ECON Lecture 1.3: Cost Benefit Analysis and the Science of Rationality

Foundations of Economic Cost-Benefit Analysis

• The goal of the current lecture, continuing from lecture 1.2, is to determine how a rational human being achieves an established goal.

• Under the assumption of rationality, human beings set specific goals and then employ systematic methods to reach them.

• The fundamental question addressed is the actual mechanism and logic used to achieve these goals.

The Rule for Rationality

• A specific rule governs rational behavior: A person is behaving rationally whenever the total economic surplus is maximized.

• Conversely, a person is behaving irrationally whenever the total economic surplus is not maximized.

• This principle is formally known as the Cost-Benefit Principle.

• To understand this principle, several core concepts must be defined:

  • Economic Surplus

  • Maximization

The Formula for Total Economic Surplus

• In order to maximize economic surplus, one must first understand how it is calculated.

• The formula for Total Economic Surplus is:     $\text{Total Economic Surplus} = \text{Total Benefits} - \text{Total Costs}$

• Total Benefits: Every goal involves some form of benefit. Whether the goal is enrolling in an online class, purchasing a BMW, or sailing on the coast, the individual must derive value or pleasure from it, or they would not pursue it.

• Total Costs: Most activities are not free and involve costs (scarcity).

  • Example: To go sailing, a person may need to pay someone (e.g., a student) $100\text{ dollars}$ to mow their grass. This $100\text{ dollars}$ is a cost of the goal.

• Surplus Evaluation:

  • If the benefit of sailing is greater than the cost of mowing the grass, the individual has a positive economic surplus.

  • If the benefit (e.g., $20\text{ utility points}$ of pleasure due to seasickness) is lower than the cost (e.g., $100\text{ dollars}$), the economic surplus becomes negative. In this case, the individual is not maximizing surplus and should not pursue the activity.

Rational Behavior and Incentives

• Whenever there is a change in either the cost or the benefit of an activity, it generates an Incentive to change behavior rationally.

• Incentive: Any motive force that causes a person to choose one thing over another.

• Case Study: The Sailing Example and the Seasickness Cure:

  • Original Scenario: An individual dislikes sailing because of seasickness. The benefit is valued at $20$, while the cost of getting away (mowing the grass) is $100$. The economic surplus is $-80$. Rational behavior is to stay home and mow the grass.

  • Modified Scenario: A cure for seasickness is introduced. This changes the benefit. The pleasure of sailing sky-rockets to $200$. The cost remains $100$.

  • New Economic Surplus: $200 - 100 = 100$.

  • Rational Response: The individual now pays the $100$ to have the grass mowed because the incentive structure has changed the rational outcome from staying home to going sailing.

• Incentives in Education:

  • Academic structures use incentive mechanisms to encourage behavior, such as watching lecture videos and PowerPoints.

  • Grades serve as the incentive. The fear of a bad grade (cost of inaction) versus the benefit of learning/passing (benefit) ensures that students choose to watch the material.

Marginal Analysis: Benefit and Cost

• To maximize total economic surplus properly, one must move beyond random amounts of surplus and find the optimal point using marginal analysis.

• Marginal Benefit ($MB$): The additional benefit accrued by consuming one more unit of a good.

• Marginal Cost ($MC$): The additional cost incurred by producing (or obtaining) one more unit of a good.

• Etymology of "Marginal": Think of the margin of a notebook page; it refers to the extra space on the edge. In economics, "marginal" always means "extra" or "additional."

The Law of Diminishing Marginal Benefit (Utility)

• Utility: The technical name for the benefit or pleasure gained from consuming a good.

• Definition: The Law of Diminishing Marginal Benefit states that as a person consumes more of a good, the total benefit increases, but the benefits of additional consumption increase at a decreasing rate.

• This law applies to everything according to economists, though food is a common illustrative example.

• Psychological Reality: The first unit of a good usually provides the highest satisfaction. As one becomes satiated, each subsequent unit provides less extra pleasure than the one before it.

Mathematical Illustration: Oyster Consumption (Benefit)

• Consider an individual named Susie/Amy eating oysters in the Florida Keys. The following table (hypothetical data) tracks her utility:

  • 0 Oysters: $TB = 0$; $MB = 0$

  • 1 Oyster: Total Benefit ($TB$) = $100$; Marginal Benefit ($MB$) = $100$

  • 2 Oysters: $TB = 180$; $MB = 180 - 100 = 80$

  • 3 Oysters: $TB = 245$; $MB = 245 - 180 = 65$

  • 7 Oysters: $TB = 360$; $MB = 5$ (Assuming previous $TB = 355$)

  • 8 Oysters: $TB = 361$; $MB = 1$

  • 9 Oysters: $TB = 361$; $MB = 0$ (Satiation Point)

  • 10 Oysters: $TB = 358$; $MB = -3$ (The result of sickness/over-consumption)

• The trend shows that while $TB$ generally rises, $MB$ declines throughout the process.

The Law of Increasing Marginal Cost

• Just as benefits diminish, the costs of obtaining extra units typically increase.

• Example: Diving for Oysters:

  • 1st Oyster: Knee-deep water. Easy to pick up. Low energy cost.

  • 2nd Oyster: Five feet deep. Requires submerging head. Moderate effort.

  • 3rd Oyster: Eight feet deep. Requires swimming out and diving. High energy cost.

  • 10th Oyster: Deep water (e.g., $15\text{ feet}$). Requires significant swimming and diving effort.

• This results in the Law of Increasing Marginal Costs: the more units you obtain, the higher the additional cost for each subsequent unit.

Mathematical Illustration: Oyster Collection (Cost)

• Tracking the effort/utility points sacrificed to get oysters:

  • 0 Oysters: Total Cost ($TC$) = $0$; Marginal Cost ($MC$) = $0$

  • 1 Oyster: $TC = 5$; $MC = 5$ (Knee-deep)

  • 2 Oysters: $TC = 15$; $MC = 15 - 5 = 10$ (Neck-deep)

  • 3 Oysters: $TC = 30$; $MC = 30 - 15 = 15$ (8-foot dive)

  • 5 Oysters: $TC = 49$ (Total cost context for comparison)

  • 6 Oysters: $TC = 69$; $MC = 69 - 49 = 20$

  • 7 Oysters: $MC = 40$

  • 10 Oysters: $TC = 380$; $MC = 80$ (Sacrificing $80\text{ units}$ of energy for the last oyster)

Synthesizing Cost-Benefit for Optimal Decision Making

• To find the rational number of oysters to consume, we compare the marginal values and calculate Total Economic Surplus at every level.

• The Rational Decision Rule: Maximize economic surplus by reaching the point where Marginal Benefit equals Marginal Cost ($MB = MC$).

• Analysis of Amy/Susie's Choice:

  • At 6 Oysters:

    • The marginal benefit of the 6th oyster is $20$.

    • The marginal cost of the 6th oyster is $20$.

    • The total economic surplus at this point is $355 - 69 = 286$. (Actually, using the lecture's provided math: $TB$ of 6 oysters is $355$, cost is $69$, surplus is $286$).

  • The 7th Oyster Problem:

    • $MB = 5$

    • $MC = 40$

    • Rational choice: Because the cost of getting the 7th oyster ($40$) is much higher than the pleasure it provides ($5$), it is irrational to consume it. Doing so would decrease the total economic surplus.

  • The 10th Oyster Problem:

    • $MB = -4$

    • $MC = 70$

    • Rational choice: It is highly irrational to spend $70\text{ units}$ of energy to achieve a negative benefit ($-4$).

Conclusion: Economics as the Science of Rational Behavior

• The principle of maximizing total economic surplus where $MB = MC$ applies to all activities, trivial or significant (e.g., from hunting oysters to going to medical school).

• Economics is effectively the science of rational human behavior, analyzing how individuals maximize their benefits in a world of costs.

• Future topics in Chapter 2 will delve further into these foundations in greater detail.