Review Topics

 Home Revenue and Profit Calculus Supply Curve Supply, Demand and Equilibrium

## 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 start-up 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?