Step One  Cost
Comprehension
The cost of producing
a barrel of oil depends on many factors.
1)
What do you think some of these factors are?
2)
Which costs are fixed costs (that is, incurred no
matter what the output)?
3)
Which costs are variable costs (that is, vary with
output)?
4)
How could you use a cost function to decide on the selling
price for a barrel of oil?
Acquisition
Some of the terms we
introduce in this section (cost, fixed cost, variable cost, marginal
cost) may be unfamiliar to you. To see precise definitions and
examples, click here or see the menu topic.
Application
In addition to startup
costs, there are production costs associated with the actual extraction
of oil. These include a fixed cost, which remains constant regardless
of the amount of oil extracted, and a variable cost per barrel
extracted. The table below gives the production cost of extracting
different quantities of oil.
barrels
of oil (_{})

cost
(_{$})

600

8520

700

9980

800

11480

The average variable
cost of extracting oil is not constant. It is more expensive
to extract oil from a greater depth, and so the higher the output
level, the greater the cost per barrel extracted. For this reason,
we will model the data provided above with a quadratic function.
Round to three places.
Questions
1)
Determine a quadratic function that fits these data.
2)
Determine the fixed cost and the variable cost per unit.
Does the variable cost per unit increase as production increases?
3)
Determine the marginal cost function.
a)
What is the marginal cost when q = 100? Give a verbal
interpretation of this number.
b)
What is the marginal cost when q = 500? Give a verbal
interpretation of this number.
4)
Determine average cost function.
a)
What is the average cost when q = 100? Give a verbal interpretation
of this number.
b)
What is the average cost when q = 500? Give a verbal interpretation
of this number.
5)
Graph the average cost function and the marginal cost function
on the same coordinate system.
6)
Determine when average cost is minimum.
7)
Verify that average cost is minimum when average cost equals
marginal cost.
Reflection
Examine solutions and
implications.
1)
Is the marginal cost function increasing or decreasing?
What does this tell you about cost?
2)
Look at the graph for question #5 above.
a)
Find the points on the graph corresponding to the quantities
computed in questions #3 and #4.
b)
When the marginal cost is less than the average cost, what
is the affect on the average cost of producing one more barrel?
Does this make sense to you?
c)
When the marginal cost is greater than the average cost,
what is the effect of producing one more barrel on the average
cost?