This activity focuses on analyzing supply-and-demand problems from business by solving systems of equations and finding the equations for lines.
Prerequisites:
It is assumed that students are familiar with:
- How to find a linear equation from a graph from 2 points or from the slope and the y‑intercept
- How to solve systems of 2 equations in 2 unknowns.
Definitions
You may wish to acquaint students with the following concepts from economics at the beginning of the activity session.
Supply
- Supply can be defined as the quantity of the item that is in stock.
- Price is a factor in the supply of an item. When the price of an item is low, more people buy the item, and the supply (stock on the shelves) decreases. When the price of an item is high, the supply remains high because fewer people buy the item, leaving more inventory on the shelves.
Demand
- Demand can be defined as the quantity of merchandise the consuming public wishes to buy.
- Price affects demand. A lower price tends to increase the demand because people may feel that the item is a bargain, while a higher price tends to decrease the demand.
Supply vs. Demand
- When supply is greater than demand, the merchant suffers. The merchant has a stockpile of merchandise that is not making any money for the business.
- When demand is greater than supply, the merchant also suffers. Customers are coming to buy an item that may be sold out, and an opportunity to make a sale is missed.
Equilibrium
- The merchant is best served when supply and demand are in equilibrium. Equilibrium occurs when the price is set so that the supply and demand equal each other. The item completely sells out, but no one who wants to purchase the item goes home without it.
Graphing Supply and Demand Against the Price
Once students have an idea of how the price of an item can affect sales, they have a context in which to understand the graphs offered on the following activity sheets.
Activity: Class Fundraiser: Having a transparency of Activity Sheet: Senior Class Buttons makes it easier for you to guide students into a discussion about supply and demand.
Students may not initially recognize what to do with 3 columns of data.
Question 1: Coach students to use the price column for x‑values and the 'supply' column for y‑values.
Question 2: Coach students to use the price column for x‑values and the demand column for y‑values.
Allow sufficient time for students to plot points and complete the graphs. If possible, check students' graphs. Students can work individually or in pairs to answer Questions 3–8. Point out that they have used 3 different ways to display and interpret the information given in this button example. The data were presented to them in a
table. They used the data to construct a
graph that allowed them to understand more about the problem. Then they wrote and solved a
system of equations that represented the same information in yet another form.
Activity: Game Cartridges and Silver Dollars: The 2 scenarios on this activity sheet can be assigned for homework or used as additional class activities.
After working through the button example from Activity Sheet 1 and the game cartridge example on Activity Sheet 2, students may get too comfortable with values that predict a straight line. Point out to students that this result rarely occurs in real-world situations.
The second problem on Activity Sheet 2, about silver dollars, is a good example of realistic data. Even though the supply-and-demand functions are not linear and no formulas are given to represent the functions, students can draw conclusions when they study and interpret the graphs. Point out to students that many times a line or a formula is used that is a good approximation based on the given data.
Answers
