Chapter 2 Part 1a Notes: (Budget Constraint, Opportunity Cost, Marginal Analysis, Sunk Costs)

Budget Constraint and Opportunity Set

• Budget constraint: shows what you can consume given income and prices for items; it’s the interaction of income and prices that limits consumption.
• Opportunity set: all bundles you can afford to purchase.
• Graphical setup (initial numbers): vertical axis = hamburgers; horizontal axis = bus tickets.
• Given income $I = 10, price of burgers $p{burger} = 2, price of tickets $p{ticket} = 0.5$:
  • Maximum hamburgers if you buy only burgers: $Q<em>{B}^{max} = \frac{I}{p</em>{burger}} = \frac{10}{2} = 5.$
  • Maximum tickets if you buy only tickets: $Q<em>{T}^{max} = \frac{I}{p</em>{ticket}} = \frac{10}{0.5} = 20.$
  • Any bundle on the straight budget line between these endpoints is affordable (e.g., bundle C with 8 tickets costs $8 \times 0.5 = 4$; remaining $6 allows 3 hamburgers at $2 each).
• Intercepts and the budget line:
  • Endpoints on the budget line reflect the two extreme affordable bundles.
  • The budget line connects (QT, QB) endpoints: (20, 0) and (0, 5) in this setup.
• Starting point and a small extension:
  • If we start from the original setup with vertical axis hamburgers and horizontal axis tickets, an intercept line might be drawn showing that the hamburger intercept is 5 and the ticket intercept is 20 (given I = 10).
  • You can deduce prices from the endpoints: if you spend all income on burgers to buy 5 burgers, then the price per burger is $p<em>{burger} = \frac{I}{Q</em>{B}} = \frac{10}{5} = 2.$
  • If you spend all income on tickets to buy 20 tickets, then the price per ticket is $p<em>{ticket} = \frac{I}{Q</em>{T}} = \frac{10}{20} = 0.5.$
• With higher income (parallel shift): income doubles to $I = 20$ while prices stay the same ($p{burger} = 2$, $p{ticket} = 0.5$).
  • New endpoints: hamburgers max = $\frac{I}{p<em>{burger}} = \frac{20}{2} = 10$; tickets max = $\frac{I}{p</em>{ticket}} = \frac{20}{0.5} = 40$.
  • The budget line shifts outward in a parallel fashion (slope unchanged) because prices stayed the same; the entire opportunity set expands.
  • Intuition: more income means you can afford more of both goods; the slope of the line is unchanged because it is determined by the price ratio (not income).
• Effect of price changes (holding income constant at $I = 10$): price of burgers falls from $2 to $1, while ticket price stays $0.50.
  • Original intercepts: maximum tickets = 20; maximum burgers = 5 (when spending all income on each good respectively).
  • New burger price $p{burger} = 1$ gives new burger intercept: $Q</em>{B}^{max} = \frac{I}{p_{burger}} = \frac{10}{1} = 10.$
  • Ticket intercept remains $Q_{T}^{max} = 20.$
  • The budget line rotates: new slope $-\frac{p<em>{burger}}{p</em>{ticket}} = -\frac{1}{0.5} = -2$ (flatter than before, which was $-\frac{2}{0.5} = -4$).
  • Result: the consumption set expands, allowing more hamburgers and potentially more tickets along the line.
• Key takeaway: increased income and lower prices expand the consumption opportunity set; price changes alter the slope and feasible combinations along the budget line.

Opportunity Cost

• Definition: the opportunity cost of a choice is the value of the next best alternative forgone.
• In this simple two-good example, the trade-off is captured by the slope of the budget line; the opportunity cost of one more burger is how many bus tickets you must give up.
• Quantitative example: with burgers at $p<em>{burger} = 2$ and tickets at $p</em>{ticket} = 0.5$, buying one more burger costs $2 = 4 \times 0.5$ in tickets, so the opportunity cost of one more burger is 4 bus tickets.
• The trade-off holds along the entire budget line because prices are constant; moving along the line keeps the relative costs unchanged.
• Opportunity cost includes explicit and implicit costs:
  • Explicit cost: direct monetary payments (e.g., buying a bicycle for $300).
  • Implicit cost: non-monetary sacrifices (e.g., time spent; foregone earnings).
• College example (explicit + implicit costs):
  • Suppose explicit cost of a full year of college is $C_{explicit} = 15{,}000$.
  • Suppose a high school graduate could otherwise work and earn $W = 20{,}000$ per year (foregone earnings) if they did not attend college.
  • If the student cannot work while in college, the opportunity cost of one year of college is:
  • $OC = C_{explicit} + W = 15{,}000 + 20{,}000 = 35{,}000.$
  • If the booming HS job market offers $W = 60{,}000$ instead, the opportunity cost would be:
  • $OC = 15{,}000 + 60{,}000 = 75{,}000.$
• Economic intuition:
  • Higher opportunity costs reduce the quantity demanded of the item (e.g., college enrollment falls when the forgone earnings rise).
  • Conversely, lower opportunity costs increase enrollment.
  • Enrollment tends to be counter-cyclical: in strong economies, high school grads earn more, so more choose not to attend college; in weaker economies, more enroll in college to avoid low wage jobs.
• Slide reference: consider the point about opportunity costs and the impact of relative earnings on decisions.

Marginal Analysis, Utility, and Opportunity Cost

• Marginal (definition): the change in total resulting from a small change in quantity of a good or action.
• Utility: usefulness or satisfaction from consuming goods; a proxy for well-being or happiness from consumption.
• Marginal Benefit (MB): the change in total benefit from doing one more unit of an action.
• Marginal Cost (MC): the change in total cost from doing one more unit of an action.
• Decision rule (marginal analysis):
  • If MB > MC, do one more unit of the activity.
  • If MB < MC, do fewer units.
  • If MB ≈ MC, you are at or near the optimum.
• If MB > MC, you gain by taking the next step; if MC > MB, you should back off.
• If you overshoot (MC > MB), dial back; if you undershoot (MB > MC), do more.
• Key idea: optimality occurs where MB ≈ MC.
• Worked mindset: when comparing MB and MC, consider only incremental costs and benefits of the next unit, not the sunk past costs.

Example: Hiring Workers (Marginal Cost and Marginal Benefit)

• Setup: firm can hire workers at a daily wage (or cost) of $200 per worker.
  • Marginal Cost (MC) of the first worker is $200; similarly, the MC of the tenth worker is also $200.
• Total cost example:
  • 1 worker: total cost = $200$.
  • 10 workers: total cost = $200 \times 10 = 2{,}000$.
  • 11 workers: total cost = $2{,}000 + 200 = 2{,}200$.
• Marginal Benefit (MB) example (revenue-based):
  • Suppose revenue with 10 workers is $2{,}400$.
  • With 11 workers, revenue becomes $2{,}700$.
  • MB of the 11th worker = $2{,}700 - 2{,}400 = 300.$
• Decision: since MB (300) > MC (200), hire the 11th worker.
• Profit comparison:
  • 10 workers: profit = revenue − cost = $2{,}400 - 2{,}000 = 400.$
  • 11 workers: profit = $2{,}700 - 2{,}200 = 500.$
  • Incremental profit from the 11th worker = $500 - 400 = 100.$
  • This confirms MB exceeds MC and adds profit.
• Important caveat: the MB example is a simplified (marginal) view; real decisions could have varying MBs and MCs across levels.
• Note: marginal analysis helps decide optimal staffing; profits can still hinge on market conditions and nonlinear MB curves.

Sunk Costs

• Definition: sunk costs are past expenditures that cannot be recovered; they should not affect current decision making.
• Common intuition trap: let sunk costs influence present choices, which leads to suboptimal decisions.
• Football analogy (Belichick anecdote): treating past performance contracts as sunk costs; instead, focus on marginal benefits of future contracts.
• Another sunk-cost example (machinery):
  • A machine breaks; if unrepaired, its value is 0.
  • If repaired, its value could be $20{,}000; estimated repair cost is $15{,}000.
  • Initial thought: fix if marginal benefit (MB) > marginal cost (MC).
  • If during repair you realize you need an additional $8{,}000 to finish and total repair would cost $23{,}000, while the finished value is $20{,}000, you should compare the incremental MB and MC from this point forward.
  • At the decision point to finish, the incremental cost is $8{,}000 and the incremental benefit (from finishing) is $20{,}000, so finishing yields a net gain of $12{,}000.$ Therefore, from this forward-looking perspective, completing the repair is justified.
  • The trap would be to subtract the sunk $15{,}000 already spent; a prudent decision maker ignores that sunk cost and focuses on future MB and MC.
• The transcript ends mid-discussion: the final sentence is cut off, but the intended takeaway is to ignore sunk costs and evaluate future costs/benefits.

Practical implications and takeaways

• Always identify budget constraints and the opportunity set when making consumption or production choices.
• Use the budget line to understand trade-offs; the slope reveals the marginal rate of transformation between goods.
• Consider both explicit and implicit costs when evaluating choices (e.g., college example).
• Apply marginal thinking to decide whether to increase or decrease consumption or production by one more unit.
• Distinguish between sunk costs and forward-looking costs/benefits; do not let past expenditures distort current decisions.
• Recognize how changes in income and prices shift or rotate the budget constraint and alter the feasible set of choices.
• Real-world relevance: opportunity costs and marginal analysis underlie personal finance, career decisions, and firm management; they help explain consumer behavior and labor hiring decisions.

// End of the transcript materials for Chapter 2 (note: the last portion about the sunk-cost example ends mid-sentence in the provided transcript).