2.1 Budget Constraint and Opportunity Cost - Vocabulary
Budget Constraint and Opportunity Sets
Core idea: Consumers have a limited income to spend on goods; the budget constraint shows all affordable combinations of two goods given their prices and income. The slope reflects the relative prices of the two goods.
Alphonso’s example:
Alphonso has a budget of 10. The price of a burger (P_burger) is 2, and the price of a bus ticket (P_bus) is 0.50. The budget constraint can be generally expressed as: \text{Budget} = P_1 Q_1 + P_2 Q_2
For Alphonso, this means: 10 = 2 \times Q_burger + 0.5 \times Q_bus
The budget constraint for the Alphonso scenario is all combinations of burgers and bus tickets that cost exactly 10. Points between A and F (on the budget frontier) are affordable; points outside cost more than 10. The budget frontier connects point A: (0 bus tickets, 5 burgers) and point F: (20 bus tickets, 0 burgers).
If Alphonso is at point D (12 bus tickets and 2 burgers), the true cost of one more burger is the number of bus tickets given up to stay within budget: here, 4 bus tickets (since each burger costs 2, adding two burgers would require giving up 4 worth of bus tickets, equivalent to 4 bus tickets).
Example points on the frontier (from burgers to bus tickets):
A: (Q_burger, Q_bus) = (5, 0)
B: (4, 4)
C: (3, 8)
D: (2, 12)
E: (1, 16)
F: (0, 20)
The slope of the budget constraint indicates the opportunity cost. For Alphonso, the slope is -0.25, meaning that for every 1 bus ticket gained, Alphonso must give up 1/4 of a burger. Equivalently, for every 4 bus tickets bought, 1 burger must be given up.
Opportunity cost concept:
Opportunity cost = the value of the next best alternative forgone to obtain something. For Alphonso, the opportunity cost of a burger is the four bus tickets he would have to give up.
In general, opportunity cost is the value of what you give up to obtain something; sometimes, the price in dollars doesn’t capture the full opportunity cost, especially when time is involved.
Link to real-world cost concepts:
Time costs can dominate monetary costs in some decisions (e.g., airline security). For example, if security improvements cost various amounts (e.g., sky marshals 3 \text{ Billion/year}, reinforced doors 450 \text{ Million}, scanners 2 \text{ Billion}) but waiting time has a value (e.g., 895.5M passengers in 2015; if average delay adds 0.5 hours per trip and time is valued at 20/\text{hour}, opportunity costs from waiting could be as high as 800 \text{ million} \times 0.5 \text{ hours} \times 20/\text{hour} = \text{about } 8 \text{ billion/year}).
The point: waiting time can have an opportunity cost comparable to, or larger than, monetary costs.
Example: If you buy lunch for 8 every day but could bring lunch for 3, the daily opportunity cost is 8-3 = 5, which adds up to 250 \text{ days} \times 5 = 1250 per year; reframing this as “a nice vacation” can change choices.
Marginal decision-making and diminishing marginal utility:
Marginal analysis focuses on the benefits and costs of a little more or a little less of a good (change analysis), not just total costs and benefits.
Utility is the satisfaction from goods; with more of a good, total utility rises, but marginal utility (the utility of the next unit) tends to decline: this is the law of diminishing marginal utility.
As Alphonso moves down the budget constraint (more bus tickets, fewer burgers), the marginal utility of bus tickets decreases while the marginal utility of foregone burgers increases. A rational consumer purchases until the marginal utility gain from one more unit equals the marginal cost (opportunity cost).
In practice, a rational choice occurs when the marginal utility per dollar spent is balanced across goods (e.g., \text{MU_burger} / \text{P_burger} \approx \text{MU_bus} / \text{P_bus} at the optimum). If the marginal utility gained from bus tickets falls below the marginal utility lost from giving up burgers, a consumer will stop increasing bus tickets.
Sunk costs:
Sunk costs are past, irrecoverable costs and should not affect current decisions.
Example: Selena pays 8 to see a movie but, after 30 minutes, realizes the movie is terrible. The decision should be based on future costs and benefits (the remaining 90 minutes of time and what else she could do), not the sunk 8 paid for the ticket.
Firms also struggle with sunk costs (e.g., investing in a poorly performing product) but the lesson remains: ignore sunk costs in decision-making and focus on future marginal costs/benefits.
From two goods to many goods:
The two-good budget constraint model is a simplification. In reality, a budget contains many goods. You can extend to many goods by considering a generalized budget constraint: \sum_i P_i Q_i = \text{Budget} where P_i and Q_i are the price and quantity of each good, i.
This extension preserves the core principle: every choice has an opportunity cost and is constrained by the budget.
Summary takeaway:
The budget constraint illustrates the tradeoffs and opportunity costs inherent in scarcity.
Rational choice involves marginal analysis and considering the costs and benefits of small adjustments along (or inside) the constraint.