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#3. Please show all work :) An oligopolist's price equation is P = 40 - 2Q...

#3. Please show all work :)

An oligopolist's price equation is P = 40 - 2Q for Q equal or smaller than 8 andP = 44 - 2.5Q for Q greater than 8.

a. Determine the firm's profit maximizing price and quantity if marginal cost is constant at $5.

b. By how much can marginal cost increase without prompting a price change?

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Answer #1

ANSWER:

,A)

  • profit maximizing price calculated are as follow
  • p = 40-2Q
  • ​p = 40-2*8
  • p = 40-16=24 when q <and = to 8
  • when p > and = to 8
  • P = 44-2.5Q
  • ​P = 44-2.5*8
  • P = 44-20
  • P = 24

B)

  • quantity
  • MR = MC
  • = change in P*Q/change in Q
  • = 40-2Q*Q/Q
  • = 40-2Q2/Q
  • MR = 40-4Q & MC = 5 when MR>MC
  • MR = 40-4*8 = 8>5
  • when MR<MC
  • MR &MC
  • 44-5Q & 5
  • 44-5*8 & 5
  • 4<5
  • for the output upto 8 MR>MC and output beyond 8 MR>MC

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