# How to Calculate a Marginal Cost Curve

In most production scenarios, costs start high, decrease as production increases, then start to rise again at a particular volume of production. If you plot these costs on a graph relative to the number of units you're producing, you'll typically see a J-shaped curve. This is what we mean by marginal costs – an increase or decrease in the total costs your business will incur by producing one more unit of a product. You calculate the marginal cost by dividing the change in total cost by the change in output.

## Marginal Cost Explained

Marginal costs are best explained by using an example like Widget Corp, a manufacturing company that makes widgets. In the early days of trading, Widget's production costs are relatively high. That's because the company is buying raw materials on an as-needed basis, as well as paying staff and investing in large-scale machinery to satisfy a relatively small number of contracts. As the volume of production increases, the manufacturing cost will decrease. This is due to economies of scale – Widget Corp is now producing more and can take advantage of discounts for bulk purchases of raw materials. The company can also run its production line at optimum capacity.

At some point, however, diseconomies of scale will kick in. Suddenly, Widget has to buy more equipment to keep up with demand, and it needs to hire more managers to oversee operations. Costs go up relative to production. It's this decrease then subsequent increase in costs relative to output that creates the J-shape of the typical marginal-cost curve.

## Understanding the Total Cost of Production

To calculate marginal costs for any product or service, you need two pieces of information: the production quantity, or how much product you're manufacturing, and the total cost of producing that quantity. Total cost is the sum of all your fixed costs and variable costs in producing the good or service. Examples include rent, mortgage, interest on loans and management salaries (these are fixed costs, which means you incur them even if production is zero), as well as hourly-rate labor costs, raw materials, utilities and shipping expenses (these are variable costs, which means they fluctuate depending on how much product you're manufacturing). Calculating the marginal cost will show you how your total costs change as you increase or decrease production.

## The Marginal Cost Formula

The formula used to calculate marginal cost is:

Marginal Cost = Change in Total Cost/ Change in Output

You may see the formula transcribed using mathematical symbols, like this:

MC = Δ TC/ Δ Q

For example, suppose the total cost of producing 1,000 widgets is $4,500. The total cost of producing 2,000 widgets is $8,000. The marginal cost is ($8,000-$4,500) / (2,000-1,000) = $3.50. Total cost increases by $3.50 with the production of one additional widget.

## The Marginal Cost Curve

Since marginal cost shows the additional costs you incur by adding another unit of production, you'll need to run the calculation for various units of output. For example, Widget Corp might calculate the total cost against production runs of 1,000, 2,000, 3,000, 4,000 and 5,000 widgets. It helps to arrange the data into a table or spreadsheet so you can easily see the marginal cost associated with each incremental increase in output.

Armed with your calculations, you can now plot a marginal cost curve. Use a simple XY graph where the production quantity (1,000, 2,000, 3,000, 4,000 and 5,000 widgets) is the X-value on the horizontal axis and marginal cost is the Y value on the vertical axis. In most production scenarios, the graph is shaped like a "J."