3.1.2 Example 2, cost function

Here's a cost function (in dollars), presented to you out of thin air: what do you make of it?

$$\fbox{$Total Cost = 1500 + 40 \times I,$ }$$

where I again is the number of units produced.

The first recognition, is that it is a linear cost function in the number of items produced.

What does it imply? Consider what happens to costs if the number of items produced increases by 1: Say we go from 30 to 31 items. 30 items cost $1500 + 40 \times 30 = 2700$, whereas 31 items costs $1500 + 31 \times 40 = 2740$, an increase of $40.

Likewise if we increase from 300 to 301 items the total costs rises from $13500 to $13540, again an increase of $40.

Convince yourself now that this cost function implies that an additional item produced leads to a $40 increase in costs, regardless of how many items have been produced.

How do you interpret the components?

Intercept. By definition the value of y when x equals zero. In this case, the total cost of producing 0 units, in other words the fixed costs are $1,500. If we define fixed costs as that component of Total Cost which, does not depend on the quantity produced, then directly from the straight line formula we can see that it is the intercept term.

$$\fbox{$Total Cost = 1500 + 40 \times I,$ }$$

Slope. The slope of the line, in this case 40, is by definition the change in y for a one unit change in x, here the change in Total Cost for a one unit increase in output, the definition of marginal cost. So the marginal cost is $40.

The LHS of the cost equation is measured in dollars. In what units must the intercept and the slope be, in order to make the equation balance?