Content
Introduction and Overview
This lecture examines supply and demand from the perspective of environmental economics, embedding these fundamental economic tools within the planetary donut framework. The central objective is to understand how individual consumer and producer decisions aggregate into market outcomes, and how these market mechanisms relate to environmental considerations.
The lecture proceeds through several interconnected topics. First, we revisit the principles of consumer choice, examining how individuals use indifference curves and budget constraints to arrive at utility-maximizing decisions. From there, we transition to understanding how these individual choices can be represented as a market demand curve through horizontal summation. Next, we build the market supply curve, which involves a simpler analytical framework than the consumer problem because producers optimize profit rather than the more abstract concept of utility. With both supply and demand curves established, we examine market equilibrium and the forces that push markets toward equilibrium outcomes. Finally, we connect all of these concepts to environmental economics and discuss the implications for resource use and sustainability.
From Individual Choice to the Demand Curve
Review of Consumer Utility Maximization
The foundation for understanding market demand lies in individual consumer behavior. As established in previous material, the consumer chooses what to consume by solving an optimization problem. The key insight is that the optimal bundle of goods, consisting of some quantity of good X and some quantity of good Y, corresponds to the point where the indifference curve is tangent to the budget constraint. This tangency condition represents the combination of goods that maximizes utility given the consumer’s income and the prices they face in the market.
This framework allows for considerable analytical flexibility by manipulating the various inputs into the optimization problem. Interactive visualizations available on the course website allow students to explore how changing parameters affects the optimal choice. The most important exercise involves varying the price of one good and observing how the utility-maximizing quantity responds.
Deriving the Individual Demand Curve
Consider the baseline case where the price of good X equals 2. Given this price, a particular consumer’s budget constraint takes a specific shape, and the tangency with their indifference curves occurs at a point corresponding to a quantity of good X equal to 25. This is simply the mathematical result of maximizing utility subject to the budget constraint at that price level.
Now consider what happens when we change the price. If we increase the price of good X to 5, the budget constraint rotates inward because the consumer can no longer afford as much of good X with their fixed income. The new tangency point shifts, and in this example, it corresponds to a quantity of only 10 units of good X. The consumer responds to the higher price by purchasing less.
The powerful insight is that for any price of X, we can observe what happens to the utility-maximizing quantity that results from that price. By systematically varying the price and recording the corresponding optimal quantity, we can construct an entirely new relationship: the individual demand curve.
The interactive demonstration on the course website makes this process visible. As the price slider moves, the budget constraint pivots, a new tangency point emerges, and the optimal quantity changes. Each price-quantity combination gets plotted on a separate graph. When all these points are connected, the resulting curve is the individual’s demand curve.
The Mathematical Foundation of Demand
In introductory economics courses, it is difficult to make the connection between utility maximization and demand explicit because doing so requires additional concepts like indifference curves. Consequently, principles courses often simply assert that individuals have demand curves without explaining where they come from. The intermediate approach reveals that the demand curve derives directly from the mathematics of utility maximization subject to a budget constraint. The demand curve is nothing more and nothing less than a description of what happens to the optimal quantity when the price changes, holding everything else constant.
This connection between consumer theory and the demand curve is fundamental. If one accepts the premise that consumer preferences can be represented by a utility function, and that consumers maximize this utility subject to their budget constraints, then the existence and shape of the demand curve follows unambiguously. The logic is internally consistent and mathematically precise, which is why some economists view economic theory as almost physics-like in its rigor.
From Individual to Market Demand
The analysis so far concerns only one consumer’s demand curve. To analyze markets using supply and demand, we need the demand curve for the entire market, which includes all consumers.
The transition from individual to market demand uses the principle of horizontal summation. Consider two different consumers, Alice and Bob, each with their own budget constraints and indifference curves. Because they are different people, they have different incomes and possibly different preferences. In a typical example, Bob might be wealthier and thus able to afford more goods. When each consumer optimizes, they arrive at different quantities demanded: perhaps Alice demands 16 units and Bob demands 26 units at a given price.
To construct the market demand, we add the quantities demanded by Alice and Bob at each price level. At any specific price, we measure how far each consumer’s demanded quantity extends from the vertical axis, then sum these distances. Geometrically, we are taking the horizontal distance from the price axis to Alice’s demand curve and adding it to the horizontal distance to Bob’s demand curve. The result is the market demand curve, which shows total quantity demanded at each price.
The same interactive tools that illustrated individual demand can demonstrate market demand. As the price varies, each individual’s optimal quantity changes, and the sum of these individual quantities traces out the market demand curve. With hundreds or thousands of consumers, the process is conceptually identical, just involving more individual demand curves to sum horizontally.
The Elegance of Consumer Theory
There is elegance in this derivation of market demand from individual preferences. The entire framework rests on basic assumptions about preferences: that individuals can express whether they prefer bundle A to bundle B, B to C, and so forth, and that these preferences can be represented by a utility function assigning numerical values to different bundles. Given these premises, everything else follows through consistent mathematical reasoning.
This theoretical cleanliness is why consumer theory occupies such a central place in economics. The logical structure is tight, the mathematics is well-defined, and the predictions are unambiguous given the underlying assumptions about preferences and rationality.
Building the Supply Curve
The Simplicity of Producer Theory
Compared to consumer theory, the theory of the firm is considerably more straightforward. The conceptual difficulty with consumers lies in defining and measuring utility, an abstract and somewhat philosophical concept. What exactly is utility, and how do we quantify satisfaction or well-being?
For producers, the analogous concept is profit, which presents no such difficulties. Profit is simply total revenue minus total cost. There is no deep philosophy involved, just arithmetic. This concreteness makes the supply side of the market much easier to analyze.
The Data Perspective on Supply
At the introductory level, supply curves often appear as empirical relationships observed in data. One might observe that when the price of coffee is six dollars, a certain quantity is demanded per month. Creating a data table showing quantities supplied at various prices and plotting these points yields the supply curve. This approach treats supply as an observable relationship without delving into the underlying optimization.
However, a deeper understanding reveals what generates this relationship. The 3000-level treatment goes beyond simply accepting the supply curve as given data and instead derives it from the producer’s decision-making process.
The Production Function
The producer’s decision is described by a production function, which is directly parallel to how a consumer’s decision is described by a utility function. The production function specifies the quantity produced as a function of the inputs used in production.
In general form, the production function can be written as Q equals f of the inputs. The basic inputs typically included are labor, denoted L, and capital, denoted K. In a standard, non-environmental economics course, these would be the only arguments in the production function.
However, environmental economics requires a crucial modification. The standard approach represents the first of many blind spots in conventional economic theory: the assumption that production depends only on labor and capital while ignoring everything else. Environmental economics explicitly adds natural resources, denoted N, as an additional input to the production function. Natural resources include land, raw minerals extracted from the ground, timber harvested from forests, water, and other environmental inputs.
This modification is fundamental because standard economics has often proceeded as though natural resource inputs are infinite, nonexistent, or irrelevant to production decisions. The failure to account for depletable natural resource stocks in production functions represents a sophisticated argument for why mainstream economics has sometimes guided society down unsustainable paths. By being explicit about labor, capital, and natural resources, environmental economics addresses this critical oversight.
The Law of Diminishing Returns in Production
To produce more output, the production function indicates that inputs must increase. Adding more labor, more capital, or more natural resources will increase the quantity produced. However, the relationship between inputs and outputs is not linear throughout the entire range.
The law of diminishing returns in production, sometimes called the law of diminishing total productivity, states that at some point, as input factors increase, total product increases at a decreasing rate. This is a special case of the more general law of diminishing returns discussed throughout economics.
The total product curve illustrates this relationship. With labor as the variable input, the horizontal axis measures different levels of labor employed, and the vertical axis measures total product, the quantity Q that results from each level of labor input. The total product curve exhibits three distinct stages.
The Three Stages of Production
In Stage One, increasing the input factor causes total product to increase at an increasing rate. This is the startup zone where coordination among workers creates synergies. Two people working together can often accomplish far more than twice what one person could accomplish alone. A classic example involves two people using a two-handed saw to cut down a tree. A single person with that same saw would be extremely inefficient, while two people working together are perhaps a hundred times more productive, not merely twice as productive. Stage One represents this coordination bonus.
In Stage Two, total product continues to increase but at a decreasing rate. Most actual production decisions occur in this zone. Adding workers still helps, but each additional worker contributes less than the previous one. This is the domain of congestion and diminishing returns proper. The restaurant example illustrates this clearly. In Stage One, a few cooks specialize and coordinate effectively: one does cutting while another handles stirring and frying. In Stage Two, more cooks join the kitchen, and while specialization continues, they begin bumping elbows. The kitchen represents a fixed input with limited space, causing each additional cook to add less to total output than the previous cook added.
In Stage Three, total product actually declines with additional inputs. Returning to the restaurant example, imagine a small restaurant kitchen serving 25 customers at a time. What would happen if a thousand cooks were crammed into that kitchen? Productivity would collapse to zero because the space cannot physically accommodate that many workers. Stage Three is conceptually interesting but practically irrelevant because no rational firm would ever operate in this region.
From Production to Supply
Introductory economics often asks students to accept on faith that the firm’s production decisions generate a supply function without explaining exactly how this derivation works. The rigorous answer involves the same kind of analysis used for consumers: systematically varying the market price and observing how the profit-maximizing quantity responds.
Interactive tools demonstrate this process. The familiar cost curves from introductory economics reappear: marginal revenue, which equals the market price for a price-taking firm, and the marginal cost curve. The profit-maximizing quantity occurs where price equals marginal cost. The profit box, representing total profit, is maximized at this point.
As the market price moves, the intersection of price with the marginal cost curve shifts, and the profit-maximizing quantity changes. Since the axes already show price and quantity, simply tracing out these profit-maximizing price-quantity combinations directly yields the supply curve. With heterogeneous firms having different cost structures, the market supply curve is the horizontal sum of all individual firm supply curves, just as market demand is the horizontal sum of individual demand curves.
This treatment of supply, which normally occupies multiple lectures in an introductory course, has been condensed but made more comprehensive by explicitly connecting it to the underlying optimization framework.
Market Equilibrium
The Power of Equilibrium Analysis
The fundamental reason for deriving both supply and demand curves is to harness the power of equilibrium analysis. The concept of equilibrium provides economists with predictive power because systematic forces in the economy push outcomes toward the equilibrium position.
When an analyst wants to predict how a business should operate under different future scenarios, or when policymakers want to understand the effects of proposed changes, they can simply identify the new equilibrium and make confident predictions that the economy will move toward that point. This is extraordinarily useful for business planning and policy analysis.
Defining Equilibrium
An equilibrium, whether in economics, physics, or any other system, is a state where opposing forces are balanced. The classic physical analogy is a marble in a glass bowl. If you tap the marble, it rides up the wall of the bowl, but gravity and the bowl’s shape create forces that inexorably pull it back to the lowest point. Whatever perturbation is applied, the marble returns to its equilibrium position.
The economy operates analogously. There is an equilibrium point where supply equals demand, and forces analogous to gravity push economic outcomes toward that point. These forces are excess supply and excess demand.
The Mechanics of Equilibrium Attainment
Consider what happens when the price is above the equilibrium level. At a high price, consumers respond by wanting to buy less of the good. If video games suddenly cost $159 each, most people would purchase fewer games. Simultaneously, producers would love this high price. New firms might enter the industry, and existing firms would expand production, hiring more workers to increase output.
The result is a mismatch: the quantity demanded falls far below the quantity supplied. This excess supply creates a problem for producers. Their warehouses fill with unsold inventory. Storage space becomes scarce and costly. The natural response is to discount prices to move the excess goods. Stores have sales precisely because they need to clear inventory that is taking up valuable space.
As prices fall, two adjustments occur. Consumers want to buy more of the now-cheaper good, and some producers exit or reduce production because the lower price makes them unprofitable. These adjustments continue until excess supply is eliminated. The price falls all the way to the equilibrium where quantity supplied equals quantity demanded.
Excess Demand and Price Increases
The reverse occurs when the price is below equilibrium. If video games cost only $1.99, consumers would want to buy far more games, including games they might never actually play. Steam sales illustrate this behavior perfectly: at 99 cents, consumers purchase games they never even open. Low prices stimulate demand dramatically.
However, at such low prices, many producers cannot operate profitably. Less efficient firms exit the market. For fish, those with poor boats or less productive fishing methods cannot cover their costs and must stop fishing. The result is that quantity demanded exceeds quantity supplied.
When consumers want to buy more than exists, secondary markets and price pressures emerge. Concert tickets provide a clear example. When Taylor Swift tickets sell out instantly at the listed price, there is excess demand. Without restrictions, people resell tickets for many times the face value. The listed price is below equilibrium, and market forces push the actual transaction price upward.
More directly, producers recognize that they could charge higher prices and still find willing buyers. They raise prices, which causes some consumers to drop out while encouraging more production. This process continues until the price rises to the equilibrium level where quantity supplied equals quantity demanded.
Equilibrium as an Attractor
Any point on the supply and demand graph other than the equilibrium point E has forces pushing it toward E. Above equilibrium, excess supply creates discounting pressure that drives prices down. Below equilibrium, excess demand creates bidding-up pressure that drives prices higher. Like the marble in the bowl, the economic outcome is drawn inexorably to the equilibrium point.
This property makes equilibrium a powerful analytical concept. Rather than tracking the complex dynamics of adjustment, analysts can simply identify the equilibrium and confidently predict that is where the market will end up.
Solving for Equilibrium Mathematically
From Graphs to Equations
The visual analysis of equilibrium is intuitive, but economics goes further by representing supply and demand as mathematical functions that can be solved explicitly. The graphical representations correspond precisely to mathematical concepts, and calculating exact equilibrium prices and quantities is straightforward once the demand and supply functions are specified.
Direct Demand and Supply Functions
The direct demand function specifies quantity demanded as a function of price. In general notation, the quantity demanded equals some function D of price. For practical calculations, we specify a linear form. A typical example might be quantity demanded equals 28.67 minus 2.67 times the price. The negative coefficient on price captures the law of demand: higher prices lead to lower quantities demanded.
This is called direct demand because quantity Q appears on the left side as the output of the function, with price P as the input. The direct form is necessary for horizontal summation because we sum quantities at each price level.
The direct supply function has a similar structure. Quantity supplied equals some function S of price. A linear example might be quantity supplied equals 4.5 times price. The positive coefficient captures the law of supply: higher prices lead to greater quantities supplied. This particular function has no intercept, but adding one would not change the fundamental approach.
The Equilibrium Condition
The key insight for solving equilibrium is simply to set supply equal to demand. All the preceding discussion of excess supply and shortage justifies this simple condition. At equilibrium, quantity demanded must equal quantity supplied.
With specific functional forms, we can solve for the equilibrium price and quantity algebraically. Taking the demand function QD equals 28.67 minus 2.67P and the supply function QS equals 4.5P, the equilibrium condition requires 28.67 minus 2.67P equals 4.5P.
The solution proceeds by isolating P. First, gather terms with P on one side: 28.67 equals 4.5P plus 2.67P, which simplifies to 28.67 equals 7.167P. Then divide both sides by the coefficient on P: P equals 28.67 divided by 7.167, which equals 4. This equilibrium price, denoted P star, is the price toward which market forces push the economy.
With P star in hand, finding the equilibrium quantity Q star is simple. Substitute P star into either the supply or demand function. Using supply, Q star equals 4.5 times 4, which equals 18. The equilibrium quantity is 18 units.
Verification
The solution can be verified graphically by plotting both curves and confirming that the equilibrium price of 4 and quantity of 18 correspond to the intersection point where supply equals demand. This graphical check ensures the algebra was performed correctly.
Inverse Supply and Demand Functions
For historical reasons, economists conventionally plot price on the vertical axis and quantity on the horizontal axis. This convention creates a slight awkwardness because mathematical convention typically places the independent variable on the horizontal axis and the dependent variable on the vertical axis. If we express demand as Q equals D of P, then P is the input and Q is the output, but we plot Q horizontally and P vertically, which is backwards from standard mathematical graphing.
To resolve this, economists often use inverse supply and demand functions. The inverse demand function expresses price as a function of quantity: P equals D inverse of Q. Similarly, inverse supply writes P as a function of Q. This formulation makes the graphs more natural because the quantity on the horizontal axis is now the input to the function, and the price on the vertical axis is the output.
The inverse form is simply a rearrangement of the direct form. If the direct demand is Q equals 28.67 minus 2.67P, solving for P gives the inverse demand. The mathematics is trivial, but keeping the forms straight helps avoid confusion.
Solving with Inverse Functions
Consider specific inverse supply and demand functions. Inverse demand might be P equals 15 minus Q divided by 2, which has a slope of negative one-half and represents a downward-sloping demand curve. Inverse supply might be P equals 6 plus Q, which has a slope of one and represents an upward-sloping supply curve.
Setting supply equal to demand in inverse form means setting the two price expressions equal: 15 minus Q over 2 equals 6 plus Q. The strategy is to isolate Q. Moving constants to one side gives 15 minus 6 equals 9. Moving Q terms to the other side gives Q plus Q over 2.
To combine these terms, they need a common denominator. Q is the same as 2Q over 2, so Q plus Q over 2 equals 2Q over 2 plus Q over 2 equals 3Q over 2. Thus 9 equals 3Q over 2.
Solving for Q requires multiplying both sides by 2 over 3: Q equals 9 times 2 over 3 equals 6. The equilibrium quantity Q star is 6.
The equilibrium price P star comes from substituting Q star into either the supply or demand function. Using supply, P star equals 6 plus Q star equals 6 plus 6 equals 12.
Graphically, these values check out. The price of 12 and quantity of 6 lie at the intersection of the supply and demand curves as expected.
Flexibility in Approach
Both the direct and inverse approaches yield correct answers. Sometimes one form is more convenient than the other depending on the specific numbers involved. Fractional expressions may be easier to handle using the fraction approach shown above, while decimal forms may be simpler with a calculator. The choice is a matter of computational convenience, not mathematical correctness.
Students should be comfortable with both approaches because different problems may lend themselves to different forms. Being able to convert between direct and inverse representations and solve equilibrium either way provides flexibility in tackling supply and demand problems.
Connecting Supply, Demand, and Equilibrium to Environmental Economics
The Environmental Blind Spot Revisited
The machinery of supply and demand developed in this lecture provides powerful tools for analyzing markets. However, the environmental economics perspective requires recognizing what standard theory leaves out. The production function modification that added natural resources N alongside labor L and capital K represents the first of many corrections environmental economics makes to conventional theory.
Standard economics often ignores the depletion of natural resource stocks in its models. By assuming that labor and capital are the only relevant inputs, conventional theory implicitly treats natural resources as infinite, freely available, or simply irrelevant. Environmental economics rejects these assumptions and insists on accounting for the scarcity of environmental inputs.
Externalities and Market Failure
The equilibrium analysis presented here assumes that supply and demand curves reflect all relevant costs and benefits. Environmental economics challenges this assumption through the concept of externalities. When production or consumption generates costs that fall on third parties rather than the market participants, the supply curve does not reflect true social costs. Similarly, when benefits spill over to non-participants, the demand curve understates true social benefits.
Pollution provides a canonical example. A factory might produce goods with costs reflected in its marginal cost curve, but if production also generates pollution that harms nearby residents, those damages are not included in the firm’s costs. The supply curve thus understates the full social cost of production, and the market equilibrium involves too much production from society’s perspective.
Future lectures will develop these concepts in detail, showing how externalities cause market equilibrium to diverge from social optimum and examining policy tools for correcting market failures.
Natural Resource Depletion
The depletion of natural resource stocks presents another challenge to standard equilibrium analysis. The supply and demand framework implicitly assumes that production can continue indefinitely at equilibrium levels. For nonrenewable resources like minerals and fossil fuels, or for renewable resources harvested beyond their regeneration rates, this assumption fails.
Environmental economics incorporates resource dynamics into market analysis, examining how optimal extraction rates depend on interest rates, future prices, and physical constraints on resource availability. The open access fisheries problem, which will be analyzed using the supply and demand tools developed here, illustrates how market equilibrium can lead to resource collapse when property rights are poorly defined.
The Planetary Donut Framework
Embedding supply and demand within the planetary donut framework means recognizing that market outcomes must be evaluated against both environmental and social boundaries. The outer ring of the donut represents ecological ceilings that cannot be exceeded without triggering dangerous environmental change. The inner ring represents social foundations that must be maintained for human wellbeing.
Market equilibria generated by supply and demand may violate either boundary. Prices that fail to reflect environmental damage can push production beyond ecological limits. Inadequate incomes or access can leave people below social foundations. Environmental economics uses the tools of supply and demand while remaining attentive to these broader constraints on what constitutes a desirable outcome.
Summary and Looking Ahead
This lecture has traced the path from individual consumer choice, through utility maximization and horizontal summation, to market demand. It has similarly derived market supply from producer profit maximization. The combination of supply and demand generates market equilibrium, a powerful concept because economic forces systematically push outcomes toward equilibrium.
The mathematical techniques for solving equilibrium problems, whether using direct or inverse functions, provide practical tools for analyzing markets. These techniques will be applied throughout the course to examine environmental issues including externalities, natural resource management, and policy design.
The key modification introduced by environmental economics adds natural resources to the production function, correcting a fundamental blind spot in conventional theory. Future material will build on this foundation, developing concepts like externalities and cost-benefit analysis that allow supply and demand tools to address environmental challenges.
Students should practice solving equilibrium problems with both direct and inverse supply and demand functions, as these skills will be required on problem sets and examinations. Interactive visualizations on the course website provide opportunities to develop intuition for how changing parameters affect equilibrium outcomes. The mathematical techniques are intentionally kept accessible so that the intellectual challenge comes from addressing substantive environmental problems with powerful analytical tools rather than from computational difficulty alone.