Final answer:
It is true that increasing output at a non-constraint does not significantly affect profits, especially within the theoretical framework of constraints in system management. Firm A may reason it beneficial to expand output competitively regardless of Firm B's actions, reflecting strategic considerations based on trust and potential profit outcomes.
Step-by-step explanation:
The statement that increasing the rate of output of a non-constraint is unlikely to have much effect on profits is generally true. This is because in a system where there are constraints or bottlenecks that limit the total output, improving a non-constraint does not increase the overall system's capacity. Only improvements to the actual bottleneck will impact the throughput and hence the profits substantially.
In the context of game theory and the trust between Firm A and Firm B, both firms face a dilemma. If Firm A considers that Firm B will not cooperate and will expand output, Firm A is incentivized to also increase output to prevent losses ($400 profit when both firms increase output vs. $200 profit if A does not increase output while B does). However, if Firm A believes Firm B will cooperate and keep output low, there is still an incentive for Firm A to cheat and increase output to maximize profits ($1,500 profit for A if they increase output while B keeps output low).