 30 -10 = 0.5Q_A

=> 0.5Q_A = 20

=> Q_A = (20 /0.5)

=> Q_A = 40

Output produced by the dominant firm is 40.

P = 30 - 0.25Q_A

=> P = 30 - 0.25(40)

=> P = 30 - 10

=> P = 20

Price estabished by the dominant firm is 20

Answer: $20