Economists use the term opportunity cost to indicate what one must give up to obtain what he or she desires. The idea behind opportunity cost is that the cost of one item is the lost opportunity to do or consume something else. In short, opportunity cost is the value of the next best alternative. For Alphonso, the opportunity cost of a burger is the four bus tickets he would have to give up. He would decide whether or not to choose the burger depending on whether the value of the burger exceeds the value of the forgone alternative—in this case, bus tickets. Since people must choose, they inevitably face tradeoffs in which they have to give up things they desire to obtain other things they desire more.

View this website for an example of opportunity cost—paying someone else to wait in line for you.

A fundamental principle of economics is that every choice has an opportunity cost. If you sleep through your economics class, the opportunity cost is the learning you miss from not attending class. If you spend your income on video games, you cannot spend it on movies. If you choose to marry one person, you give up the opportunity to marry anyone else. In short, opportunity cost is all around us and part of human existence.

The following Work It Out feature shows a step-by-step analysis of a budget constraint calculation. Read through it to understand another important concept—slope—that we further explain in the appendix The Use of Mathematics in Principles of Economics.

## Understanding Budget Constraints

Budget constraints are easy to understand if you apply a little math. The appendix The Use of Mathematics in Principles of Economics explains all the math you are likely to need in this book. Therefore, if math is not your strength, you might want to take a look at the appendix.

Step 1: The equation for any budget constraint is:

$\text{Budget}={\text{P}}_{1}{\text{\xd7Q}}_{1}{\text{+P}}_{2\phantom{\rule{0ex}{0ex}}}{\text{\xd7Q}}_{2}$
where P and Q are the price and quantity of items purchased (which we assume here to be two items) and Budget is the amount of income one has to spend.

Step 2. Apply the budget constraint equation to the scenario. In Alphonso’s case, this works out to be:

$\begin{array}{ccc}\text{Budget}& =& {\text{P}}_{1}{\text{\xd7 Q}}_{1}{\text{+ P}}_{2\phantom{\rule{0ex}{0ex}}}{\text{\xd7 Q}}_{2}\\ \text{\$10budget}& =& \text{\$2perburger\xd7quantityofburgers+\$0.50perbusticket\xd7quantityofbustickets}\\ \text{\$10}& =& {\text{\$2\xd7Q}}_{\text{burgers}}{\text{+\$0.50\xd7Q}}_{\text{bustickets}}\end{array}$
Step 3. Using a little algebra, we can turn this into the familiar equation of a line:

$\begin{array}{ccc}\text{y}& \text{=}& \text{b+mx}\end{array}$
For Alphonso, this is:

$\begin{array}{ccc}\text{\$10}& \text{=}& {\text{\$2\xd7Q}}_{\text{burgers}}\text{+}\text{\$0.50}\text{\xd7}{\text{Q}}_{\text{bustickets}}\end{array}$
Step 4. Simplify the equation. Begin by multiplying both sides of the equation by 2:

$\begin{array}{ccc}\text{2\xd710}& \text{=}& {\text{2\xd72\xd7Q}}_{\text{burgers}}{\text{+2\xd70.5\xd7Q}}_{\text{bustickets}}\\ \text{20}& \text{=}& {\text{4\xd7Q}}_{\text{burgers}}{\text{+1\xd7Q}}_{\text{bustickets}}\end{array}$
Step 5. Subtract one bus ticket from both sides:

$\begin{array}{ccc}{\text{20 \u2013 Q}}_{\text{bus tickets}}& \text{=}& {\text{4 \xd7 Q}}_{\text{burgers}}\end{array}$
Divide each side by 4 to yield the answer:

$\begin{array}{ccc}{\text{5 \u2013 0.25 \xd7 Q}}_{\text{bus tickets}}& \text{=}& {\text{Q}}_{\text{burgers}}\\ & \text{or}& \\ {\text{Q}}_{\text{burgers}}& \text{=}& {\text{5 \u2013 0.25 \xd7 Q}}_{\text{bus tickets}}\end{array}$
Step 6. Notice that this equation fits the budget constraint in Figure. The vertical intercept is 5 and the slope is –0.25, just as the equation says. If you plug 20 bus tickets into the equation, you get 0 burgers. If you plug other numbers of bus tickets into the equation, you get the results (see Table), which are the points on Alphonso’s budget constraint.

Point |
Quantity of Burgers (at $2) |
Quantity of Bus Tickets (at 50 cents) |

A |
5 |
0 |

B |
4 |
4 |

C |
3 |
8 |

D |
2 |
12 |

E |
1 |
16 |

F |
0 |
20 |

Step 7. Notice that the slope of a budget constraint always shows the opportunity cost of the good which is on the horizontal axis. For Alphonso, the slope is −0.25, indicating that for every bus ticket he buys, he must give up 1/4 burger. To phrase it differently, for every four tickets he buys, Alphonso must give up 1 burger.

There are two important observations here. First, the algebraic sign of the slope is negative, which means that the only way to get more of one good is to give up some of the other. Second, we define the slope as the price of bus tickets (whatever is on the horizontal axis in the graph) divided by the price of burgers (whatever is on the vertical axis), in this case $0.50/$2 = 0.25. If you want to determine the opportunity cost quickly, just divide the two prices.