Finding the profit-maximizing output requires the business owner to understand the economic concept of marginal analysis. Marginal analysis considers the law of diminishing returns. For example, after two slices of pizza, enjoyment decreases for every piece eaten. Similarly, selling as many products as possible may result in unexpected costs. Marginal analysis tells us that the profit-maximizing output is where marginal revenue equals marginal cost.

Things You Will Need

• Paper

• Profit and Loss Statement

## Step 1.

Set up your table. Using a spreadsheet or piece of paper draw a table with six columns. Name the columns as follows: Quantity, Total Revenue, Total Cost, Total Profit, Marginal Revenue, and Marginal Cost.

## Step 2.

Determine how to incrementally divide the quantity sold for the first column. For example, a car dealership owner may decide to divide his products singly, and enter the following in the first column: 0, 1, 2, 3, etc. An office supply store owner analyzing paper clip sales may divide her product by hundreds: 0, 100, 200, 300, etc. paper clips sold.

## Step 3.

Calculate total revenue for each increment. Using the car dealership example, selling no cars would result in total revenue of \$0. Enter this number under Total Revenue for 0. For the next two rows, total revenue might equal \$20,000 for one car sold, and \$40,000 for two cars sold. Fill in the rest of the column. Be sure to take into account quantity discounts.

## Step 4.

Calculate total variable cost for each increment. For selling no cars, total costs are \$0. Fixed costs are not included in marginal analysis, unless they increase to accommodate increased sales. Adding capacity might be an example of increasing fixed costs to accommodate increased sales. Variable costs such as labor costs and raw materials should be included. For our dealership example, the costs to sell one car might include the costs for one salesperson’s daily wages (\$150), commission for the sale (\$250), and the cost of the car (\$15,000), totaling \$15,400. To sell two cars, costs might include two commissions totaling \$500 (the same salesperson sells the car, so daily wages would not increase) and the cost of two cars (\$30,000), totaling \$30,650. Note: in some cases, at least one salesperson must be on the floor every day, whether a car is sold or not. In this case, do not include his daily wages in your variable costs. The wages for the minimum number of salespeople should be included in fixed costs.

## Step 5.

Calculate total profit. For each increment, calculate total profit by subtracting total costs from total revenue. You will use this column to verify that total profit is maximized where marginal costs equal marginal revenue.

## Step 6.

Calculate marginal revenue. For each increment, subtract the change in total revenue. For our dealership example above, increasing sales from one to two cars would equal a marginal revenue of \$20,000. Marginal revenue may be the same for all increments, unless quantity discounts are included.

## Step 7.

Calculate marginal cost. For each increment, subtract the change in total costs. For our example above, the marginal cost of selling two cars would be \$30,650 minus \$15,400, which equals \$15,250. Since marginal cost of \$15,250 is less than marginal revenue of \$20,000, the car dealership should increase sales to optimize profit until marginal cost equals marginal revenue.