March 22, 2019 

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Because variable cost is largely associated with the cost of employing at least one variable input in the short run, the total variable cost curve can be derived from the total product curve. This admittedly simplistic connection between total product and total variable cost is designed to illustrate the fundamental role that the law of diminishing marginal returns plays in the slope and shape of the total variable cost curve. Because he slope of the total variable cost curve, which is also the slope of the total cost curve, is marginal cost, this analysis also indicates how the law of diminishing marginal returns relates to marginal cost.
The total variable cost curve can be derived from the total product curve. The changes needed to transform the total product curve into the total variable cost curve are:
  1. Change the orientation of the horizontal and vertical axis by first rotating the axes then flipping the curve.

  2. Change the variable input measure from quantity of inputs to cost of inputs.

  3. Eliminate that portion of the curve associated with Stage III of production.

Setting the Stage

Stuffed Amigo Production
Total Product Curve
The conversion begins with a standard total product curve, such as the one for Wacky Willy Stuffed Amigos (those cute and cuddly turtles, tarantulas, and scorpions) displayed to the right. The quantity of variable input used, hours of labor, is measured on the horizontal axis and the resulting total product generated by this input, the production of Stuffed Amigos, is measured on the vertical axis. The relation between variable input and output is the total product curve.

The shape of the total product curve reflects increasing, then decreasing marginal returns. The slope of the total product curve becomes increasingly steeper for the first few units of labor employed due to increasing marginal returns, which is Stage I of production. The slope of the total product curve then begins to flatten because of decreasing marginal returns in Stage II of production. The law of diminishing marginal returns also sets in with production Stage II.

Analysis of the total product curve usually asks the question: How much output is produced and for different amounts of the variable input? This total product curve indicates that 1 Stuffed Amigo is produced with 2 workers and that 8 Stuffed Amigos are produced with 5 workers.

Onto Cost

However, the derivation of total variable cost asks a different question: How much does it cost to employ the labor needed to produce different quantities of output? If, for example, 1 Stuffed Amigo is produced, how much does it cost to hire the labor? Alternatively, if production is 8 Stuffed Amigos, how much does it cost to employ the necessary labor?

To answer these questions, a little more information is needed, the wage rate. Suppose that the cost of hiring each workers is $5.

It should now be clear that to produce 1 Stuffed Amigo, 2 workers are needed, which incurs a cost of $5 per worker. The cost of producing 1 Stuffed Amigos is therefore $10. The cost of producing 8 Stuffed Amigos, which requires 5 workers, is thus $25. These numbers are the "total cost of the variable input," which can be shorten somewhat to just "total variable cost." Of course, this assumes that labor is the only variable input and thus the only component of variable cost, which is probably not completely realistic, but it serves the immediate analysis.

Making the Conversion

From Production to Cost
From Production to Cost

The transformation of the total product curve presented in the exhibit to the right incurs four steps--rotate the axes, flip the curve, covert the input from quantity to cost, and chop off that portion of the curve for Stage III.
  • Rotate the Axes: The first step in this transformation is to rotate this diagram 90 degrees, into a position that puts the quantity of output on the horizontal axis and the variable input on the vertical axis. As this diagram presently stands, quantity (total product) is measured on the vertical axis and cost (total variable cost) is measured on the horizontal axis. However, for total variable cost, quantity should be on the horizontal axis and total variable cost should be on the vertical axis. Click the [Rotate the Axes] button to demonstrate this step. Note that all three production stages and thus the shape of the curve remain intact.

  • Flip the Curve: The second step is to flip the curve into a more traditional position. The primary consequence of the 90-degree rotation is that the origin lies to the far right of the diagram rather than the far left. In other words, the curve is a reserved, or mirror, image of what it needs to be. To reposition the curve with a flip from right to left, click the [Flip the Curve] button. Note that all three production stages and the shape of the curve remain intact.

  • Convert to Cost: The third step is to change the scale on that is now on the vertical axis from the quantity of the variable input (workers) to the cost of using the variable input (dollars). Click the [Convert to Cost] to show this transformation. Make note that the curve itself has not changed. As such, all three production stages can still be identified by the changing slope of the curve.

  • Chop Stage III: The last step is the eliminate Stage III of production. While Stage III is important and relevant to short-run production, it is not relevant to the cost of short-run production. To eliminate that portion of the curve related to Stage III, click the [Chop Stage III] button.
Having clicked all four buttons, the resulting curve displayed is a traditional-looking total variable cost curve. The primary conclusion is that this total variable cost curve is essentially the total product curve. The curve is flipped and rotated. The variable input measurement scale is changed. And Stage III production is deleted. But the basic curve does not change. As such, production Stage I, with increasing marginal returns, and Stage II, with decreasing marginal returns, can still be identified by the slope of the curve.


Recommended Citation:

TOTAL VARIABLE COST AND TOTAL PRODUCT, AmosWEB Encyclonomic WEB*pedia,, AmosWEB LLC, 2000-2019. [Accessed: March 22, 2019].

Check Out These Related Terms...

     | marginal cost and marginal product | U-shaped cost curves | total cost curves | marginal cost and law of diminishing marginal returns | total variable cost and marginal cost | total cost and marginal cost |

Or For A Little Background...

     | total variable cost curve | total cost curve | total product curve | short-run production analysis | law of diminishing marginal returns | marginal returns |

And For Further Study...

     | total cost | total variable cost | total fixed cost | marginal cost | average cost | variable cost | fixed cost | average total cost | average variable cost | average fixed cost | profit maximization | long-run average cost | opportunity cost, production possibilities |

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