# How to Find a Marginal Cost Function

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If you own a small business, particularly in the production or manufacturing industry, it might be helpful to you to understand your marginal cost function. This figure can help you understand whether producing one more unit of your product is worthwhile, and what the resource cost is to do so. In order to calculate a marginal cost function, you also need to know the fixed cost and variable cost.

## What is a Marginal Cost Function?

When economists study the marginal cost of production, they are hoping to better understand the change in total production cost that results when one additional unit of product is created. This is important because it allows organizations to determine how best to optimize production and their larger operation process.

Companies need to know where this marginal cost comes into play, as it is a sweet spot for profit gains. To further explain, if the marginal cost of producing one additional unit of a product is lower than the per-unit price, it is possible that profits will increase.

Ideally, a company will choose to produce its goods up to the point where marginal cost is equal to marginal revenue. This will help to maximize profits and optimize production efficiency.

## Understanding Fixed Costs

When calculating marginal costs, you will also need to know the fixed costs connected to the production of a given item. A fixed cost does not change no matter how high your production level goes. As such, the higher the rate of production, the lower the fixed cost per unit produced. This is because the cost is spread out over more of those produced units.

For instance, assume the cost to purchase your factory and the machine needed to produce your widgets is \$100,000. Whether you produce 5,000 widgets or 5 million widgets, you will still be spending \$100,000 on your fixed costs. At the high end of production, therefore, you can lower the fixed cost per item produced to just \$0.02 per widget. If you only made 5,000 widgets, your fixed cost each would be much higher, at \$20 per widget.

## Understanding Variable Costs

You will also need to understand the variable costs. The variable costs involved in producing an item change based on how many you produce. For instance, the plastic needed to make 5,000 widgets will be much less than the plastic needed to make 5 million widgets. Variable costs include things like supplies and materials to keep machines in operation, since the more you produce the higher your variable costs are.

To determine your variable cost function, calculate the cost to produce one widget, but disregard fixed costs. If you are working to make X number of widgets, it might cost X^2 + 3X thousand dollars.

Next, you will need to add your fixed costs and variable costs to get the total cost. In our widget example, the cost function is Total Cost (X) = X^2 + 3X + 7.

## Determine the Marginal Factor Cost Function

To calculate marginal cost, try some marginal cost example problems. You’ll need to find the first derivative of the total cost function to find the marginal cost function. In our widget example, dTotalCost(X)/dX = 2X+ 3. You may wish to use a derivative calculator for this math.

Be aware that when you calculate the marginal cost that you understand fixed cost does not impact the marginal cost function.

With our widget example, you can see that 2X plus 3 is equal to one additional unit produced. To determine the cost of producing that unit, complete the function with applicable numbers for your business.