The Concepts: A Graphical View

We have now looked at the relationship between outputs and inputs using a simple example of a tutoring "business." Here we will look at the graphs that go with this example.  Each one of these graphs corresponds to a column in one of the tables so you will see the same information, its simply presented in a different way.  We will look first at the production relationship where we will be able to "see" diminishing marginal product.  This will be followed by the cost curves where we will "see" increasing marginal cost. 

Production Relationships

Total Product

Total (physical) product: amount of output obtained from given input. The positive slope indicates that output increases as the input increases.

Marginal and Average Product

Average (physical) product: amount of output obtained per unit of input.  This is calculated by dividing total output by number of units of inputs.

Marginal (physical) product: additional output obtained by 1 more unit of input. You will note the marginal product curve has a negative slope after 3 units of input are used which indicates that if you keep adding labor to an operation with a fixed facility, eventually the additional output produced by the additional labor will begin to decline.  When this happens we enter a situation in which we have diminishing marginal product.

One of the features of the graph is that the MP curve cuts through the maximum point on the AP curve.

Cost Relationships

When you see cost curves they tend to come in two sets.   The first set includes some combination of the total cost concepts - Total Cost, Variable Cost, and Fixed Cost.  The second set would include some combination of the average and marginal cost concepts - Average Total Cost, Average Variable Cost, Average Fixed Cost, and Marginal Cost.  The reason there are two very distinct sets of graphs is the two sets have very different orders of magnitude.  Total costs may be in millions of dollars, while average or marginal costs may be in terms of dollars.  In our example the orders of magnitude are not that different, but the ranges for the total cost variables are different from the range for the average, and marginal variables.

Total Costs (Total, Fixed and Variable)

• Total Cost: all costs of production
• Fixed Cost: costs of production that do not vary with output
• Variable Cost: costs of production that vary with output

Average Costs (Total, Fixed, and Variable)

• Average Cost: costs per unit of output.  Diminishing average product translates into increasing average cost.  As an example, consider the situation where the input labor is paid $8 an hour and that the average productivity of a worker is 4 units of output per hour of labor. Since each unit of output can be produced in .25 hours, the cost per unit of output will be $2 [.25*$8].  If the average productivity of a worker is 2 units of output per hour of labor, then each unit of output can be produced in .5 hours, the cost per unit of output will be $4 [.5*$8].
• Average Variable Cost: variable costs per unit of output. Tends to look very similar to the Average Cost curve except that it lies above it.
• Average Fixed Cost: fixed costs per unit of output. This curve declines with output since you are dividing ever larger outputs into the same level of costs.  Average fixed costs equals the difference between average cost and average variable.

Marginal Cost

• Marginal Cost: additional costs of producing more output.  Diminishing marginal product translates into increasing marginal cost. As an example, consider the situation where the input labor is paid $8 an hour and that the marginal productivity of a worker is 4 units of output per additional hour of labor.  Since each unit of additional output can be produced in .25 hours, the cost per unit of additional output will be $2 [.25*$8]. If the marginal productivity of a worker is 2 units of output, then each additional unit of output can be produced in .5 hours, the cost per unit of additional output will be $4 [.5*$8].

You will find there is a relationship between average and marginal cost curves.  The marginal cost curve and average cost curves tend to be U-shaped and the marginal cost curve cuts through the average cost curves at their minimum points.