The text uses the notions of fixed costs, sunk costs and variable costs. Fixed costs are costs which do not change as the output of the firm changes. In our earlier discussion, the cost of using the asset to produce widgets was a fixed cost, because it would not change if we changed the number of widgets we produced. Sunk costs are costs that cannot be avoided, at least over some period of time, even if the firm ceases production altogether. In our story, the fixed cost was avoidable. All the firm had to do was choose the best alternative to widget-making and earn the return it provided. The cost of using the asset to make widgets would thereby be avoided. But suppose there is no alternative use for the asset. Then there is no cost for using the asset in this way. This would be hard to imagine for most assets. One example might be a railroad tunnel. It might well have no alternative use, so the cost of using it as a railroad tunnel (once it is built) would be zero, regardless of how much cost was incurred in making it. Thus whatever cost was incurred in making it would be a "sunk" (unavoidable) cost. (The opposite extreme would be an office building, which you paid $1 mil. for and could immediately resell for $1 mil. The interest one could get by investing the proceeds would be a totally avoidable cost.) The way the authors of your text get at the notion of sunk cost is to imagine that you lease your building instead of owning it. If the lease is unbreakable and you are not allowed to sub-lease (i.e., lease it to someone else) then the lease expense is unavoidable or sunk. Another way to get at it is to imagine that you own the asset and will want to continue to own it, but you are approaching a "slow season." If you have already determined that you want to continue to own the asset (and not use it for any other purpose during the slow season) then the cost of using the asset for this purpose during the slow season is sunk and unavoidable. That is, it will not go away if you decide to shut down. You have closed off certain options (such as selling the asset or putting it to a different use), and the only options that are left (operating or not operating) do not affect the size of that cost. In that situation, the cost of using the asset is sunk and unavoidable and should be ignored. Then in order to justify operating during the slow season, it is only necessary for the revenue generated to be greater than the extra (i.e. variable) cost that is incurred by operating.

The way in which direct operating (or variable) cost changes as output changes is related to the concepts of incremental cost and marginal cost. If we have a sizable change in output, the change in cost due to that change in output is an incremental cost. When we put the change in cost on a per unit basis (i.e., when we divide the change in cost by the change in output that brought it about) we have marginal cost. If we divide the total operating (or variable) cost by the output produced, we have the Average Variable Cost (or per unit variable cost). If we divide the sum of operating cost and continued possession cost by the quantity produced, we have what we will call the Average Total Cost (or total cost per unit) for a firm that is already set up. (For this purpose, we ignore the Acquisition Cost, because it is sunk and irrelevant once the firm is set up.)

There are certain arithmetic relationships between the Marginal Cost (MC) and the Average Variable Cost (AVC). All marginals and the corresponding averages have this relationship. The MC and Average Total Cost (ATC) have the same relationship.

The size of MC depends on the Marginal Productivity of the variable inputs. The reason operating cost (total variable cost) increases as output increases is that the firm must use more of certain inputs (such as labor and raw materials) when it produces more output. Suppose a firm can by using various amounts of labor produce various amounts of output, as shown below.

L Q

0 0

1 3

2 7

3 12

4 18

5 23

6 27

7 30

Suppose that every unit of the good produced requires $4 worth of raw materials. Suppose also that each unit of labor must be paid $60. Then the total variable cost the firm would have to pay for any amount of output would be $4 times the amount of output, plus $60 times the number of workers required. When the firm produces 7 units instead of 3 (because it hires a second worker), its cost increases by 4x$4 plus $60, a total of $76. This is the incremental cost of the extra 4 units of output. The marginal cost is $76/4 = $19. If the firm hired a third worker, enabling it to produce 12 units of output instead of 7, the firm's cost would go up by 5x$4 plus $60, or a total of $80. The marginal cost over this range is only $16. Why is it lower? The answer is that the marginal product of the variable input (labor) was higher when the third unit of labor was hired than when the second unit was hired. The extra labor cost $60 in both cases, but in the case of the third unit, the extra labor enabled the firm to add 5 units to its output instead of only 4. You should confirm for yourself that the marginal cost over the output range from 12 to 18 is $14; over the range from 18 to 23, it is $16; over the output range from 23 to 27, it is $19; and over the range from 27 to 30, it is $24. Thus as the Marginal Product of Labor falls, the Marginal Cost of producing more output increases.