## The Concept of Opportunity Cost

Economists use the term **opportunity cost** to indicate what must be given up to obtain something that is desired. 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 get other things they desire more.

**Note: **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 (not recommended, by the way), 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 section shows a step-by-step analysis of a budget constraint calculation. Read through it to understand another important concept—slope—that is further explained in a section from the previous tutorial on The Use of Mathematics in Principles of Economics.

### Understanding Budget Constraints

Budget constraints are easy to understand if you apply a little math. The section on The Use of Mathematics in Principles of Economics explains all the math you are likely to need in these Economics tutorials. So 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:

\(\text{Budget}={\text{P}}_{1}{\text{× Q}}_{1}{\text{+ P}}_{2\;}{\text{× Q}}_{2}\)

where P and Q are the price and quantity of items purchased 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:

\(\begin{array}{rcl}\text{Budget}& =& {\text{P}}_{1}{\text{× Q}}_{1}{\text{+ P}}_{2\;}{\text{× Q}}_{2}\\ \text{\$10 budget}& =& \text{\$2 per burger × quantity of burgers + \$0.50 per bus ticket × quantity of bus tickets}\\ \text{\$10}& =& {\text{\$2 × Q}}_{\text{burgers}}{\text{+ \$0.50 × Q}}_{\text{bus tickets}}\end{array}\)

Step 3. Using a little algebra, we can turn this into the familiar equation of a line:

\(\begin{array}{rcc}\text{y}& \text{=}& \text{b + mx}\end{array}\)

For Alphonso, this is:

\(\begin{array}{rcl}\text{\$10}& \text{=}& {\text{\$2 × Q}}_{\text{burgers}}\text{+}\text{\$0.50}\text{×}{\text{Q}}_{\text{bus tickets}}\end{array}\)

Step 4. Simplify the equation. Begin by multiplying both sides of the equation by 2:

\(\begin{array}{rcl}\text{2 × 10}& \text{=}& {\text{2 × 2 × Q}}_{\text{burgers}}{\text{+ 2 × 0.5 × Q}}_{\text{bus tickets}}\\ \text{20}& \text{=}& {\text{4 × Q}}_{\text{burgers}}{\text{+ 1 × Q}}_{\text{bus tickets}}\end{array}\)

Step 5. Subtract one bus ticket from both sides:

\(\begin{array}{rcl}{\text{20 – Q}}_{\text{bus tickets}}& \text{=}& {\text{4 × Q}}_{\text{burgers}}\end{array}\)

Divide each side by 4 to yield the answer:

\(\begin{array}{rcl}{\text{5 – 0.25 × Q}}_{\text{bus tickets}}& \text{=}& {\text{Q}}_{\text{burgers}}\\ & \text{or}& \\ {\text{Q}}_{\text{burgers}}& \text{=}& {\text{5 – 0.25 × Q}}_{\text{bus tickets}}\end{array}\)

Step 6. Notice that this equation fits the budget constraint in this 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 shown in this 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 four bus 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, the slope is defined 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. So if you want to determine the opportunity cost quickly, just divide the two prices.

## Self-Check Question

Suppose Alphonso’s town raised the price of bus tickets to $1 per trip (while the price of burgers stayed at $2 and his budget remained $10 per week.) Draw Alphonso’s new budget constraint. What happens to the opportunity cost of bus tickets?

### Solution

The opportunity cost of bus tickets is the number of burgers that must be given up to obtain one more bus ticket. Originally, when the price of bus tickets was 50 cents per trip, this opportunity cost was 0.50/2 = .25 burgers. The reason for this is that at the original prices, one burger ($2) costs the same as four bus tickets ($0.50), so the opportunity cost of a burger is four bus tickets, and the opportunity cost of a bus ticket is .25 (the inverse of the opportunity cost of a burger). With the new, higher price of bus tickets, the opportunity cost rises to $1/$2 or 0.50. You can see this graphically since the slope of the new budget constraint is flatter than the original one. If Alphonso spends all of his budget on burgers, the higher price of bus tickets has no impact so the horizontal intercept of the budget constraint is the same. If he spends all of his budget on bus tickets, he can now afford only half as many, so the vertical intercept is half as much. In short, the budget constraint rotates clockwise around the horizontal intercept, flattening as it goes and the opportunity cost of bus tickets increases.

## Critical Thinking Question

Suppose Alphonso’s town raises the price of bus tickets from $0.50 to $1 and the price of burgers rises from $2 to $4. Why is the opportunity cost of bus tickets unchanged? Suppose Alphonso’s weekly spending money increases from $10 to $20. How is his budget constraint affected from all three changes? Explain.