Cost Structures

In the previous section, we talked of production functions and input factors. When a firm converts factors of production into products (or output), it has to incur costs for those inputs before it can sell the output in the market. In this section, we will examine some of these costs, and how they fit into the concept of a supply curve.

There are several different types of costs that a firm incurs, broken down as follows:

Fixed Costs

This is the amount of money a firm has to spend to produce something that is not related to the amount produced. It is sometimes called the Sunk Cost or Overhead. Remember: in the short run, capital is fixed, so it is capital that forms the fixed cost part of any production process. Put another way, this is money you have to spend before you produce anything. For a pizzeria, it is the cost of the building, the ovens, the meat slicer, and so on. In the oil and gas industry, it is the wells, pipelines and refineries that have to be built to extract, transport and transform the crude oil or gas into saleable products. In the electricity industry, it is the power plants and transmission lines.

Variable Costs

These are costs that change with respect to the quantity produced. This basically describes the non-capital factors of production: material, labor and energy. All of these things change with respect to the amount of output a firm creates. An electricity generator has to burn more coal or gas to make more electricity. A pizzeria has to consume more flour, cheese and tomatoes to sell more pizza. A consulting company needs more staff if it is to take on more projects. These factors are all variable costs in the sense that they vary with output. Sometimes, certain types of labor might be seen as "overhead," and thus, basically, a fixed cost, because this labor does not vary with output, but this is a minor detail we need not worry about at this point.

Total Cost

Total Cost = Fixed Cost + Variable Cost

Figure 3.1 Total Cost = Fixed Cost + Variable Cost

Using abbreviations, we say that TC = FC + VC. When we mathematically represent a cost function, it might look something like this: TC = 10 + 2Q + 0.05Q²

So, you will know that the Fixed Cost is the constant term (the term that does not include any mention of Q), and the Variable cost is the sum of all of the terms that include Q in some way. If a term does not include Q, then, clearly, it does not change when Q changes. In the above example, the fixed cost is 10 and the variable cost is 2Q + 0.05Q².

Average Cost

An average cost is the total cost divided by the quantity:

AC = TC/Q. (Can also be labeled as ATC: average total cost)

We can also have average fixed cost and average variable cost:

AFC = FC/Q
AVC = VC/Q

Marginal Cost

Marginal Cost is the most important cost of all. Greg Mankiw, whom we mentioned in the first lesson, calls this the “most important concept in economics.” The marginal cost is the cost of producing one more unit (or can be thought of as the cost of producing the last item). So, it is the change in total cost for some change in quantity:

MC = (delta TC)/(delta Q) = (TC₂ – TC₁)/(Q₂-Q₁)

where TC₁ is the total cost of producing Q₁ units, TC₂ is the total cost of producing Q₂ units of output.

If we use the cost function from above, TC = 10 + 2Q + 0.05Q², the cost of producing 10 units will be given as:

TC₁ = 10 + 2(10) + 0.05(10)²

TC₁ = 10 + 20 + 5 = 35

Using the same function, the total cost of producing 11 units will be:

TC₂ = 10 + 2(11) + 0.05(11)²

TC₂ = 10 + 22 + 6.05 = 38.05

So, the marginal cost of the 11th unit = (38.05 - 35)/(11-10) = 3.05/1= 3.05

Note: TC₁ = FC + VC₁ and TC₂ = FC + VC₂, so TC₂ – TC₁= FC + VC₂ – FC – VC₁.

So, by cancelling out the FC term, we get DTC = DVC, and we can say that:

MC = delta VC/delta Q

Of course, anything defined in discrete difference (“delta”) terms can also be described in continuous terms by using a derivative:

MC = d(TC)/d(Q) = d(VC)/d(Q)

Note: If you have not studied calculus, don't worry - this will not be used in this course. I am merely illustrating the concept for those who have had calculus.

Assume that the fixed cost for a shoe firm is 500, and it costs 100 to produce each individual pair of shoes. For Q=1 to 10, determine the fixed cost, variable cost, total cost, average variable cost, average fixed cost, and marginal cost.

Table 3.4 Marginal Cost Chart
Q	FC	VC	TC	ATC	AFC	AVC	MC
1	500	100	600	600.00	500.00	100	100
2	500	200	700	350.00	250.00	100	100
3	500	300	800	266.67	166.77	100	100
4	500	400	900	225.00	125.00	100	100
5	500	500	1000	200.00	100.00	100	100
6	500	600	1100	183.33	83.33	100	100
7	500	700	1200	171.43	71.43	100	100
8	500	800	1300	162.50	62.50	100	100
9	500	900	1400	155.56	55.56	100	100
10	500	1000	1500	150.00	50.00	100	100

Your turn

Assume the fixed costs for a pizza restaurant is 150 and it costs 15 to produce each pizza. For Q=1 to 10, determine the fixed cost, variable cost, total cost, average variable cost, average fixed cost, and marginal cost.

Click for answer...

Table 3.5 Marginal Cost Chart
Q	FC	VC	TC	ATC	AFC	AVC	MC
1	150	15	165	165	150	15	15
2	150	30	180	90.00	75.00	15	15
3	150	45	195	65.00	50.00	15	15
4	150	60	210	52.50	37.50	15	15
5	150	75	225	45.00	30.00	15	15
6	150	90	240	40.00	25.00	15	15
7	150	105	255	36.43	21.43	15	15
8	150	120	270	33.75	18.75	15	15
9	150	135	285	31.67	16.67	15	15
10	150	150	300	30	15	15	15

Take Aways

After working through the material on this page and reading the associated textbook content, you should be able to confidently:

define and calculate the following terms:
- fixed cost, average fixed cost
- variable cost, average variable cost
- total cost, average total cost
- marginal cost
derive the fixed cost, variable cost, average costs and marginal cost when given a total cost function.