Under perfect competition, for the producer to be in equilibrium:

AR = MR = MC and MC must be rising.

The correct answer is Option (4) → AR = MR = MC and MC must be rising.

Under perfect competition, the producer is in equilibrium when:

• Marginal Revenue (MR) = Marginal Cost (MC)

• Since Average Revenue (AR) = Price and remains constant in perfect competition, we also have AR = MR.

However, this condition is not sufficient alone. To ensure profit maximization, the MC curve must be rising at the point of intersection with MR. This ensures that the firm is at the lowest possible cost for that level of output and not at a point where increasing output further would lower costs.

This second-order condition ensures that the equilibrium point is a point of maximum profit (or minimum loss), not minimum profit (or maximum loss). If MC were falling and equal to MR, increasing output slightly would lead to MC falling further below MR, indicating that more profit could be made by increasing output.