Graphing a Firm's Costs

Introduction

Welcome back! In our last two lessons, we explored a firm's production in the short run. We learned that with at least one fixed input (like a factory), adding more of a variable input (like labor) leads to the law of diminishing marginal returns—where the productivity of each additional worker eventually decreases.

Today, we shift our focus from production quantities to production costs. Your goal is to calculate and graph a firm's total fixed cost, total variable cost, and total cost. We will see how the concepts of fixed and variable inputs directly translate into fixed and variable costs, and how the law of diminishing returns you just learned about gives the cost curves their distinctive shapes. Understanding these total cost curves is the first step toward analyzing how firms make decisions to maximize profit.

1. The Building Blocks: Defining Total Costs

Every cost a firm incurs can be classified into one of two categories in the short run: fixed or variable.

• Fixed Costs (FC or TFC): These are costs that do not change regardless of the quantity of output produced. Think of them as the costs of the firm's fixed inputs. Even if a car factory produces zero cars, it still has to pay rent on the factory, insurance, and payments on its assembly line machinery. These costs are "sunk" in the short run.

• Variable Costs (VC or TVC): These are costs that change directly with the level of output. They represent the costs of the firm's variable inputs. To produce more cars, the factory must hire more workers (wages) and buy more steel, tires, and electronics (raw materials). If the factory produces nothing, its variable costs are zero.

• Total Cost (TC): This is simply the sum of the two. It represents the full cost of production for a given level of output. The relationship is fundamental:

  $$TC=TFC+TVC$$

To see how these costs are calculated in practice, let's start with a short, clear video example.

2. A Toolkit for Calculating Costs

As the video demonstrated, the three total costs are directly related. Knowing any two allows you to find the third. This is a practical skill for solving economic problems.

For a more in-depth guide on the different ways you can calculate these costs, please review the following text. It presents these relationships as a practical toolkit.

3. Graphing the Total Cost Curves

Now that we can calculate these costs, let's visualize them. Graphing the cost curves reveals important patterns about a firm's production process.

The Total Fixed Cost (TFC) Curve

Since fixed costs are constant, the TFC curve is a horizontal line. The cost is the same whether the firm produces 1 unit or 1000 units.

The Total Variable Cost (TVC) Curve

The shape of the TVC curve is a direct consequence of the law of diminishing marginal returns from our previous lesson.

1. Initially (Increasing Marginal Returns): When the first few workers are hired, they are very productive (high marginal product). This means output increases significantly for each new worker hired. As a result, variable costs rise relatively slowly. The TVC curve starts off with a gentle slope.
2. Eventually (Diminishing Marginal Returns): As more workers are added, they become less productive (falling marginal product) due to a crowded workspace or limited machinery. To get the same increase in output, the firm now needs to hire more and more workers, causing variable costs to rise more and more steeply. The TVC curve gets steeper.

The Total Cost (TC) Curve

Since $TC=TFC+TVC$, the TC curve has the exact same shape as the TVC curve. It is simply shifted vertically upwards by the amount of the total fixed cost. At zero output, TVC is zero, so TC equals TFC.

The following video does an excellent job of explaining the logic behind these shapes.

This graph provides a static summary of the relationships you just saw in the video.

4. From Table to Graph: A Complete Example

To bring everything together, let's look at a comprehensive example that shows how a firm's cost data in a table is translated into the graphs we've just analyzed.

This example solidifies the link between the numerical calculation of costs and their graphical representation, fully addressing today's learning outcome.

Conclusion

In this lesson, we laid the foundation for cost analysis by defining, calculating, and graphing the three total cost curves. You now understand not only what these costs are, but also why their graphs have their characteristic shapes.

Here are the key takeaways:

• Total Fixed Cost (TFC) does not vary with output and is represented by a horizontal line.
• Total Variable Cost (TVC) increases with output. Its shape reflects the law of diminishing marginal returns: it rises slowly when marginal product is high and steeply when marginal product is low.
• Total Cost (TC) is the vertical sum of TFC and TVC ($TC=TFC+TVC$). Its curve has the same shape as the TVC curve, but is shifted upward by the value of TFC.

While total costs give us the big picture, firms often make decisions by looking at costs on a per-unit basis. In our next lesson, we will build directly on today's concepts to calculate and graph the average costs (AFC, AVC, ATC) and, most importantly, marginal cost (MC). We will discover that the marginal cost curve is a mirror image of the marginal product curve, completing the crucial link between production and cost.