#### Version 1: the potato problem

**1960s:**

A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?

**1970s:**

A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?

**1970s (new math):**

A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?

**1980s:**

A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word “potatoes” and discuss with your classmates.

**1990s:**

A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue versus costs. Run the `POTATO`

program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

Adapted from The American Mathematical Monthly, Vol. 101, No. 5, May 1994.

#### Version 2: the logging problem

**1960s:**

A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount. What is his profit?

**1970s:**

A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount, i.e. $80. What is his profit?

**1970s (new math):**

A logger exchanges a set *L* of lumber for a set *M* of money. The cardinality of set *M* is 100. The set *C* of production costs contains 20 fewer points. What is the cardinality of Set *P* of profits?

**1980s:**

A logger cuts and sells a truckload of lumber for $100. *Her* cost is $80 and *her* profit is $20. Find and circle the number 20.

**1990s:**

An unenlightened logger cuts down a beautiful stand of 100 trees in order to make a $20 profit. Write an essay explaining how you feel about this as a way to make money. Topic for discussion: How did the forest birds and squirrels feel?

Adapted from Reader’s Digest, February 1996.