Which is the first-order condition for the profit of a firm to be maximum?

AC=MR
MC=MR
MR=AR
AC=AR

The correct answer is B. MC=MR.

The first-order condition for the profit of a firm to be maximum is that marginal revenue (MR) must equal marginal cost (MC). This is because if MR is greater than MC, the firm can increase its profit by producing more output. Conversely, if MR is less than MC, the firm can increase its profit by producing less output.

Option A is incorrect because average cost (AC) is not relevant to the first-order condition for profit maximization. The firm’s goal is to maximize profit, not to minimize AC.

Option C is incorrect because marginal revenue (MR) is not equal to average revenue (AR). MR is the additional revenue that the firm earns by selling one more unit of output, while AR is the revenue that the firm earns per unit of output.

Option D is incorrect because average cost (AC) is not equal to average revenue (AR). AC is the total cost of production divided by the number of units produced, while AR is the revenue that the firm earns per unit of output.