 The cost equation is a mathematical formula used to predict costs at various levels of volume. We will learn three methods to predict costs at various levels of volumes. Each uses the cost equation. The cost equation is y equals vx plus f. y is the total mixed cost, v is the variable cost per unit, x is the volume, and f is the total fixed costs. Another way to think of the cost equation is as follows. Total cost equals variable cost per unit times volume plus fixed costs. The cost equation is only valid within a relevant range. Outside the relevant range of volume, the cost equation changes. For example, if I owned one airplane, I could predict costs at various levels of volume for flights from Salt Lake to Las Vegas. I could determine how many passengers I could fly and how many flights I could make in a day. All of those things are within the relevant range. However, once demand got so large that I needed a second airplane to meet the demand, the relevant rain changes, and the original cost equation is no longer valid. In this case, my fixed costs would go way up when I had to buy a second aircraft. Graphically, you can see how the costs change over time. Total variable costs are often curvy linear, which means they increase, but not always proportion to the volume at any level of volume. Think about the purchasing power of Walmart versus a local store. As Walmart gets larger and larger, they can get discounts at volume levels that many smaller stores cannot. Fixed costs are fixed until volume increases too much that a new production plant or airplanes have to be placed into service. Fixed costs tend to be step costs as volume increases. So our ability to predict costs using the cost equation is only valid when we are within the relevant range of volume.