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## Profit Maximization

Profit maximization is a process by which a firm determines the price and output of a product that yields the greatest profit. The total revenue-total cost method relies on the fact that profit equals revenue minus the cost and the marginal revenue-marginal cost method is based on the fact that total profit in a perfectly competitive market reaches its maximum point where marginal revenue equals marginal cost.

Any costs incurred by a firm may be divided into two groups: fixed cost and variable cost. Fixed costs are incurred by the business at any level of output, including zero output. These include equipment maintenance, rent, wages, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category. Fixed cost and variable cost are combined together to form the total cost.

Revenue is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services. Marginal cost and revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced, or the derivative of cost and revenue with respect to quantity output. It may also be defined as the addition to total cost or revenue as output increases by a single unit. For instance, taking the first definition, if it costs a firm \$400 to produce 5 units and \$480 to produce 6 units, then the marginal cost of the 6th unit is \$80.

Total Cost Total Revenue Method: To obtain the profit-maximizing output quantity, we start by recognizing that profit is equal to total revenue minus total cost. Given a table of costs and revenues for each quantity, we can plot the data directly on a graph.

Marginal Cost Marginal Revenue Method: If total cost and total revenue are difficult to procure, then this method may also be used. For each unit sold, marginal profit equals marginal revenue minus marginal cost. Then, If marginal revenue is greater than the marginal cost, marginal profit is positive and if the marginal revenue is less than the marginal cost then marginal profit is negative. And when marginal cost and marginal revenue are equal then the marginal profit is zero. Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, total profit must be maximum when marginal profit is zero – or where marginal cost equals marginal revenue.

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