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Perfect Competition in Math Terms

Perfect Competition in Math Terms. Say you have a competitive market where the demand for consumers has been added up to be Qd = 6000/9 – (50/9)P. Also say there are 50 identical firms, where each has the total cost TC = 100 + 10Q + Q 2 . The marginal cost for each firm would be MC = 10 + 2Q.

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Perfect Competition in Math Terms

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  1. Perfect Competition in Math Terms

  2. Say you have a competitive market where the demand for consumers has been added up to be Qd = 6000/9 – (50/9)P. Also say there are 50 identical firms, where each has the total cost TC = 100 + 10Q + Q2. The marginal cost for each firm would be MC = 10 + 2Q. We know that firms that maximize profit produce the level of output where MR = MC (as long as P>=AVC). For a competitive firm P = MR, so MR = MC means P = 10 + 2Q, or Q = (P – 10)/2 for each firm.

  3. We know the supply curve in the competitive industry is basically the summation of the MC of each firm in the industry. For one firm we have in our example MC = 10 + 2Q. To add across all 50 firms we re-express MC as Q = .5MC – (10/2). Now we add all 50 firms together: Q = .5MC – (10/2) Q = .5MC – (10/2) … Q = .5MC – (10/2) Qs = 25MC - 250 The supply curve

  4. Note the supply curve, Qs, adds up the supply curve of each firm. .5MC 50 times is 25MC and (10/2) 50 times is 250. So for the supply curve we have Qs = 25MC – 250. But, since each firm had P = MC (profit max rule) we rewrite the supply as Qs = 25P – 250. The market price and quantity traded are determined where Qs = Qd, so we have 25P – 250 = 6000/9 – (50/9)P, or (225/9)P + (50/9)P = 6000/9 + 2250/9, or (275/9)P = 8250/9, or P = 8250/275 = 30. Plug P = 30 into either Qd or Qs to get the quantity traded in the market. In Qs we have 25(30) – 250 = 500.

  5. Since the market price is 30, each firm will make Q= (P – 10)/2 = (30-10)/2 = 10. The profit for each firm TR – TC. TR for a firm is P times Q, or PQ. TR = 30(10) = 300. TC = 100 + 10Q + Q2 for each firm in this example. So, TC = 100 + 10(10) + 102 = 300. Profit = 300 – 300 = 0. So we know there is no incentive for other firms to enter the industry.

  6. P D1 S1 ATC1 MC1 P1 =30 P=MR1 Q q Q1=500 Q1=10 Market Firm

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