# How to Calculate the Profit-Maximizing Quantity

by Sara Huter; Updated September 26, 2017Calculating the quantity that will maximize profits requires that you understand the economic concept of marginal analysis. Marginal analysis is the study of incremental changes in profit. The quantity that maximizes profit is where marginal profit shifts from positive to negative. In this case, we will assume that quantity is the amount of product that a business owner hopes to sell. As our business owner increases sales, so do expenses. When expenses increase to an amount that no longer maximizes profits, marginal profit becomes negative.

#### Items you will need

- Sales report
- Expense report
- Spreadsheet or paper and pen
- Calculator

Determine the profit at each level of sales. Assume that a business sells fountain pens for $25 each. As sales increase, he must account for labor costs, quantity discounts, increased shortage (loss, theft and breakage) and other variable costs. Therefore, if he sells 20 pens, his profit would be $250, 40 pens, profit would be $350, for 60 pens, it would be $550, and for 80 pens it would be $500.

Determine the marginal profit at each incremental increase in sales. Marginal profit is defined as the change in profit for each additional unit sold. In our example above, we’ve determined that a unit is an increment of 20 pens. To increases sales from zero to 20 pens, marginal profit would be $250. To increase sales from 20 to 40 pens, marginal profit would be $100. Increasing sales from 40 to 60 pens results in a marginal profit of $200. Finally, increasing sales from 60 to 80 pens results in a marginal profit of negative $50.

Determine the profit maximizing quantity. In this case, the profit-maximizing quantity is 60 pens. This is the point before marginal profit becomes negative. Why? It is likely that the more pens sold, the higher variable costs are. Variable costs include labor, commissions, raw materials and shortage. In addition, when large quantities are sold to one party, a quantity discount is often given, resulting in lower per-unit revenue.

Determine where expenses could be lessened and revenue could be increased to optimize sales. Marginal analysis is not static. Assume our pen sales company finds a way to reduce shortage with an inventory tracking system. Therefore, the total profit for selling 80 pens is $600 instead of $500. Marginal profit for selling 80 pens is now $100. The company now must find its new profit-maximizing quantity. If selling 100 pens results in a total profit of $675, marginal profit is $75, and we still have not reached the profit-maximizing quantity. Selling 120 pens results in a total profit of $650, and the marginal profit is negative $25. We have found the new profit-maximizing quantity of 100 pens.

#### Tips

Another method that will return the profit-maximizing quantity is to find where marginal costs equal marginal revenue. Instead of calculating the profit for each increment, calculate total revenue and total variable costs. Calculate marginal revenue and marginal cost in the same manner as marginal profit, by determining the change in the amount for each increment.

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