Starting with Slope

Slope and the Curve

For a production possibilities curve that illustrates the production of crab puffs and storage sheds, this is the change in the quantity of crab puffs (rise) divided by the change in the quantity of storage sheds (run).

Here is a handy formula for calculating the slope of the production possibilities curve.

slope

=

rise run

=

change in crab puffs change in sheds

For example, the slope of the production possibilities curve between points I (8 sheds and 270 dozen crab puffs) and J (9 sheds and 200 dozen crab puffs). The slope between I and J is -70. The rise is a decrease of 70 and the run is an increase of 1.

slope, I to J

=

change in crab puffs change in sheds

=

-70 1

=

-70

Click the [Slope I to J] button to illustrate. For other slope values click the [Show The Rest] button.

Now for Opportunity Cost

The Schedule

This production possibilities schedule can be used to illustrate opportunity cost.

• The opportunity cost of producing the first shed is 5 dozen crab puffs.

• As the economy moves from bundle A to bundle B, the production of sheds increases from 0 to 1 and the production of crab puffs decreases from 450 dozen to 445 dozen.

• In order to produce the first shed, the economy must switch resources from crab puff production to shed production.

• As such, 5 dozen crab puffs are given up to produce the first shed.

Increasing Opportunity Cost

Increasing Opportunity Cost

Moving along the production possibilities curve, the slope becomes steeper (that is, the absolute value of the slope increases), reaching a value of -200 (an absolute value of 200) between points J and K. This reflects an increasing opportunity cost of producing storage sheds, resulting in a convex shape for the production possibilities curve.

The reason for this convex shape rests with the law of increasing opportunity cost, one of the more important principles studied in economics. The law of increasing opportunity cost states that the opportunity cost of producing a good increases as more of the good is produced.

• With relatively few sheds produced, the opportunity cost is low and the curve is flat. The production of the first shed, moving from point A to point B, uses resources best suited for shed production and least suited for crab puffs production. As such, very few puffs are given up to produce one shed.


• However, as more sheds are produced, the opportunity cost is higher and the curve is steeper. Resources removed from puff production are more suited for puff production and less suited for shed production.


• With production of the tenth shed, going from point J to point K, the resources switched are those least suited for storage sheds and best suited for crab puffs. As such, a relatively large number of puffs are given up to produce one shed.
  
• As more sheds are produced, the opportunity cost of production increases. The end result is a convex production possibilities curve.