Opportunity Cost and Sunk Costs — Study Notes

Definition of Opportunity Cost

• Opportunity cost is what you give up when you make a choice: the value of the next best alternative that you forego.
• Formal idea: Let A be the set of feasible alternatives and V(a) be the value/benefit of alternative a. If you choose i ∈ A, your opportunity cost is the value of the best forgone alternative a^* where
  $a^* = \arg\max<em>{a \in A \setminus {i}} V(a)$ and $OC</em>i = V(a^*).$
• Key points:
  • OC can be positive, zero, or even change if alternatives’ values change.
  • Opportunity cost is about time, resources, and forgone benefits, not just money spent.
  • It helps explain trade-offs in decisions when resources are scarce.

Direct costs vs. opportunity costs

• Direct (out-of-pocket) costs are dollars paid (tuition, room, board, etc.).
• Opportunity cost is the foregone benefit of the next best alternative due to choosing a particular option.

Examples of opportunity cost

• College decision (illustrative values):
  • Direct costs: tuition, room and board, etc.
  • Opportunity cost: the earnings forgone by not working during college. If you could earn $30{,}000$ per year by working instead of attending college, then the opportunity cost includes the forgone $30{,}000$ per year in addition to direct costs.
  • Note: changes in this forgone earning potential alter the overall cost-benefit comparison even if direct costs stay the same.
• Singer scenario (varying opportunity costs):
  • If you could earn $5{,}000{,}000$ per year by performing instead of going to college, the opportunity cost of attending college rises dramatically, possibly changing the decision.
• Free promo donuts/burgers (perceived “free” but not actually free):
  • A free-taco promotion with a long line has an opportunity cost: time you could have spent doing something else (e.g., hanging out with friends) or earning wages (e.g., $10/hour).</li> <li>Therefore, the Taco isn’t truly free when you account for the value of the time spent waiting.</li></ul></li> <li>Trade-offs due to scarcity: decisions involve choosing among limited options, e.g., waiting for free food, investing in a factory, or setting education policy.</li> </ul> <h3 id="nextbestalternativeandtheallincost">Next-best alternative and the all-in cost</h3> <ul> <li>The “all-in cost” includes: direct costs, opportunity costs, and any negative feelings or psychological costs from the choice (e.g., feeling bad for missing a friend’s party).</li> <li>Revealed preference concept: if you choose the party over the movie and studying, the revealed preference is that the party’s benefits outweighed both the movie and studying, given your stated choices.</li> <li>Example with party, movie, and studying:<ul> <li>If top choice is the party, then next is the movie, then studying. If you choose the party, your opportunity cost is the movie, not both the movie and studying.</li></ul></li> <li>Takeaway: these trade-offs reflect the costs and benefits you actually value in a scarce environment.</li> </ul> <h3 id="sunkcostsdefinitionandimplications">Sunk costs: definition and implications</h3> <ul> <li>A sunk cost is a cost that has already been paid and cannot be recovered.<ul> <li>Example: buying three breakfast tacos because you’re hungry, but stopping after two — the third taco is a sunk cost.</li></ul></li> <li>Rational behavior: ignore sunk costs in future decisions because the money is already spent and cannot be recovered.</li> <li>Common pitfalls (sunk-cost fallacy): letting past expenditures influence ongoing decisions even when they should not.</li> <li>Car repair example:<ul> <li>You spent$3{,}000$on repairs last month; today you learn you need another$2{,}000$.</li> <li>Some might think you should keep repairing to avoid wasting the$3{,}000$already spent.</li> <li>The correct decision: the$3{,}000$is sunk; the new decision should be based on whether spending$2{,}000$today yields a better outcome, regardless of the earlier spend.</li></ul></li> <li>Business implication: firms often pour more resources into failing projects ("good money after bad") because of prior investment.</li> <li>Extreme example: staying in a bad relationship due to long investment in time and emotions.</li> <li>Decision rule: ignore sunk costs when deciding what to do next.</li> </ul> <h3 id="practicalimplicationsandtakeaways">Practical implications and takeaways</h3> <ul> <li>Use opportunity cost to compare options: always consider what you give up when choosing one path over another.</li> <li>Remember that time, feelings, and other non-monetary factors can have opportunity costs that are as real as monetary costs.</li> <li>Be wary of the sunk-cost fallacy: do not let past expenditures dictate future decisions.</li> <li>When evaluating policies or business decisions, include next-best alternatives and potential forgone benefits to obtain a true cost/benefit picture.</li> </ul> <h3 id="summaryofkeypoints">Summary of key points</h3> <ul> <li>Opportunity cost = value of the next best alternative forgone when a choice is made.</li> <li>The formal expression: if you choose i, then<br />$OCi = V(a^), \quad a^ = \arg\max{a \in A \setminus {i}} V(a).$$
  • Direct costs are not enough to assess a choice; ignore sunk costs in future decision-making.
  • All-in cost = direct costs + opportunity costs + any non-monetary costs (e.g., negative feelings).
  • Sunk costs should not influence future decisions, but people often fall prey to the sunk-cost fallacy (e.g., continuing a bad project or relationship).
  • Real-world relevance: personal finance, education decisions, marketing promos, corporate strategy, and public policy all hinge on correct consideration of opportunity and sunk costs.