  Friday  July 1, 2022
 AmosWEB means Economics with a Touch of Whimsy! TOTAL PRODUCT AND MARGINAL PRODUCT: A mathematical connection between marginal product and total product stating that marginal product IS the slope of the total product curve. If the total product curve has a positive slope (that is, is upward sloping), then marginal product is positive. If the total product curve has a negative slope (downward sloping), then marginal product is negative. If the total product curve has a zero slope (horizontal), then marginal product is zero. Moreover, if the total product curve has a positive and increasingly steeper slope, then the marginal product is positive and rising. If the total product curve has a positive and decreasingly steeper slope, then the marginal product is positive but falling.                              U-SHAPED COST CURVES:

The family of short-run cost curves consisting of average total cost, average variable cost, and marginal cost, all of which have U-shapes. Each is U-shaped because it begins with relatively high but falling cost for small quantities of output, reaches a minimum value, then has rising cost at large quantities of output. Although the average fixed cost curve is not U-shaped, it is occasionally included with the other three just for sake of completeness.
The U-shapes of the average total cost, average variable cost, and marginal cost curves are directly or indirectly the result of increasing marginal returns for small quantities of output (production Stage I) followed by decreasing marginal returns for larger quantities of output (production Stage II). The decreasing marginal returns in Stage II result from the law of diminishing marginal returns.

The U-shaped cost curves form the foundation for the analysis of short-run, profit-maximizing production by a firm. These three curves can provide all of the information needed about the cost side of a firm's operation.

### Bring on the Curves

U-Shaped Cost Curves The diagram to the right displays the three U-shaped cost curves--average total cost curve (ATC), average variable cost curve (AVC), and marginal cost curve (MC)--for the production of Wacky Willy Stuffed Amigos (those cute and cuddly snakes, armadillos, and turtles).

All three curves presented in this diagram are U-shaped. In particular, the production of Wacky Willy Stuffed Amigos, like other goods, is guided by increasing marginal returns for relatively small output quantities, then decreasing marginal returns for larger quantities.

Consider a few reference points:

• The marginal cost curve reaches its minimum value at 4 Stuffed Amigos.

• The average variable cost curve reaches its minimum at 6 Stuffed Amigos.

• The average total cost curve reaches its minimum at 6.5 Stuffed Amigos.
The marginal cost curve for Stuffed Amigos production is the only one of these three curves that is DIRECTLY affected by the law of diminishing marginal returns. Up to a production of 4 Stuffed Amigos, increasing marginal returns is in effect. From the 5th Stuffed Amigo on, decreasing marginal returns (and the law of diminishing marginal returns) takes over. The U-shaped pattern for the marginal cost curve that results from increasing and decreasing marginal returns is then indirectly responsible for creating the U-shape of the average variable cost and average total cost curves.

### The Average-Marginal Relation

The average total cost, average variable cost, and marginal cost curves depict the basic mathematical relation that exists between any average and the corresponding marginal.
• Average Variable Cost: First, note the relation between the average variable cost curve and the marginal cost curve. The marginal cost curve intersects the average variable cost curve at its minimum value. Moreover, when average variable cost is declining (the average variable cost curve is negatively sloped), marginal cost is less than average variable cost. And when average variable cost is rising (the average variable cost curve is positively sloped), marginal cost is greater than average variable cost.

• Average Total Cost: Second, the average-marginal relation is also seen with the average total cost curve. The marginal cost curve intersects the average total cost curve at its minimum value, as well. When average total cost is declining (the average total cost curve is negatively sloped), marginal cost is less than average total cost. When average total cost is rising (the average total cost curve is positively sloped), marginal cost is greater than average total cost.
Note that the minimum values of the average total cost curve and the average variable cost curve occur at different quantities. This results because: (1) marginal cost intersects each average curve at its minimum value, (2) the marginal cost curve has a positive slope, and (3) there is a gap between the two average curves, which is average fixed cost. As such, the marginal cost intersects the minimum of the average variable cost curve at 6 Stuffed Amigos, then rises a bit before intersecting the minimum of the average total cost curve at 6.5 Stuffed Amigos.

### What About Average Fixed Cost?

Although the average fixed cost curve is not displayed in this exhibit, average fixed cost can be derived from the average total cost and the average variable cost curves.

First, note that the distance separating the average total cost curve and the average variable cost curve is relatively wide for small quantities of output, but narrows with greater production. The reason for the narrowing gap is that the difference between the two curves is average fixed cost. Because average fixed cost declines with greater production, so too does the gap between these curves.

As such, average fixed cost can be derived from this diagram by calculating the vertical distance between the average total cost and the average variable cost curves. While an average fixed cost curve is sometimes included in a diagram such as this one, it is not really needed. So long the average total cost and the average variable cost curves are available, average fixed cost can be obtained.

### And What About the Totals?

All total cost values--total cost, total variable cost, and total fixed cost--can also be derived from this diagram. If the output quantity, average total cost, and average fixed cost, are known, then the total cost measures can be derived. Total cost is quantity times average total cost. Total variable cost is quantity times average variable cost. And total fixed cost is quantity times average fixed cost.

As such, this diagram of the three U-shaped cost curves provides all of the information available about the cost incurred by a firm for short-run production.

 UNCERTAINTY => Recommended Citation:

U-SHAPED COST CURVES, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2022. [Accessed: July 1, 2022].

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