How price and output is determined under joint profit maximization goal of cartel?

Under the joint profit maximization goal, a cartel of oligopolists coordinates through a central agency that determines price and output for the whole group so as to maximise their combined profit, behaving like a single monopolist.

1. Meaning: members surrender independent price and output decisions to a central board acting for the entire cartel.
2. Objective: to maximise the industry's joint profit rather than each firm's individual profit.
3. Functions of the central agency: it fixes total output, the common price, each member's output share, and the division of joint profit.
4. Market demand and MR: the agency treats the combined market demand as its own and derives the industry marginal revenue curve from it.
5. Industry MC: it forms the industry marginal cost curve by horizontally summing the members' individual MC curves.
6. Equilibrium output: total cartel output is set where industry MC = industry MR, with MC cutting MR from below — the monopoly profit-maximising rule.
7. Price setting: the common price is read off the industry demand (AR) curve above that total output, and all members charge it.
8. Cost-minimising allocation: output is shared so that each firm's MC equals the common industry MR, so low-cost firms produce more and high-cost firms less, minimising total cost.
9. Profit distribution: the joint profit is divided among members as per the cartel agreement, not necessarily in proportion to each firm's output.
10. Instability: because each member can gain by secretly cutting price or exceeding its quota, and cartels are illegal in most countries, the arrangement tends to be unstable.

Thus, a joint profit maximization cartel sets total output where combined MC equals combined MR, charges the monopoly price off the demand curve, and allocates that output among members by equating each firm's marginal cost to the industry marginal revenue.