Question

. Consider a market with four firms in a cartel agreement which explicitly colludes to set a price by collectively restricting market output. The inverse market demand is P-1000-5 Q, and each firm has total costs of C(Q)-7000 +40 Q. (27 points) a) Determine the equilibrium price and quantity in the market. b) Calculate the output each individual firm will produce. c) Calculate the profits each firm will earn. Suppose one firm decides to unilaterally increase output by ten while the other firms hold their output constant. This means one firms breaks from the explicit collusion agreement of restricting output. Assume this condition for all the following questions d) Determine the equilibrium price and quantity in the market. e) Calculate the profits of the cheating firm. f) Calculate the profits of the other three firms. g) What is the change in profits of the cheating firm? h) What is the change in the profits of the non cheating firms? i) In the context of game theory, what may be the consequences in the long run for a firm to cheat the cartel agreement of restricting output?

Answer 1

P: 1000-59,89 then a ) at 89 m MA-Mc looo lo8 40 C. 4s 34, w ile 4th fin devtates, 2o 44-34 4x) 341o G d) let 30. n om = (440-40) 34 자 = 14620 (↑by 3100) = 33100 유 Δ下扣" Non cheating= 10380-11580

I) cartels are unstable, bcoz profitable deviations exist from what there is written in agreement, each firm has incentive to deviate to increase their profits .

So If a firm cheats , then cartels will break down