Explained the MC=MR Rule
MR = MC
A firm’s profit is defined as its total revenue minus its total cost. In symbols, p (Q) = R(Q) - C(Q). [ A firm that wishes to maximize its profits may find the corresponding output by differentiating p (Q) with respect to output and finding the output that equates the derivative to zero:
dp (Q)/dQ = dR(Q)/dQ - dC(Q)/dQ = MR - MC = 0. That is, profit maximization requires that, if the
firm chooses to produce anything at all, it should equate marginal revenue and marginal cost. In the specific case of competitive firms, this takes the form P = MC. The second-order condition is:
- PQ* - (FC + VC(Q*)) = p (Q*). Dividing both sides of this inequality by Q* and rearranging, the firm maximizes profit at Q = 0 if and only if P < , that is, if and only if the firm’s price is less than its average variable cost at the MR = MC output. Since average variable cost is equal to marginal cost at the former’s minimum, we can state the complete short-run profit-maximizing rule as follows: produce at the output for which MR = MC, provided price is greater than minimum average variable cost; otherwise shut down. to understand the formula visit this website ]
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