Which of these best describes the concept of slope?
- [A mathematical formulation of the steepness of a line.]
- An expression of the curvature of a line.
- A function of two variables used to solve inequalities.
An algebraic notation of absolute value.
Barney and his friends enjoy doing two things: painting pictures and writing poetry. However, they must allocate their time. If they are doing one activity, they cannot be doing the other. Barney and his friends have the following points on their production possibilities frontier (the first number represents the number of pictures painted, the second the number of poems written): (5, 15) and (3, 29). Which of these expresses Barney’s opportunity cost?
- Give up 1 painting to write 5 poems.
- [Give up 1 painting to write 7 poems.]
- Give up 1 poem to paint 2 pictures.
Give up 1 poem to paint 4 pictures.
- At a given Point A on the production possibilities frontier, Atlantis has a slope of -1/3 between Good X and Good Y. At Point B on the production possibilities frontier, Atlantis has a slope of -1. Assuming we are moving production from Point A to Point B, which of the following best describes the opportunity cost of choosing more of Good X?
- [The opportunity cost is increasing.]
- The opportunity cost is decreasing.
- The opportunity cost is constant.
- The opportunity cost is positive.
Imagine you are the Chief Production Officer at a factory which can make two toys: plastic dolls and teddy bears. You have been given the task by the owner of the factory to model the use of inputs in producing both products.
Assume that the same resources can be used to make teddy bears or plastic dolls. If you put all available resources into making plastic dolls, you can manufacture 160. If you focus only on making teddy bears, you can manufacture 20. Draw a linear production possibilities frontier and calculate the slope.
Using your data from part a, give any two combinations of plastic dolls and teddy bears which would also be feasible to produce.
[Answers will vary, but must fall between the outer bounds of production given in Part A and still maintain the same slope generated in Part A.]
Explain why the production possibilities frontier between plastic dolls and teddy bears is not likely to be linear.
[Resources used to make teddy bears, such as soft stuffing and thread, are not likely to be efficient in making hard plastic dolls. Thus, if the factory converts from making one good to making the other, they will have to give up more and more to gain fewer and fewer.]
- Assume that the same resources can be used to make teddy bears or plastic dolls. If you put all available resources into making plastic dolls, you can manufacture 160. If you focus only on making teddy bears, you can manufacture 20. Draw a linear production possibilities frontier and calculate the slope.
The concept of opportunity cost is a foundation of economic study, and while advanced mathematics is generally used to compute it from a production possibilities frontier, the computation of slope (“rise over run”) can be used to approximate the opportunity cost by using production possibilities curves. Students will be using their math skills to compute the slopes of various production possibilities frontiers in order to determine the opportunity cost of producing different combinations of two goods. Ultimately, students will move from computing slope on a linear production possibilities frontier to one that is concave to the origin where the slope changes. This lesson is best taught in a high school Introductory Algebra course. The teacher should note that this lesson does not cover all aspects of slope. For example, all of the slopes examined in this lesson, due to the nature of the production possibilities frontier, are negative. Further, the slopes are located exclusively in the first quadrant of the coordinate plane. However, the lesson is designed to teach students a practical application of slope.
- Slides 3, 6, and 7 in Using Slope to Compute Opportunity Cost PowerPoint from Henrico County, Virginia
Grades 3-5, 6-8, 9-12