perfect cartel, do firms play a best response to each other’s quantities? if not in which direction would they like to change their output. What does this say about stability of cartels?
In a perfectly competitive market, firms do not play a best response to each other's quantities because they are price takers. Each firm takes the market price as given and chooses the quantity of output that maximizes their profit, based on their costs and the market price. Therefore, there is no direct interaction or strategic decision-making between the firms in terms of quantity adjustments.
However, in the case of a cartel, firms would ideally like to coordinate their output levels in order to maximize their joint profits. They would aim to reduce output compared to what they would produce in a competitive market, in order to raise the market price and increase their individual and collective profits.
This desire to reduce output indicates that firms in a cartel would like to change their output in a downward direction, compared to their individual profit-maximizing level in a competitive market. By doing so, they can restrict supply, increase prices, and collectively benefit from higher profits.
The stability of cartels is generally considered to be low. The reason is that each firm has an incentive to cheat on the agreed-upon output level in order to increase their own profits. If one firm increases its output, it can capture a larger market share and benefit from selling more units at the higher price. As a result, the stability of a cartel is often fragile, as firms have an inherent incentive to deviate from the agreed-upon output levels and revert back to a more competitive behavior.