Chapter 13.a
Cartels: Deadweight Loss and the Incentive to Cheat
Collusion is the act of firms getting together to agree over quantity produced and the price to charge for the good produced. The group of firms acting together in this agreement is called a cartel. The ideal cartel will seek to restrict quantity to raise the price of the good. By restricting quantity and increasing price, the firms attempt to increase the industries profits and therefore their own individual profits. The cartel will behave like a monopoly and will try to earn monopoly profits. When a cartel is formed, the ideal quantity and price is the monopoly quantity and price; so the cartel will produce an output where marginal cost (MC) is equal to marginal revenue (MR). In Figure 13.a.1, the ideal cartel quantity is found by taking the point where MC=MR (point D) and going down to the x-axis; the price is found from taking the point where MC=MR and going up to the demand curve and over to the y-axis. The competitive price and quantity is at point C where the marginal cost is equal to the demand curve. Since the cartels produce at the monopoly output of point B, there exists a deadweight loss similar to the deadweight loss of a monopoly firm. The yellow shaded area A illustrates the deadweight loss in Figure 13.a.1.
Figure 13.a.1 Industry Model. In competition, the optimal price and quantity occurs at point C where the marginal cost curve intersects the demand curve; the quantity of the good would be Qc at price Pc. Like a monopoly, the ideal cartel point is B on the demand curve above where marginal cost (MC) is equal marginal revenue (MR). With a cartel, the quantity of the good would be restricted to the monopoly quantity, which increases price to the monopoly level. The quantity would reduce to Qm and the price would increase to Pm. The total deadweight loss created by the cartel is equal to the yellow shaded area A.
Since a cartel produces less than the competitive quantity, the cartel acts inefficiently and creates a deadweight loss. The deadweight loss of a cartel can be described the same way as the deadweight loss for a monopoly. In Figure 13.a.2, the competitive output is at the intersection of marginal cost (MC) and the demand curve at point C. This is the most efficient output and the industry is in equilibrium. The consumer surplus (CS) is the gray shaded area A below the demand curve and above the price. The producer surplus (PS) is the green area B above the marginal cost (MC) curve and below price. Figure 13.a.2 has no deadweight loss since the industry is in equilibrium, producing the competitive output.
Figure 13.a.2 Industry with No Deadweight Loss. The output produced by this industry is in equilibrium. The price and quantity is at the competitive level so the output is efficient. The consumer surplus (CS) is the gray shaded area A and the producer surplus (PS) is the green shaded area B.
Figure 13.a.3 illustrates the deadweight loss for a cartel. When the cartel forms and reduces output to the monopoly output at MC=MR, the cartel will charge a higher price and a lower quantity than a competitive industry. At this new level, the consumer surplus becomes the gray shaded area A. The producer surplus is the green area B plus the green striped area D. Compared to Figure 13.a.2, the consumer surplus is reduced by areas D plus E while the producer surplus is reduced by area F. However, the cartel captures some consumer surplus, the green-stripped area D. Capturing consumer surplus is not considered part of the deadweight loss. The gain in producer surplus to the cartel of area D is still smaller than the total loss to consumers (areas D plus E) and producers (area F) so there is a deadweight loss. The total deadweight loss to society is the areas E plus F; the loss in consumer surplus is E and the loss in producer surplus is F.
Figure 13.a.3 Industry with Deadweight Loss. With the formation of a cartel, the consumer surplus is now area A and the producer surplus is now areas B and D. The loss in consumer surplus is area D and E and the loss in producer surplus is F. The gain in producer surplus is area D, captured by the cartel from consumer surplus when the cartel restricts quantity and raises price. The total loss in consumer surplus and producer surplus is greater than the small gain in producer surplus so a deadweight loss exists. The total deadweight loss is equal to the areas E and F.
For a cartel to be successful, all firms in the cartel must cooperate. A single firm reducing output will not be able to raise price in the industry. In Figure 13.a.4B, the individual firm has a horizontal demand curve so a single firm reducing output will not increase price. After forming a cartel, each firm must agree to follow the production quota set by the cartel agreement. All firms in the industry must act together to restrict output and raise price. In Figure 13.a.4, the competitive quantity for the industry is 500 units with twenty firms each producing 25 units; the competitive price is $12. When the firms form a cartel and agree to set a quota for each firm to produce only 20 units, then the effect is an industry decrease in units produced to 400 units. The decrease in production from each firm will successfully raise the price for the product to $15. Note this is an ideal cartel with each firm colluding to restrict quantity to the monopoly quantity and price, which will earn the cartel monopoly profits.
In a cartel, each firm will have an incentive to cheat on their quota. If a single firm cheats on the cartel agreement then the single firm can increase its profit. When a cartel forms, each firm in the industry will decrease its output to increase price in the industry. After the cartel successfully increases price, a single firm can increase its profits by increasing its quantity produced. As in Figure 13.a.4B, a firm faces a horizontal demand curve; one single firm increasing its output will not affect the price in the industry. When the cheating firm increases its output from 20 units to 30 units, the cheating firm will still receive the cartel price, but will produce a higher quantity than other firms in the cartel. With the higher quantity at the same cartel price, the cheating firm will have a greater profit than other firms in the cartel. The incentive to cheat is equal to the yellow area B in Figure 13.a.4B; the cheater will maximize profit by producing at point C where quantity is 30 units and price is $15. Therefore, every firm in the cartel has incentive to cheat, but cheating can lead to cartel failure. If every firm in the cartel decides to cheat, then the quantity produced in the industry will increase which will decrease the price. The price will fall below monopoly price and profit will not be maximized.
Figure 13.a.4 Incentive to Cheat. Diagram A represents the industry and diagram B represents the firms in the industry. There are 20 firms; the competitive quantity produced by each firm is 25 units so the competitive industry quantity is 500 units at $12. After the cartel forms, each firm agree to restrict output to 20 units so the industry quantity reduces to 400 units at $15. When the cartel successfully raises the price, firms in the industry have an incentive to cheat. If a single firm increases output to 30 units while the rest of the firms are producing 20 units, the single firm will earn larger profits. The incentive to cheat is illustrated by the yellow shaded area B in part B of the diagram. Profit is maximized when the cheating firm produces 30 units at point C while receiving the cartel price. Point C is where the marginal cost (MC) curve intersects the new marginal revenue (MR’) curve after the cartel successfully raises price. The competitive firm’s profit is equal to the blue shaded area A.
Practice problems
Chapter 13 1a
1. Where would the ideal cartel operate and what is the price they will charge its customers?
1)H and P4
2)H and P2
3)C and P3
4)G and P2
5)G and P1
Answer: 2) the price that cartel will charge is P2
2. Where would the competitive firm operate and what is the price they will charge?
1)H and P4
2)H and P2
3)C and P3
4)G and P2
5)G and P1
Answer: 3) the price that competitive firms will charge is P3
3. What is the deadweight loss created by cartel?
1)A
2)A+D+E
3)E
4)E+F
5)Cartel does not create deadweight loss
Answer: 5) Deadweight loss created by Cartel is area E and F
What is the consumer surplus and producer surplus in this graph?
1)CS: APS: D+E+B+F
2)CS: APS: D+B
3)CS: A+DPS: B
4)CS: A+D+E PS: B+F
5)CS: A+B+DPS: E+F
Answer: 2) CS equals to area A and PS equals to area D+B
What quantity would cooperating firm produce and what price would it charge?
1)Q1 and P2
2)Q1 and P3
3)Q2 and P1
4)Q2 and P3
5)Q3 and P3
Answer: 2) A cooperating firm will produce Q1, according to the quota and will charge a higher price of P3.
What is the benefit that cooperating firms would receive and what is firm’s incentive to cheat?
1)Benefit: Aincentive to cheat: B
2)Benefit: A incentive to cheat: B + D
3)Benefit: A + Dincentive to cheat: B
4)Benefit: A + D + Eincentive to cheat: B
5)Benefit: A + D + Eincentive to cheat: B +D
Answer: 1) A cooperating firm will get the benefit A and they will be tempted to produce more than they are supposed to and also get B as their benefit.