Content
Introduction and Course Context
This lecture marks the beginning of a deeper exploration into the theoretical foundations that underpin environmental economics. The material covered today builds directly on the individual utility theory discussed in previous sessions, which serves as the essential groundwork for all subsequent analysis in environmental economics, particularly when we eventually address complex questions such as placing monetary values on biodiversity and ecosystem services.
Before diving into the substantive content, several administrative matters deserve attention. The course website has been updated to reflect the current lecture topic, which has been renamed “Surplus and Welfare in Equilibrium, or Why Economists Think They Are Good” as part of ongoing refinements to the course materials. Students should have reviewed Chapter 2 in the textbook, which represents the first assigned reading from the text because this chapter provides particularly strong coverage of the relevant concepts.
Assignments and Assessment in the AI Era
The weekly questions assignment has been extended from its usual Monday deadline to Wednesday, owing to the instructor’s delayed posting. This accommodation reflects a commitment to fairness when assignment timelines are not met as planned. Assignment 1 will be posted following this class session.
The structure of assignments versus weekly questions represents a pedagogical innovation designed to address the challenges posed by artificial intelligence tools in education. In previous iterations of similar courses, frequent quizzes served as the primary assessment mechanism, but this approach has significant drawbacks. The preference now is for more hands-on, interactive, in-class exercises that build engagement and intuition. However, the reality remains that certain content requires mastery that can only be verified through answering questions, and in the era of ChatGPT, take-home exercises have become problematic because students can simply screenshot problems and receive immediate solutions.
The goal of this course is not to train students in the rapid deployment of chatbots, but rather to build genuine economic intuition. To address this tension, a new assessment structure has been developed. Assignments will be given to complete at home using whatever methods students prefer, including AI tools if they so choose. However, on the day each assignment is due, there will be a mini-quiz administered in class. This quiz will be nearly identical to the homework assignment but with different numerical values. Students who completed the assignment thoughtfully and independently will find the quiz straightforward, while those who relied entirely on AI assistance may struggle with the slightly modified problems.
This approach reflects the broader challenges facing educators as AI becomes increasingly capable. In a writing-intensive course designated with the “W” suffix that satisfies graduation requirements, the very nature of writing is undergoing transformation. The questions facing instructors are no longer simply about assessing student writing or teaching writing skills, but about the fundamental question of what writing even means when AI tools are readily available. Some instructors have adopted policies prohibiting AI use entirely, though such policies were once even codified as potential academic dishonesty by universities. The perspective taken here embraces AI as a tool, recognizing that professionals routinely use these technologies to accelerate their research and programming work. One writing assignment in this course will actually require students to use a large language model, reflecting this embrace of evolving technology.
The difficulty with treating AI use as cheating lies partly in the impossibility of detection. The only reliable indicator of AI assistance is when a previously weak writer suddenly produces polished prose, but accusing students of being “too good” is hardly a fair standard for identifying misconduct.
Surplus and Welfare: Foundational Concepts
The Economic Definition of Well-Being
Economists refer to well-being in a very specific and precisely defined way through the concept of surplus. The particular appeal of focusing on surplus is that free markets, when left to operate without intervention, maximize the combined total of consumer and producer surplus. This observation connects to the core ethical theory underlying the microeconomic tools employed throughout economics.
The ethical framework embedded in this approach can be characterized as utilitarianism on mathematical steroids. When classical utilitarian philosophers John Stuart Mill and Jeremy Bentham developed their theories of utility, they contemplated how utility might be aggregated or measured through specific indicators. However, it was not until later economists, including Adam Smith and his successors, that a rigorous mathematical formalization emerged. The result resembles utilitarianism but departs from it significantly through its highly quantitative specification.
Consumer Surplus Defined
Consumer surplus represents the gap between what consumers would have been willing to pay for a good and what they actually paid at the market price. This definition introduces a crucial concept that will recur throughout environmental economics: willingness to pay, often abbreviated as WTP. Willingness to pay becomes central when attempting to assign dollar values to environmental goods and services that lack traditional markets.
In graphical terms, the standard supply and demand diagram represents the behavior of many different consumers across an entire market. Some consumers have very high willingness to pay and would have purchased the good even at prices far above the equilibrium level. Yet in a competitive market, these high-valuation consumers pay only the equilibrium price, just like everyone else. Every consumer purchasing at quantities up to the equilibrium point receives more value than they surrender in payment. This excess value is literally surplus, and it accumulates as the triangular area between the demand curve and the equilibrium price line.
Producer Surplus Defined
Producer surplus operates analogously but from the sellers’ perspective. It represents the gap between what producers actually receive for their goods and the minimum amount they would have accepted to supply those goods. The terminology differs slightly from consumer surplus: rather than willingness to pay, the relevant concept is the minimum acceptable payment.
The difference in framing arises because for producers, the actual price received is the higher value, while the minimum acceptable payment forms the lower bound. This minimum acceptable payment derives from marginal costs of production. Any producer who can sell at a price exceeding their marginal costs receives surplus value from the transaction, which represents the fundamental condition for profitable business operation.
Mathematical Calculation of Surplus
The mathematics of surplus calculation builds on simple geometry when supply and demand curves are linear. Given an equilibrium with price equal to 5 and quantity equal to 10, and assuming additional information about the demand curve’s intercept, the consumer surplus equals the area of the triangle above the equilibrium price and below the demand curve. Using the standard triangle area formula of one-half times base times height, with a height of 4 (calculated as 9 minus 5) and a base of 10, the consumer surplus equals 20.
Producer surplus follows the identical geometric approach, representing the triangle below the equilibrium price and above the supply curve. In the symmetric example where the supply curve intercept yields a height of 4 (calculated as 5 minus 1) and the same base of 10, producer surplus also equals 20.
The Welfare Theorems of Economics
Why Economists Love Equilibrium
Economists display a notable enthusiasm for the concept of equilibrium, which warrants explanation. One relatively uncontroversial reason is that equilibrium provides predictive power. The belief that economic systems exhibit strong tendencies to return to equilibrium states allows analysts to make predictions. When observing changes in market conditions and understanding what the new equilibrium should be, investors and business decision-makers can profitably apply this knowledge.
But economists go further than merely finding equilibrium useful for prediction. They argue that equilibrium is good in a moral sense, with the emphasis on “good” as a value judgment. This moral claim rests on the mathematical utilitarianism embedded in welfare economics and finds its formal expression in the welfare theorems.
Physics Envy and Mathematical Rigor
Economists are sometimes characterized as suffering from physics envy, meaning they aspire to describe economic phenomena with the precision that physicists bring to natural phenomena. The welfare theorems exemplify this aspiration toward mathematical rigor. In first-year PhD economics courses, nearly every qualifying examination requires students to prove the first and second welfare theorems, testing their command of real analysis and advanced mathematics. While this lecture will not reproduce those proofs, understanding what these theorems assert and imply remains essential.
The First Welfare Theorem
The first welfare theorem can be stated concisely: under ideal conditions, a competitive market equilibrium is Pareto efficient. In its shortest formulation, equilibrium is Pareto efficient.
This statement requires understanding Pareto efficiency, named after the Italian economist Vilfredo Pareto. A situation is Pareto efficient if it is impossible to make any individual better off without making at least one other individual worse off. This criterion applies to any distribution of money, goods, and services within society.
Many argue that Pareto efficiency carries significant moral weight. If society could make someone better off without harming anyone else, that change seems obviously desirable since it produces a winner with no losers. As a moral criterion, pursuing such improvements appears compelling. The difficult territory emerges when every possible Pareto-improving change has been exhausted. At that point, society has reached a state where any redistribution that benefits someone necessarily harms someone else.
Assumptions Required for the First Welfare Theorem
The first welfare theorem holds only under specific ideal conditions, which fall into two main categories. The first category encompasses the standard assumptions of perfect competition familiar from introductory economics courses.
Perfect competition requires many buyers and sellers, often described as price-taking behavior. This assumption matters because its violation, as in monopoly, means some market participant possesses price-setting power. A monopolist like a regional cable provider can dictate prices rather than accepting market-determined prices.
Perfect competition also requires perfect information, meaning all market participants know the prices of all available goods. Free entry and exit constitutes another essential condition, ensuring that profitable opportunities attract new firms while underperforming firms exit the market. Finally, well-defined property rights must exist so that ownership is clear and secure against forcible taking.
Additional Assumptions for Environmental Economics
Beyond perfect competition, environmental economics highlights additional assumptions that must hold for the first welfare theorem to apply.
Complete markets represents a crucial additional assumption, requiring that everything people value has a corresponding market where it can be bought and sold. This assumption relates to having well-defined property rights for all valued goods and services. Environmental goods frequently fail this test. Consider the aesthetic pleasure derived from walking past a neighbor’s beautifully maintained garden. This value is real, but no market exists to capture or compensate for it, so competitive market equilibrium will not provide optimal levels of such goods. The broader category of ecosystem services, which will occupy multiple lectures later in the course, encompasses numerous valuable functions that nature provides without any market representation.
The absence of market failures, particularly externalities and public goods, constitutes another essential assumption. These two types of market failure hold particular relevance for environmental economics and will be explored in subsequent lectures.
Although perfect information falls under perfect competition, it deserves special emphasis given real-world conditions. Economic models assume perfect information, but actual decision-makers lack complete knowledge of all relevant prices and conditions. The utility maximization games explored earlier in the course demonstrated how challenging it is to always make perfectly rational, utility-maximizing choices under realistic informational constraints.
The Efficiency Result
When all these assumptions hold, the first welfare theorem establishes that total economic surplus, combining both consumer and producer surplus, reaches its maximum at the equilibrium quantity where supply equals demand. Any quantity other than the equilibrium quantity would generate less total surplus. A quantity below equilibrium leaves potential surplus unrealized in the form of mutually beneficial trades that do not occur. A quantity above equilibrium creates negative surplus because marginal costs exceed marginal benefits, actually subtracting from the positive surplus generated by earlier units.
The formal mathematical proof proceeds by contradiction, demonstrating that any deviation from the equilibrium cannot be Pareto efficient because some reallocation could make at least one party better off without harming others. PhD coursework dedicates substantial time to mastering these proofs, though their practical application outside examinations proves limited.
Limitations of the First Welfare Theorem
Beyond the possibility that the required assumptions may be violated in real-world conditions, the first welfare theorem suffers from additional problems. Most significantly, the theorem addresses efficiency but says absolutely nothing about distribution. The first welfare theorem completely ignores equity and equality.
In principle, the utilitarian calculus embedded in the theorem could endorse a world where a single individual possesses 100 percent of all wealth while everyone else starves. Such an outcome might technically be Pareto efficient since any redistribution would harm the wealthy individual. This extreme scenario tests whether Pareto efficiency truly captures our moral intuitions about what constitutes a good outcome.
Intuitively, taking a small amount of wealth from someone who owns everything and distributing it to starving people seems obviously beneficial on net. Yet this redistribution fails the Pareto criterion because it makes the wealthy person worse off. The first welfare theorem thus reveals that initial endowments, which may depend on intelligence, talent, or sheer luck, determine final outcomes even in Pareto efficient equilibria. This implication strikes many as deeply unsatisfying from a moral standpoint.
The political spectrum reflects different tolerances for wealth inequality. Environmental economics students may generally favor more egalitarian distributions, but the broader population spans a range of views on acceptable inequality levels. While virtually no one would defend the extreme scenario of one person holding all wealth, people differ substantially in their comfort with more moderate inequality.
The Second Welfare Theorem
The second welfare theorem addresses the equity concerns left unresolved by the first theorem. It states that any Pareto-efficient allocation can be achieved through competitive market equilibrium, provided that initial endowments are appropriately redistributed.
This theorem offers a hopeful message for those who value both efficiency and equity. If society desires a specific outcome, such as an equilibrium where utility is distributed equally across all individuals, that outcome can be reached through market mechanisms alone. The key is adjusting what people start with before letting markets operate.
In its shortest formulation, the second welfare theorem says that competitive equilibrium can always achieve any desired Pareto-efficient outcome. Markets alone suffice to reach any target allocation, but only if society is willing to redistribute initial resources. Taking from those with excessive holdings and giving to those with insufficient holdings enables markets to then produce the desired final distribution.
Historical examples approach extreme concentration of wealth. Julius Caesar, by some estimates, personally controlled approximately 25 percent of the Roman Empire’s wealth at its peak, representing extraordinary concentration of resources in a single individual. Some historical figures may have achieved even higher concentrations.
Calculating Surplus with Supply and Demand
Review of Equilibrium Calculation
Building on previous work solving supply and demand systems, we now extend the analysis to calculate surplus and then examine how taxes affect these calculations. The tax analysis matters because environmental problems, as subsequent lectures will argue, can often be addressed through environmental taxes such as carbon taxes or Pigouvian taxes.
Consider a market with demand given by P equals 15 minus Q divided by 2, and supply given by P equals 6 plus Q. The graph is drawn to scale, with demand intercepting the price axis at 15 and the quantity axis at 30, while supply intercepts the price axis at 6 and slopes upward.
Setting supply equal to demand and solving yields an equilibrium price P star of 12 and an equilibrium quantity Q star of 6. This equilibrium determination was covered in the previous lecture.
Computing Consumer and Producer Surplus
Given the equilibrium values, calculating net social benefits requires determining consumer and producer surplus separately. Consumer surplus equals the area of the triangle above the equilibrium price and below the demand curve. Using the formula one-half times base times height, with base equal to the equilibrium quantity of 6 and height equal to the demand intercept minus equilibrium price (15 minus 12 equals 3), consumer surplus equals one-half times 6 times 3, which equals 9.
Producer surplus equals the area of the triangle below the equilibrium price and above the supply curve. With the same base of 6 and height equal to equilibrium price minus supply intercept (12 minus 6 equals 6), producer surplus equals one-half times 6 times 6, which equals 18.
These calculations follow directly from the geometry of the supply and demand diagram, requiring only the equilibrium values and the intercepts of the linear curves.
Analyzing the Effects of a Tax
Shifting the Supply Curve
The analytical tools developed for calculating surplus become particularly valuable when examining policy interventions. To build toward understanding Pigouvian taxes that correct externalities, we first analyze the mechanics of how taxes affect market outcomes.
Consider imposing a tax of 3 dollars per unit on producers. This tax shifts the supply curve upward by the amount of the tax. The original supply curve P equals Q plus 6 becomes the tax-inclusive supply curve P equals Q plus 9. Graphically, the supply curve shifts vertically upward by 3 dollars at every quantity, reflecting that producers now require 3 dollars more per unit to cover their costs plus the tax.
Solving for the New Equilibrium
Finding the new equilibrium requires setting the tax-inclusive supply curve equal to the unchanged demand curve. The tax-inclusive supply is P equals Q plus 9, and demand remains P equals 15 minus Q over 2.
Setting these equal: Q plus 9 equals 15 minus Q over 2.
Subtracting 9 from both sides: Q equals 6 minus Q over 2.
Combining the Q terms: Q plus Q over 2 equals 6, which gives three-halves times Q equals 6.
Solving for Q: Q star equals 6 divided by three-halves, which equals 4.
The new equilibrium quantity is 4 units, reduced from the original 6 units due to the tax.
Finding the new equilibrium price requires substituting back into either equation. Using the tax-inclusive supply curve: P star equals 4 plus 9 equals 13.
Welfare Effects of the Tax
With the new equilibrium established at price 13 and quantity 4, all information needed to calculate the welfare effects of the tax is available. The relevant welfare measures include consumer surplus under the tax, producer surplus under the tax, government tax revenue, and deadweight loss.
Consumer surplus shrinks because consumers face a higher price and purchase fewer units. Producer surplus also decreases because producers receive a lower net-of-tax price and sell fewer units. The government collects tax revenue equal to the tax rate times the quantity sold. Deadweight loss represents the value of mutually beneficial trades that no longer occur due to the tax-induced quantity reduction.
These calculations, which follow the same triangular area approach as before, will be assigned as practice problems in the weekly questions to reinforce the mathematical techniques while building intuition about tax effects.
Looking Ahead: The Optimal Level of Pollution
The analytical framework developed in this lecture provides essential tools for addressing environmental economics questions. Having established how to calculate surplus and how taxes affect market outcomes, the next lectures will turn explicitly to environmental applications.
The upcoming topic concerns the optimal level of pollution, a question that might initially seem to have an obvious answer of zero but actually requires careful economic analysis. Chapter 3 in the textbook should be read in preparation for this discussion. The weekly questions covering today’s material, which include working with interactive graphs in a gamified format, should be completed by Wednesday.
The progression from individual utility theory through surplus and welfare analysis to explicit environmental applications follows a deliberate logical structure. Each component builds on previous material, and the theoretical foundations established now will prove essential when tackling complex questions about valuing ecosystem services, designing environmental policies, and evaluating tradeoffs between economic activity and environmental protection.