Exhaustive Notes on Perfect Competition, Supply, Demand, and Market Equilibrium

Administrative Guidelines and Course Structure

• Course materials and lectures are co-authored by Iris Au, who instructs course A06 in subsequent academic terms.

• The academic term spans exactly twelve academic weeks, operating on a schedule where the start of a week does not align with calendar Mondays.

• October includes a designated Reading Week, during which no academic classes or tutorials are conducted.

• Tutorial sessions commence in the second academic week of the term.

• Consistent study habits throughout the twelve-week schedule reduce academic pressure and optimize performance.

Foundations of Economics and Production Possibilities Review

• Economics is defined as the study of the allocation of scarce resources among competing uses, acknowledging that scarcity necessitates individual and societal choices.

• Opportunity Cost represents the true, all-inclusive cost of acquiring an item or pursuing an activity. It encompasses both explicit (out-of-pocket) costs and implicit (opportunity) costs:

$\text{Opportunity Cost} = \text{Explicit Costs} + \text{Implicit Costs}$

• Implicit costs must reflect realistic valuation based on actual skill levels and next-best alternatives rather than arbitrary or inflated figures.

• For example, purchasing a item for an explicit cost of

$\$35$

also involves the implicit cost of the consumer's time spent searching for the product.

• A economic model consists of a set of assumptions designed to yield analytical conclusions. The validity of a model is judged by the realism of its conclusions rather than the strict literal accuracy of its underlying assumptions.

• The Production Possibility Frontier (PPF) model operates under three core restrictive assumptions:

  • The economy produces only two distinct goods ($X$ and $Y$).

  • The level of production technology is fixed.

  • The supply of productive factors (land, labor, and capital) is fixed.

• The PPF illustrates the trade-offs and input allocations required between sectors. Allocating more resources to sector $X$ reduces available inputs for sector $Y$.

• The slope and opportunity cost dynamics of the PPF depend on its structural shape:

  • Linear PPF: Possesses a constant slope, indicating a constant opportunity cost between goods. The opportunity cost of Good $X$ in terms of Good $Y$ is:

$\text{Opportunity Cost}_X = -1 \times \text{Slope}_{PPF}$

• Non-linear (Bowed-Out) PPF: Exhibits a negative slope that becomes progressively steeper (more negative) as the production of Good $X$ increases. This shape demonstrates increasing opportunity costs due to factor specificity.

  • Opportunity cost calculations relative to the PPF boundary:

• Points inside the PPF (Inefficient points): Opportunity cost of expanding output is zero ($0$) because underutilized resources allow for an increase in the output of one good without sacrificing the output of another.

• Points on the PPF (Efficient points): Opportunity cost is positive and measurable. Output of one good can only increase by sacrificing output of the other good.

• Points outside the PPF (Unattainable points): Opportunity cost is undefined because production at these levels is impossible given current technology and resource constraints.

  • Social Value Optimization on a PPF:

• Social value can be defined by a linear social value function:

$V(X, Y) = aX + bY$

where $a > 0$ and $b > 0$, establishing both $X$ and $Y$ as economic goods.

• Indifference/Value lines represent combinations of $X$ and $Y$ yielding equal social value, featuring a constant slope of:

$\text{Slope}_{Value} = -\frac{a}{b}$

• Maximizing social value requires identifying the highest attainable value line tangent to the PPF.

• Mathematically, the tangency condition occurs where the slope of the PPF equals the slope of the social value function:

$\text{Slope}_{PPF} = -\frac{a}{b}$

• Optimization technique: Substitute the non-linear PPF equation into the linear value function to express social value as a univariate function $V(X)$. Calculate the first derivative, set it equal to zero ($\frac{dV}{dX} = 0$) to determine optimal $X^*$, and substitute $X^*$ back into the PPF equation to solve for $Y^*$.

• Even if society values Good $Y$ significantly more than Good $X$ (e.g., $a = 3, b = 6$), increasing opportunity costs dictate that optimal production will generally involve positive quantities of both goods rather than a corner solution.

• In a closed economy (no international trade), the production point exactly equals the consumption point. International trade allows production and consumption points to diverge.

Introduction to Market Structure and Perfect Competition

• Over the course of microeconomic analysis, three primary market structures are evaluated:

  • Perfect Competition: The baseline benchmark model of market structure.

  • Monopoly: A market structure consisting of a single seller.

  • Oligopoly: A market structure dominated by a small number of large firms.

• A Market is defined as a set of rules and institutional arrangements that bring potential buyers and sellers together to exchange information, negotiate terms, and execute transactions for goods (tangible output) or services (intangible output).

• Market negotiations establish terms including transaction quantities, product qualities, and transaction prices.

• In graphical market representations (e.g., the Toronto apple market):

  • The vertical axis measures price ($P$), such as dollars per bushel ($\$/\text{bushel}$).

  • The horizontal axis measures quantity per period ($Q$), such as thousands of bushels per month.

  • Endogenous Variables: Variables determined within the model via market equilibrium, primarily price ($P^*$) and quantity ($Q^*$), alongside derived variables such as total firm revenue ($TR = P \times Q$) and total consumer expenditure ($TE = P \times Q$).

  • Exogenous Variables: Variables originative outside the model that remain fixed in the background unless explicitly altered.

• Core Assumptions of the Model of Perfect Competition:

  • Atomistic Agents (Price Takers): Highly numerous buyers and sellers, each holding an infinitesimally small market share. No individual buyer or seller possesses market power to influence the market price.

  • Homogeneous Products: All firms produce identical, highly standardized goods (e.g., commodities like sugar, wheat, or ball bearings) with zero product differentiation.

  • Perfect Information: All market participants possess complete, symmetric, and instantaneous information regarding prices, quality, and technology. No transaction mistakes or price dispersions occur in equilibrium.

  • Free Entry and Exit in the Long Run: Zero structural, legal, or financial barriers to entry or exit. Economic profits are driven to exactly zero in long-run equilibrium, meaning firms earn exactly their opportunity cost:

$\Pi_{\text{Long-Run}} = 0$

Demand Theory, Marginal Utility, and Consumer Choice

• The Demand Curve reflects the willingness to pay and consumption behavior of purchasers (households).

• The Demand Curve slopes downward due to the Law of Diminishing Marginal Utility, which establishes that the incremental utility derived from consuming additional units of a good decreases as total consumption increases.

• Discrete utility and willingness-to-pay (WTP) schedule (e.g., daily consumption of rice bowls):

  • $0$ bowls: Total Utility = $\$0.00$

  • $1$st bowl: Total Utility = $\$8.00$, Marginal Utility = $\$8.00$, Maximum WTP = $\$8.00$

  • $2$nd bowl: Total Utility = $\$13.00$, Marginal Utility = $\$5.00$, Maximum WTP = $\$5.00$

  • $3$rd bowl: Total Utility = $\$15.00$, Marginal Utility = $\$2.00$, Maximum WTP = $\$2.00$

  • $4$th bowl: Total Utility = $\$16.75$, Marginal Utility = $\$1.75$, Maximum WTP = $\$1.75$

• Rational consumers will never pay a price higher than their marginal utility for a given unit. Consequently, the height of the demand curve measures the maximum price buyers are willing to pay for marginal units.

• Graphical interpretations of points along a demand curve:

  • At a given quantity $Q = 10,000\,\text{bushels}$, the height of the demand curve ($P = \$50$) represents the maximum willingness to pay for the $10,000$\text{th} bushel.

  • At a given price $P = \$50$, the horizontal distance to the demand curve ($Q = 10,000\,\text{bushels}$) represents the maximum quantity consumers are willing to purchase at that price.

Supply Theory, Marginal Cost, and Production Horizons

• The Supply Curve represents the behavior of producers and sellers. In supply models, manufacturers and distributors are consolidated into a single entity.

• The height of the supply curve represents the minimum price suppliers are willing to accept to produce and sell incremental units. This minimum acceptable price equals the Marginal Cost ($MC$) of production:

$P_{\text{minimum}} = MC$

• Time Horizons in Supply Analysis:

  • Short Run: A time frame short enough that the number of operating firms is fixed, capital stock ($K$) is fixed, and production technology is fixed. Labor ($L$) is the sole variable input. The short-run supply curve slopes upward due to increasing marginal costs ($MC$) caused by diminishing marginal returns to labor and overtime premiums.

  • Long Run: A time frame long enough for existing firms to adjust capital inputs ($K$) and for new firms to enter or existing firms to exit the market. The long-run supply curve is significantly flatter (more elastic) than the short-run supply curve and can be perfectly horizontal (zero slope).

• Physical Byproducts and Supply at Zero Price: A supply curve can intersect the horizontal axis, indicating positive supply at $P = \$0$. This occurs when output is an unavoidable byproduct of another industrial process (e.g., petroleum refining producing jet fuel alongside candle wax, or industrial factories near urban centers producing excess heat/steam as a byproduct).

Market Equilibrium and the Mechanics of the Invisible Hand

• Market Equilibrium occurs at the unique price ($P^*$) and quantity ($Q^*$) where the quantity demanded by buyers equals the quantity supplied by sellers:

$Q_d(P^*) = Q_s(P^*)$

• In equilibrium, the market clears completely; there are no surpluses, no shortages, and no endogenous pressures for price or quantity to change.

• The Invisible Hand Principle (formulated by Adam Smith in The Wealth of Nations, 1776): In a decentralized market, self-interested buyers (maximizing utility) and self-interested sellers (maximizing profits) react to price signals. The price system coordinates these independent actions toward market equilibrium as if guided by an invisible hand, requiring no central planning body.

• Disequilibrium Adjustment Dynamics:

  • Excess Supply (Surplus): Occurs when market price is above equilibrium ($P_1 > P^*$), causing $Q_s > Q_d$. Unsold inventory accumulates, inducing sellers to undercut prices. As price falls, $Q_d$ expands along the demand curve and $Q_s$ contracts along the supply curve until $P^*$ is reached.

  • Excess Demand (Shortage): Occurs when market price is below equilibrium ($P_2 < P^*$), causing $Q_d > Q_s$. Bidding by unsatisfied buyers drives prices upward. As price rises, $Q_s$ expands along the supply curve and $Q_d$ contracts along the demand curve until $P^*$ is reached.

Mathematical Mechanics and Comparative Statics of Demand

• Direct Demand Function Equation Example:

$Q_d = 60 - P$

• Inverse Demand Function Equation Example (historically formulated by Alfred Marshall):

$P = 60 - Q_d$

• The Demand Function incorporates both own-price and exogenous determinants:

$Q_d = f(P, P_s, P_c, I, N, T, E)$

where:

• $P$ = Own price of the good.

• $P_s$ = Price of a substitute good ($\frac{\partial Q_d}{\partial P_s} > 0$). Substitutes possess similar characteristics and serve similar functional purposes (e.g., butter and margarine).

• $P_c$ = Price of a complementary good ($\frac{\partial Q_d}{\partial P_c} < 0$). Complements are consumed jointly (e.g., popcorn and soda, coffee and sugar).

• $I$ = Consumer income ($\frac{\partial Q_d}{\partial I} > 0$ for normal goods; $\frac{\partial Q_d}{\partial I} < 0$ for inferior goods).

• $N$ = Population size ($\frac{\partial Q_d}{\partial N} > 0$).

• $T$ = Tastes, preferences, and information.

• $E$ = Expectations regarding future prices or economic conditions.

  • Multivariate Demand Equation Structure Example:

$Q_d = 40 - P + a P_s - b P_c + c I + d N$

• Distinguishing Movements Along vs. Shifts of the Demand Curve:

  • Change in Quantity Demanded: A movement along a static demand curve caused exclusively by a change in the good's own price ($P$).

  • Change in Demand: A parallel shift of the entire demand curve caused by a change in any background exogenous variable ($P_s, P_c, I, N, T, E$).

• Comparative Statics Examples for Demand:

  • Increase in Income ($I \uparrow$):

  • Normal Good (e.g., restaurant meals): Demand shifts right $\rightarrow P^* \uparrow, Q^* \uparrow$.

  • Inferior Good (e.g., plain white bread, instant ramen, walking as transit): Demand shifts left $\rightarrow P^* \downarrow, Q^* \downarrow$.

  • Increase in Price of Substitute ($P_{s} \uparrow$):

  • Example: Price of multigrain bread rises $\rightarrow$ Quantity demanded of multigrain bread falls $\rightarrow$ Demand for plain white bread shifts right via the substitution effect \rightarrow P^* \uparrow, Q^* \uparrow$.\n\n - Increase in Price of Complement (P_{c} \uparrow):\n\n - Example: Price of coffee rises \rightarrow$Quantity demanded of coffee falls$\rightarrow$Demand for sugar shifts left$\rightarrow P^* \downarrow, Q^* \downarrow$.

  • Decrease in Population ($N \downarrow$):

  • Example: Population declines in a region $\rightarrow$ Demand for rental housing shifts left \rightarrow P^* \downarrow, Q^* \downarrow$.\n\n - Change in Preferences/Information (T):\n\n - Example: Information reveals grapefruit juice inhibits medication function \rightarrow$Consumer preference declines$\rightarrow$Demand for grapefruit juice shifts left$\rightarrow P^* \downarrow, Q^* \downarrow$.

Mathematical Mechanics and Comparative Statics of Supply

• Direct Supply Function Equation Example:

$Q_s = 24 + 2P$

• Inverse Supply Function Equation Example:

$P = -12 + 0.5 Q_s$

• The Supply Function incorporates own-price and exogenous production cost determinants:

$Q_s = f(P, P_L, P_K, Tech, t)$

where:

• $P$ = Own price of the good.

• $P_L$ = Rental price of labor / wage rate ($w$).

• $P_K$ = Rental price of capital ($r$).

• $Tech$ = Technology index.

• $t$ = Per-unit excise tax imposed on production.

  • Multivariate Supply Equation Structure Example:

$Q_s = 48 + 2P - 4 P_L - 2 P_K + f Tech$

• Distinguishing Movements Along vs. Shifts of the Supply Curve:

  • Change in Quantity Supplied: A movement along a static supply curve caused exclusively by a change in the good's own price ($P$).

  • Change in Supply: A shift of the entire supply curve caused by a change in an exogenous factor influencing marginal costs ($P_L, P_K, Tech, t$).

• Comparative Statics Examples for Supply:

  • Increase in Input Prices ($P_L \uparrow$ or $P_K \uparrow$):

  • Increases marginal cost ($MC$) at all output levels. Supply curve shifts vertically upward and to the left (decrease in supply) \rightarrow P^* \uparrow, Q^* \downarrow$.\n\n - Technological Advancement (Tech \uparrow):\n\n - Lowers marginal cost (MC$) at all output levels. Supply curve shifts downward and to the right (increase in supply)$\rightarrow P^* \downarrow, Q^* \uparrow$.

  • Per-Unit Excise Tax ($t$):

  • A tax of $t$ dollars per unit increases marginal cost directly by $t$. The supply curve shifts vertically upward by exactly $t$ dollars $\rightarrow P^* \uparrow, Q^* \downarrow$. (Note: Lump-sum taxes affect fixed costs and do not shift short-run supply curves).

Simultaneous Curve Shifts and Market Outcomes

• When two exogenous variables change simultaneously, both the demand curve and the supply curve shift, altering the predictability of the new equilibrium outcome:

• Case 1: Simultaneous Shift in Demand and Supply in Opposite Directions (Union Power and Wages Increase):

  • Increase in worker wages increases household income ($I \uparrow$), shifting demand for normal goods (e.g., hamburgers) to the right ($D \uparrow$).

  • Increase in worker wages increases labor input costs ($P_L \uparrow$), shifting supply of hamburgers to the left ($S \downarrow$).

  • Impact on Price ($P^*$): Unambiguously increases ($P^* \uparrow$).

  • Impact on Quantity ($Q^*$): Ambiguous. If $\Delta D > \Delta S$, $Q^* \uparrow$; if $\Delta S > \Delta D$, $Q^* \downarrow$; if $\Delta D = \Delta S$, $Q^*$ remains unchanged.

• Case 2: Simultaneous Demand Expansion and Supply Reduction (University Education Market):

  • Preferential demand for higher education increases ($D \uparrow$).

  • Faculty compensation and operating costs increase ($MC \uparrow \rightarrow S \downarrow$).

  • Result: Equilibrium tuition price unambiguously rises ($P^* \uparrow$); equilibrium enrollment quantity ($Q^*$) is indeterminate without exact shift magnitudes.

• Case 3: Simultaneous Opposite Demand Shifts (Automobile Market):

  • Consumer income increases ($I \uparrow$), shifting demand for automobiles right ($D \uparrow$).

  • Gasoline price increases ($P_{\text{gas}} \uparrow$), and because gasoline is a complement to automobiles, car demand shifts left ($D \downarrow$).

  • Result: The net shift in demand depends on whether the income effect dominates the complement price effect. Both equilibrium price ($P^*$) and quantity ($Q^*$) are indeterminate without magnitude parameters.

Government Interference: Price Ceilings and Price Floors

• Market interference occurs when government policies suppress price flexibility, blocking the market from reaching competitive equilibrium.

• Binding Constraint Principle: A price control alters market outcomes only if it prevents market-clearing equilibrium:

  • A Price Ceiling must be set below equilibrium price ($P_{\text{ceiling}} < P^*$).

  • A Price Floor must be set above equilibrium price ($P_{\text{floor}} > P^*$).

• Price Ceiling Mechanics (e.g., Rent Control):

  • Imposes a statutory maximum price ($P_{\text{ceiling}} < P^*$).

  • Outcome: Quantity demanded exceeds quantity supplied ($Q_d > Q_s$), creating a persistent market Shortage (Excess Demand).

  • Economic Consequences:

  • Short-End Principle: Actual transaction quantity is constrained by the lesser of supply or demand:

$Q_{\text{traded}} = \min(Q_d, Q_s) = Q_s$

- Non-price rationing mechanisms emerge (long waitlists, discrimination).

- Underground/Black Markets develop, where transactions occur illicitly above the ceiling price.

- Product Quality Deterioration: Landlords reduce expenditures on maintenance, heating, cooling, and structural safety.

- Historical Rent Control Case: An apartment in Manhattan rented under 1940s price controls for approximately

$\$300\,\text{per month}$

lacked running water, indoor plumbing, flush toilets, and central heating/cooling, requiring the tenant to utilize three fireplaces and external facilities (YMCA).

• Price Floor Mechanics (e.g., Statutory Minimum Wage, Agricultural Marketing Boards):

  • Imposes a statutory minimum price ($P_{\text{floor}} > P^*$).

  • Outcome in Labor Markets ($W_{\text{min}} > W^*$): Labor supplied exceeds labor demanded ($L_s > L_d$), generating persistent Unemployment (Excess Supply).

  • Short-End Principle applies:

$L_{\text{traded}} = \min(L_d, L_s) = L_d$

• Economic Consequences:

  • Underground cash economies emerge (unreported under-the-table labor below minimum wage).

  • Misallocation of resources across industries.

• Outcome in Agricultural Marketing Boards (e.g., Canadian Milk, Poultry, and Egg Boards):

  • Government boards establish legally binding price floors for agricultural commodities.

  • To eliminate physical surplus accumulation at $P_{\text{floor}}$, boards issue strict production licenses and quotas to farmers, capping aggregate market supply.

  • Production exceeding quota limits cannot be legally sold and must be destroyed (e.g., dumping excess raw milk).

  • Forecasting Errors: An error by the Egg Marketing Board overestimating market demand generated an unallocated surplus of

$750,000\,\text{dozen eggs}$

which were ultimately exported to Saudi Arabia.