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Compare Competition to Monopoly in Math Terms

Compare Competition to Monopoly in Math Terms. Say in a market consumers have the demand curve added across all consumers as Qd = (6000/9) – (50/9)P, or in inverse form P = 120 – (9/50)Qd. P.

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Compare Competition to Monopoly in Math Terms

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  1. Compare Competition to Monopoly in Math Terms

  2. Say in a market consumers have the demand curve added across all consumers as Qd = (6000/9) – (50/9)P, or in inverse form P = 120 – (9/50)Qd. P Note that at a price of 120 nothing is demanded. Price has to be lower than 120 for consumers to demand any units. 120 D Q

  3. Say the market is competitive with 50 identical firms, each with TC = 100 + 10Q + Q2, and thus MC = 10 +2Q. The market supply is the summation of the MC of each firm (remember you have to express each MC in Q form before adding and set P = MC.) P The market supply curve is P = 10 + (1/25)Qs. At prices below 10 the sellers will supply nothing. 120 S 10 D Q

  4. To get the market price and quantity traded express demand and supply in Q form, then set Qd = Qs and solve for P. Take the P found and substitute back into Qd or Qs to get the market quantity traded. P We found before that P = 30 and Q = 500. 120 Consumer surplus = .5(90)(500) = $22,500. Producer surplus = .5(20)(500) = $5,000. S 30 10 D Q 500

  5. If the industry is monopolized and the monopoly is run as a multi-plant monopoly then the competitive supply is changed to the firm marginal cost by changing P to MC. Find the MR from the demand. Sell Q where MR = MC. Find P at this Q by plugging the Q into the demand curve. P We found before that P = 70.50 and Q = 275 (and MR = 21). 120 Consumer surplus = .5(49.5)(275) = $6,806.25. Producer surplus = .5(11)(275) + (49.50)(275) = $15,125. 70.50 MC 30 21 10 MR D Q 500 275

  6. Summary so far So when the industry is monopolized price goes up, output falls, consumer surplus falls and producer surplus rises.

  7. P 120 a b c d e 70.50 MC 30 f g h 21 i 10 MR D Q 500 275

  8. On the previous screen I show the competition/monopoly comparison with letters in the consumer surplus and producer surplus areas. In the following table I will show those ideas: Competition Monopoly Mon – Comp. CS a+b+c+d+e a+b -(c+d+e) PS f+g+h+i c+d+f+g+i c+d-h Total a+b+c+d+e a+b+c+d -e-h +f+g+h+i +f+g+i First not the change in producer surplus when the industry in monopolized. The seller gains c and d but loses h. Would the seller make the change if c+d-h were negative (h bigger than c and d combined)? NO, why make a change and be worse off. So we assume c+d-h is a positive number.

  9. Now note that what the consumer loses is partly captured by the monopoly, areas c and d. This is a transfer in society from consumers to producers. Also note that consumers lose e as well and it is not captured by the producer. The producers gain is less than the loss to the consumer in terms of surplus values. When you look at the net change in total surplus you see minus (e+h). Monopoly leads to a neat loss of surplus in the market. Areas e and h are above the quantities lost when the industry was monopolized. These areas were surplus value, but are lost. The areas make up what is called the deadweight loss due to monopoly.

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