Comprehensive Microeconomics Notes: Trade, Supply, Demand, Surplus, and Elasticity

Principles of Specialization, Opportunity Cost, and Trade

• Basis of Exchange:

  • Individuals exchange goods and services because specialization allows individuals, firms, and nations to concentrate on activities where they possess relative efficiency.

  • Specialization increases aggregate output, permitting society to consume beyond its individual self-sufficiency capabilities.

• Cost-Benefit Principle in Individual Decision-Making:

  • An individual performs an activity $x$ if and only if the marginal benefit $B(x)$ exceeds or equals the marginal cost $C(x)$:     $\text{Do } x \iff B(x) \ge C(x)$

  • When providing labor or goods to others, the minimum required compensation must at least cover the opportunity cost of the foregone activity.

• Absolute Advantage vs. Comparative Advantage:

  • Absolute Advantage: The ability to perform a task or produce a good using fewer total input resources (such as labor hours) than another producer.

  • Comparative Advantage: The ability to perform a task or produce a good at a lower opportunity cost than another producer.

  • Core Identity: Having a comparative advantage is logically identical to having a lower opportunity cost and possessing greater relative efficiency.

• Workplace Example: Paul and Ron (Painting and Roofing):

  • Labor requirements for two distinct tasks:

  • Paul: Requires $300\,\text{hrs}$ to paint a house and $400\,\text{hrs}$ to roof a house.

  • Ron: Requires $200\,\text{hrs}$ to paint a house and $100\,\text{hrs}$ to roof a house.

  • Absolute Advantage Analysis:

  • Ron has an absolute advantage in painting ($200\,\text{hrs} < 300\,\text{hrs}$).

  • Ron has an absolute advantage in roofing ($100\,\text{hrs} < 400\,\text{hrs}$).

  • Opportunity Cost Analysis:

  • Paul's Opportunity Costs:

    • Opportunity cost of painting $1$ house = $\frac{300}{400} = 0.75\,\text{roofing jobs}$.

    • Opportunity cost of roofing $1$ house = $\frac{400}{300} = 1.33\,\text{painting jobs}$.

  • Ron's Opportunity Costs:

    • Opportunity cost of painting $1$ house = $\frac{200}{100} = 2.0\,\text{roofing jobs}$.

    • Opportunity cost of roofing $1$ house = $\frac{100}{200} = 0.5\,\text{painting jobs}$.

  • Comparative Advantage Identification:

  • Paul holds a comparative advantage in painting ($0.75 < 2.0\,\text{roofing jobs}$).

  • Ron holds a comparative advantage in roofing ($0.5 < 1.33\,\text{painting jobs}$).

  • Gains from Trade and Specialization:

  • Without Trade (Autarky): Paul needs $700\,\text{hrs}$ ($300 + 400$) to complete both tasks for himself; Ron needs $300\,\text{hrs}$ ($200 + 100$) for himself. Total combined labor = $1,000\,\text{hrs}$.

  • With Trade and Terms of Trade (ToT) = $1.0\,\text{painting job per roofing job}$:

    • Paul specializes in painting (paints two houses = $600\,\text{hrs}$) and trades $1$ painting job for $1$ roofing job.

    • Ron specializes in roofing (roofs two houses = $200\,\text{hrs}$) and trades $1$ roofing job for $1$ painting job.

    • Savings: Paul spends $600\,\text{hrs}$ (saves $100\,\text{hrs}$); Ron spends $200\,\text{hrs}$ (saves $100\,\text{hrs}$). Total combined labor falls to $800\,\text{hrs}$.

  • With Trade and Terms of Trade (ToT) = $1.1\,\text{painting jobs per roofing job}$:

    • Paul spends $636.36\,\text{hrs}$ (saves $63.64\,\text{hrs}$).

    • Ron spends $190.91\,\text{hrs}$ (saves $109.09\,\text{hrs}$).

  • Feasible Range for Terms of Trade:

  • Mutually beneficial terms of trade for painting must lie strictly between the two producers' opportunity costs:       $0.75\,\text{roofing jobs} < \text{ToT} < 2.0\,\text{roofing jobs per painting job}$

• Mechanics Example I: George and Tom:

  • George: Can perform $10\,\text{clutch replacements/day}$ or $15\,\text{brake replacements/day}$.

  • Opportunity cost of $1\,\text{brake replacement}$ = $\frac{10}{15} = 0.67\,\text{clutches}$.

  • Tom: Can perform $15\,\text{clutch replacements/day}$ or $10\,\text{brake replacements/day}$.

  • Opportunity cost of $1\,\text{brake replacement}$ = $\frac{15}{10} = 1.5\,\text{clutches}$.

  • Production Without Specialization (Equal Output of Both Services):

  • George sets $C = 10 - \left(\frac{2}{3}\right)B$. For $C = B \implies B = 6, C = 6$.

  • Tom sets $C = 15 - \left(\frac{3}{2}\right)B$. For $C = B \implies B = 6, C = 6$.

  • Total daily combined production = $12\,\text{clutches}$ and $12\,\text{brakes}$.

  • Production With Full Specialization:

  • Tom performs $15\,\text{clutch replacements}$;

  • George performs $15\,\text{brake replacements}$.

  • Combined output rises to $15\,\text{of each service}$, representing a $25\%$ productivity increase.

• Mechanics Example II: Eric and Gary:

  • Eric: Can perform $30\,\text{clutches/day}$ or $6\,\text{brakes/day}$. Opportunity cost of $1\,\text{brake}$ = $5\,\text{clutches}$.

  • Gary: Can perform $6\,\text{clutches/day}$ or $30\,\text{brakes/day}$. Opportunity cost of $1\,\text{brake}$ = $0.2\,\text{clutches}$.

  • Without Specialization: Eric produces $5$ of each; Gary produces $5$ of each. Total = $10\,\text{of each service}$.

  • With Specialization: Eric produces $30\,\text{clutches}$ and Gary produces $30\,\text{brakes}$. Total = $30\,\text{of each service}$.

  • Key Insight: The gain from specialization rises from $25\%$ to $200\%$ because the difference in opportunity costs is substantially larger.

• Sources of Comparative Advantage:

  • Individual Level: Inborn talent, education, specialized training, and experience.

  • Collective / National Level: Natural resource endowments, cultural factors, language, institutions, legal infrastructure, and climate.

The Production Possibility Curve and Economic Growth

• Definition of Production Possibility Curve (PPC):

  • A graphical representation displaying the maximum attainable combinations of two goods or services an economy can produce using its available productive resources and technology efficiently.

• Attainability and Efficiency Categories:

  • Points on the PPC: Attainable and productive-efficient.

  • Points inside the PPC: Attainable but inefficient (resources are underutilized or misallocated).

  • Points outside the PPC: Unattainable given current resources and technological constraints.

• Slope and Opportunity Cost:

  • The absolute value of the slope of the PPC measures the opportunity cost of producing an additional unit of the good plotted on the horizontal axis in terms of the good on the vertical axis:     $\text{Absolute Slope} = \frac{|\Delta \text{Vertical Good}|}{|\Delta \text{Horizontal Good}|} = \text{Opportunity Cost}$

• Principle of Increasing Opportunity Cost (Low-Hanging-Fruit Principle):

  • In expanding the production of any good, society should first allocate resources with the lowest opportunity cost, turning to resources with higher opportunity costs only after the lower-cost resources are fully deployed.

  • This principle causes multi-person and economy-wide PPCs to be bowed outward (concave) from the origin.

• Deriving a Multi-Person PPC (Chris, Dana, and George):

  • Individual Productive Capacities:

  • Chris: $6\,\text{sq yds/wk shelter}$ or $12\,\text{lbs/wk food}$. Opportunity cost of $1\,\text{lb food}$ = $0.5\,\text{sq yds shelter}$. Opportunity cost of $1\,\text{sq yd shelter}$ = $2\,\text{lbs food}$.

  • Dana: $4\,\text{sq yds/wk shelter}$ or $4\,\text{lbs/wk food}$. Opportunity cost of $1\,\text{lb food}$ = $1.0\,\text{sq yd shelter}$. Opportunity cost of $1\,\text{sq yd shelter}$ = $1\,\text{lb food}$.

  • George: $2\,\text{sq yds/wk shelter}$ or $1\,\text{lb/wk food}$. Opportunity cost of $1\,\text{lb food}$ = $2.0\,\text{sq yds shelter}$. Opportunity cost of $1\,\text{sq yd shelter}$ = $0.5\,\text{lb food}$.

  • Sequential Allocation for Food Production:

  1. Start at total shelter specialization: $(0\,\text{food}, 12\,\text{shelter})$.

  2. Allocate Chris first (lowest OC of food = $0.5$): yields $(12\,\text{food}, 6\,\text{shelter})$.

  3. Allocate Dana second (next lowest OC of food = $1.0$): yields $(16\,\text{food}, 2\,\text{shelter})$.

  4. Allocate George last (highest OC of food = $2.0$): yields $(17\,\text{food}, 0\,\text{shelter})$.

• Factors Shifting the PPC Outward (Economic Growth):

  • Increases in productive factor inputs: capital accumulation, infrastructure investment, and population growth.

  • Progress in human capital: improved education, skills acquisition, and health.

  • Technological advancements and innovation.

  • Division of labor and expanded specialization possibilities.

• International Trade and the Consumption Possibility Curve (CPC):

  • In a closed economy (autarky), an economy's Consumption Possibility Curve is identical to its Production Possibility Curve ($\text{CPC} = \text{PPC}$).

  • In an open economy, international trade decouples consumption from production, allowing an economy to consume outside its PPC ($\text{CPC} > \text{PPC}$).

  • Islandia Example (Elizabeth and Dennis):

  • Production capacities: Corner points $(0\,\text{tea}, 120\,\text{bananas})$, $E = (100\,\text{tea}, 100\,\text{bananas})$, and $(120\,\text{tea}, 0\,\text{bananas})$.

  • World Market Prices: Tea = $\$2/\text{lb}$, Bananas = $\$1/\text{lb}$.

  • Optimal Production Mix Choice:

    • Income at $(0, 120)$ = $0(2) + 120(1) = \$120$.

    • Income at $(120, 0)$ = $120(2) + 0(1) = \$240$.

    • Income at Point $E (100, 100)$ = $100(2) + 100(1) = \$300$ (Maximum national income).

  • Consumption Possibilities:

    • With $\$300$ income, Islandia can consume anywhere along line $FG$ connecting $(0\,\text{tea}, 300\,\text{bananas})$ to $(150\,\text{tea}, 0\,\text{bananas})$.

    • Point $K (75\,\text{tea}, 150\,\text{bananas})$ provides $75(2) + 150(1) = \$300$, a combination unobtainable without trade.

Market Structures and Bargaining Power

• Market Definition:

  • A market consists of all actual or potential buyers and sellers of a specific good or service within a defined geographic location and time period (e.g., the lobster market in Portland, Maine on July 20, 2004, or the Shau Kei Wan and Sai Kung Pier markets in Hong Kong).

• Determinants of Bargaining Power:

  • Bargaining power is dictated by the existence and availability of outside options (alternatives).

  • A market participant facing no alternatives holds maximal bargaining power.

  • A market participant facing numerous competing options holds weak bargaining power.

• Taxonomy of Market Structures:

• Monopsony:

  • Buyers: One (Maximal bargaining power).

  • Sellers: Many (Weak bargaining power).

• Monopoly:

  • Buyers: Many (Weak bargaining power).

  • Sellers: One (Strong bargaining power).

• Perfect Competition:

  • Buyers: Many (Weak bargaining power).

  • Sellers: Many (Weak bargaining power).

  • Price Taking behavior: Because every individual buyer and seller has negligible market power, all participants take the market price as given.

Demand Theory, Consumer Choice, and Market Demand

• Consumer Decision Rule:

  • A consumer purchases an additional unit of a good if and only if the Willingness to Pay ($\text{WTP}$ or marginal valuation $V_i$) equals or exceeds the market price $P$:     $\text{Buy} \iff V_i \ge P, \quad \text{Do Not Buy} \iff V_i < P$

• Derivation of the Demand Schedule:

  • By varying price $P$ across a spectrum of discrete levels and summing the number of individuals whose $V_i \ge P$, a demand schedule and demand curve are established.

  • Lobster Market Demand Schedule (Discrete Example):

• Interpretations of the Demand Curve:

  • Horizontal Interpretation: Quantifies the total units consumers are willing and able to purchase at a specific market price.

  • Vertical Interpretation: Identifies the exact marginal willingness to pay (the highest price the marginal buyer will accept) for an additional unit at a given quantity.

• Reasons for Downward Sloping Demand Curves:

  • Heterogeneity Across Consumers: Higher prices restrict purchases to consumers with high valuations; lower prices induce participation by consumers with lower valuations.

  • Substitution Effect: As price $P_x$ increases, the relative price $\frac{P_x}{P_y}$ rises, prompting consumers to replace good $x$ with substitute goods $y$ ($Q_x$ falls).

  • Income Effect: An increase in price $P_x$ reduces consumer purchasing power (real income):

  • Normal Goods: Real income falls $\implies Q_x$ falls.

  • Inferior Goods: Real income falls $\implies Q_x$ rises.

  • Law of Demand: Combining substitution and income effects, an increase in price generally leads to a decrease in quantity demanded ($\frac{\Delta Q}{\Delta P} < 0$).

• Horizontal Aggregation of Market Demand:

  • Market demand is constructed by horizontally summing the individual quantities demanded by all consumers at every fixed price level:     $Q_{\text{market}}(P) = \sum_{i=1}^{n} Q_i(P)$

Supply Theory, Cost Structures, and Market Supply

• Producer Decision Rule:

  • A producer supplies an additional unit of a good if and only if the market price $P$ equals or exceeds the marginal production cost or Willingness to Accept ($\text{WTA}$ or cost $C_i$):     $\text{Supply} \iff P \ge C_i, \quad \text{Do Not Supply} \iff P < C_i$

• Derivation of the Supply Schedule:

• Interpretations of the Supply Curve:

  • Horizontal Interpretation: Quantifies the total units suppliers are willing and able to sell at a specific market price.

  • Vertical Interpretation: Identifies the minimum price required by marginal sellers to bring a specific quantity to market.

• Reasons for Upward Sloping Supply Curves:

  • Heterogeneity Across Firms: Low prices cover costs for efficient, low-cost producers only; higher prices are required to draw higher-cost producers into production.

  • Increasing Marginal Costs: For an individual firm, producing additional output incurs increasing marginal costs due to diminishing returns to inputs (e.g., harvesting low-hanging fruit first).

• Horizontal Aggregation of Market Supply:

  • Market supply is derived by horizontally summing the quantities supplied by all individual producers at each price point:     $Q_{\text{market}}(P) = \sum_{j=1}^{m} Q_j(P)$

Market Equilibrium, Disequilibrium, and the Trading Locus

• Definition of Market Equilibrium:

  • Market equilibrium occurs at the price $P^*$ and quantity $Q^*$ where quantity demanded equals quantity supplied ($Q_d(P^*) = Q_s(P^*)$).

  • At equilibrium, all buyers and sellers are able to execute their desired transactions, producing a stable condition with no internal pressure to change.

• Disequilibrium Dynamics:

  • Excess Supply (Surplus): Occurs when market price lies above equilibrium ($P > P^*$).

  • Excess Supply equation:       $\text{Excess Supply}(P) = Q_s(P) - Q_d(P) > 0$

  • At $P = \$8$ in the discrete lobster market, $Q_s = 4,000$ and $Q_d = 2,000$, producing an excess supply of $2,000\,\text{lobsters}$.

  • Dissatisfied sellers lower prices to clear unsold inventory, pushing price down toward $P^*$.

  • Excess Demand (Shortage): Occurs when market price lies below equilibrium ($P < P^*$).

  • Excess Demand equation:       $\text{Excess Demand}(P) = Q_d(P) - Q_s(P) > 0$

  • At $P = \$4$ in the discrete lobster market, $Q_d = 4,000$ and $Q_s = 2,000$, producing an excess demand of $2,000\,\text{lobsters}$.

  • Unserved buyers bid up prices to secure limited goods, driving price up toward $P^*$.

• The Trading Locus:

  • In unadjusted or price-regulated disequilibrium markets, the volume of actual executed market transactions is constrained by the short side of the market:     $\text{Quantity Transacted}(P) = \min\left[Q_d(P), Q_s(P)\right]$

Economic Surplus, Consumer and Producer Surplus, and Welfare Optimality

• Definitions of Economic Surplus:

  • Consumer Surplus (CS): The net benefit gained by consumers, calculated as willingness to pay minus market price paid:     $\text{CS} = V_i - P$

  • Producer Surplus (PS): The net benefit gained by producers, calculated as market price received minus marginal production cost:     $\text{PS} = P - C_i$

  • Total Economic Surplus (TES): The total net economic gain generated by trade:     $\text{TES} = \text{CS} + \text{PS} = V_i - C_i$

• Continuous Calculation of Surplus (Integration):

  • For continuous demand $P_d(Q)$ and supply $P_s(Q)$ functions:     $\text{CS} = \int_{0}^{Q^*} \left(P_d(Q) - P^*\right) dQ$     $\text{PS} = \int_{0}^{Q^*} \left(P^* - P_s(Q)\right) dQ$     $\text{TES} = \int_{0}^{Q^*} \left(P_d(Q) - P_s(Q)\right) dQ$

• Worked Numerical Problem (Linear Model):

  • Demand function: $P_d = 13 - Q_d$

  • Supply function: $P_s = 1 + Q_s$

  • Equilibrium Calculation:     $13 - Q^* = 1 + Q^* \implies 2Q^* = 12 \implies Q^* = 6, \quad P^* = 7$

  • Surplus Computations:     $\text{TES} = \frac{1}{2} \times (13 - 1) \times 6 = 36$     $\text{CS} = \frac{1}{2} \times (13 - 7) \times 6 = 18$     $\text{PS} = \frac{1}{2} \times (7 - 1) \times 6 = 18$

• Social Optimality of Market Equilibrium:

  • A social central planner seeking to maximize total economic surplus continues expanding production as long as marginal benefit $MB(Q)$ exceeds marginal cost $MC(Q)$.

  • The surplus-maximizing output point occurs where $MB(Q) = MC(Q)$, which coincides with competitive market equilibrium ($P_d(Q) = P_s(Q)$).

  • Producing less than $Q^*$ forfeits potential surplus gains; producing more than $Q^*$ creates deadweight loss because $MC(Q) > MB(Q)$.

  • Social Surplus Conditions: Market surplus reflects true social welfare if and only if all production costs are borne by sellers and all consumption benefits accrue to buyers.

Fundamentals of Price Elasticity of Demand

• Definition of Price Elasticity of Demand:

  • A measure of the responsiveness of the quantity demanded of a good to a change in its price.

  • Defined mathematically as the percentage change in quantity demanded divided by the percentage change in price:     $\eta = \frac{\%\Delta Q^d}{\%\Delta P}$

• Elasticity Classification Categories:

  • Perfectly Elastic: $\eta = -\infty$

  • Elastic: $-\infty < \eta < -1$ (or $|\eta| > 1$)

  • Unitary Elastic: $\eta = -1$ (or $|\eta| = 1$)

  • Inelastic: $-1 < \eta < 0$ (or $|\eta| < 1$)

  • Perfectly Inelastic: $\eta = 0$

• Calculation Formulas:

  • Standard Percentage Formula:     $\%\Delta Q = \frac{Q_1 - Q_0}{Q_0} \times 100\%, \quad \%\Delta P = \frac{P_1 - P_0}{P_0} \times 100\%$

  • Mid-Point Formula (Arc Elasticity):

  • Eliminates directional asymmetry when computing elasticity between two points $(P_0, Q_0)$ and $(P_1, Q_1)$:       $\eta = \frac{\frac{Q_1 - Q_0}{(Q_0 + Q_1)/2}}{\frac{P_1 - P_0}{(P_0 + P_1)/2}} = \frac{Q_1 - Q_0}{P_1 - P_0} \times \frac{(P_0 + P_1)/2}{(Q_0 + Q_1)/2}$

  • Point Price Elasticity Formula:

  • Evaluates elasticity at a single point $(P, Q)$ along the demand curve:       $\eta = \lim_{\Delta P \to 0} \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} = \frac{dQ}{dP} \times \frac{P}{Q} = \frac{1}{\text{Slope}} \times \frac{P}{Q}$

• Worked Example: Oil Price and Demand Changes:

  • Price rises from $\$100$ to $\$110$ per barrel; quantity falls from $100$ to $95\,\text{trillion barrels}$.

  • Using initial point ($\text{Old} = 100$):       $\eta = \frac{(95 - 100)/100}{(110 - 100)/100} = \frac{-5\%}{10\%} = -0.5$

  • Price falls from $\$110$ to $\$100$; quantity rises from $95$ to $100\,\text{trillion barrels}$ ($\text{Old} = 110$):       $\eta = \frac{(100 - 95)/95}{(100 - 110)/110} = \frac{5.26\%}{-9.09\%} = -0.579$

  • Applying the Mid-Point Formula:       $\eta = \frac{(95 - 100)/97.5}{(110 - 100)/105} = \frac{-5.13\%}{9.52\%} = -0.538 \quad (|\eta| = 0.538)$

• Point Elasticity along a Linear Demand Curve:

  • For a linear demand curve $P = a - bQ$, the slope $\frac{dP}{dQ} = -b$ is constant, but elasticity $\eta = -\frac{1}{b} \times \frac{P}{Q}$ varies at every point:

  • Top half ($P > \frac{a}{2}$): Elastic ($\eta < -1$).

  • Midpoint ($P = \frac{a}{2}, Q = \frac{b}{2}$): Unitary Elastic ($\eta = -1$).

  • Bottom half ($P < \frac{a}{2}$): Inelastic ($-1 < \eta < 0$).

  • Vertical Intercept ($Q=0$): $\eta \to -\infty$.

  • Horizontal Intercept ($P=0$): $\eta = 0$

• Point Elasticity Comparison at an Intersection Point:

  • If two demand curves $D_1$ and $D_2$ intersect at a common point $(P, Q)$, the flatter curve (smaller absolute slope) is more elastic than the steeper curve:     $\text{slope}_1 > \text{slope}_2 \implies |\eta_1| < |\eta_2|$

Revenue, Expenditure, and Elasticity Dynamics

• Total Revenue / Expenditure Relationship:

  • Total Revenue ($TR$) earned by sellers equals Total Expenditure ($TE$) spent by buyers:     $\text{TR} = \text{TE} = P \times Q$

• Elasticity and Revenue Responses to Price Changes:

  • Elastic Demand ($|\eta| > 1$):

  • Price increase ($P \uparrow$) $\implies$ Quantity decrease ($Q \downarrow\downarrow$) $\implies$ Total Revenue decreases ($TR \downarrow$).

  • Price reduction ($P \downarrow$) $\implies$ Quantity increase ($Q \uparrow\uparrow$) $\implies$ Total Revenue increases ($TR \uparrow$).

  • Inelastic Demand ($|\eta| < 1$):

  • Price increase ($P \uparrow$) $\implies$ Quantity decrease ($Q \downarrow$) $\implies$ Total Revenue increases ($TR \uparrow$).

  • Price reduction ($P \downarrow$) $\implies$ Quantity decrease ($Q \uparrow$) $\implies$ Total Revenue decreases ($TR \downarrow$).

  • Unitary Elastic Demand ($|\eta| = 1$):

  • Total revenue is maximized at the midpoint of a linear demand curve, where a price change produces an offsetting percentage change in quantity demanded.

• The Paradox of Agricultural Productivity:

  • Technological advancements expand crop yields, shifting agricultural supply rightward.

  • Because demand for basic agricultural food products is price inelastic, the resulting decline in market price reduces total agricultural sector revenues.

  • Unimproved, higher-cost farmers are forced out of business because revenue falls below operating costs.

• Narcotics Prohibition and Enforcement:

  • Illegal drug demand is highly price inelastic.

  • Law enforcement interventions reduce drug supply, shifting the supply curve leftward and increasing drug prices dramatically.

  • Due to inelastic demand, higher drug prices increase total supplier revenues, providing high profits that incentivize traffickers to develop concealment methods (e.g., drug-smuggling submarines).

Determinants of Price Elasticity of Demand

• Availability of Close Substitutes (Fundamental Determinant):

  • Goods with abundant substitutes exhibit high demand elasticity because consumers easily switch brands or products when price increases (e.g., green peas $\eta = -2.80$).

  • Goods with few substitutes exhibit low elasticity (e.g., coffee $\eta = -0.25$, theater/opera $\eta = -0.18$).

  • Patent Expiry and Generics: When a drug patent expires and five identical generic substitutes enter the market, the demand for the brand-name drug becomes substantially more elastic.

• Time Horizon:

  • Demand is more inelastic in the short run because consumers require time to adjust habits and discover substitutes.

  • Demand becomes more elastic in the long run as consumers adapt choices and technological alternatives develop.

• Product Category Definition (Broad vs. Narrow):

  • Broad product categories (e.g., "food") have few substitutes and are highly inelastic.

  • Narrowly defined product categories (e.g., "green peas" or "Chiquita bananas") have many substitutes and are highly elastic.

• Necessities versus Luxuries:

  • Necessities (e.g., basic electricity $\eta = -1.20$) are inelastic.

  • Luxuries (e.g., restaurant meals $\eta = -1.63$ or foreign air travel $\eta = -0.77$) are more elastic.

• Share of Consumer Budget:

  • Goods representing a small fraction of a consumer's total budget exhibit low price elasticity.

  • Goods representing a large expenditure relative to total income exhibit high price elasticity.

Other Elasticities of Demand: Income and Cross-Price

• Cross-Price Elasticity of Demand:

  • Measures the percentage change in the quantity demanded of good $x$ resulting from a percentage change in the price of good $y$:     $\eta_{xy} = \frac{\%\Delta Q_x^d}{\%\Delta P_y} = \frac{\Delta Q_x^d / Q_x^d}{\Delta P_y / P_y}$

  • Substitutes: $\eta_{xy} > 0$ (An increase in the price of milk increases the demand for soy milk).

  • Complements: $\eta_{xy} < 0$ (An increase in the price of coffee decreases the demand for donuts).

• Income Elasticity of Demand:

  • Measures the percentage change in the quantity demanded of good $x$ resulting from a percentage change in consumer income $I$:     $\eta_I = \frac{\%\Delta Q_x^d}{\%\Delta I} = \frac{\Delta Q_x^d / Q_x^d}{\Delta I / I}$

  • Normal Goods: $\eta_I > 0$ (Demand increases as income increases).

  • Luxury Goods: $\eta_I > 1$ (Demand increases disproportionately as income rises).

  • Inferior Goods: $\eta_I < 0$ (Demand decreases as income rises).

• Log-Linear Empirical Demand Functions:

  • In a constant-elasticity log-linear regression specification:     $\ln\left(Q_x^d\right) = 1000 - 0.5\ln\left(P_x\right) + 1.2\ln\left(P_y\right) - 3.4\ln\left(P_z\right) - 0.2\ln(I) + v$

  • The estimated coefficients represent constant elasticities directly:

  • Own-Price Elasticity of Demand: $\eta_{xx} = -0.5$ (Inelastic).

  • Cross-Price Elasticity with respect to Good $y$: $\eta_{xy} = +1.2 \implies$ Good $y$ is a substitute for good $x$.

  • Cross-Price Elasticity with respect to Good $z$: $\eta_{xz} = -3.4 \implies$ Good $z$ is a complement to good $x$.

  • Income Elasticity of Demand: $\eta_I = -0.2 \implies$ Good $x$ is an inferior good.

Price Elasticity of Supply and Its Determinants

• Definition of Price Elasticity of Supply:

  • Measures the responsiveness of the quantity supplied of a good to a change in its market price:     $\eta_s = \frac{\%\Delta Q^s}{\%\Delta P} = \frac{dQ^s}{dP} \times \frac{P}{Q} = \frac{1}{\text{Slope}} \times \frac{P}{Q}$

• Classification Categories for Supply Elasticity:

  • Perfectly Elastic Supply: $\eta_s = \infty$ (Horizontal supply line; constant marginal cost).

  • Elastic Supply: $1 < \eta_s < \infty$

  • Unitary Elastic Supply: $\eta_s = 1$ (Any linear supply curve passing directly through the origin has $\eta_s = 1$ at all points).

  • Inelastic Supply: $0 < \eta_s < 1$

  • Perfectly Inelastic Supply: $\eta_s = 0$ (Vertical supply line, such as land in Central, Hong Kong).

• Determinants of Price Elasticity of Supply:

  • Flexibility of Per-Unit Production Costs (Fundamental Determinant): If marginal cost rises steeply as output expands, supply is inelastic; if marginal cost stays flat, supply is elastic.

  • Time Horizon: Short-run supply is constrained by existing plant capacity (inelastic); long-run supply is elastic as firms build new factories and enter the industry.

  • Share of Input Markets: If an industry uses a small fraction of total available inputs, expanding production does not bid up input prices, resulting in elastic supply.

  • Geographic Scope: Broad geographic scope restricts external input borrowing, making supply less elastic; narrow local scope allows drawing supply from outside regions, increasing local elasticity.

Policy Applications: Taxes, Prohibitions, Buybacks, and Regulations

• Sudan Slave Redemption Program Analysis:

  • A program aimed at redeeming enslaved individuals by purchasing their freedom increases total slave demand.

  • Under Perfectly Inelastic Supply: Slave redemption increases price (\15 \to \$50$) without increasing the equilibrium quantity of individuals captured, freeing $800$ slaves net.

  • Under Elastic Supply: The demand increase raises price (\15 \to \$30$) and expands quantity captured from $1,000$ to $2,200$. Total redeemed = $1,600$, but net freed = $400$, resulting in $600$ additional people captured into slavery.

• Municipal Gun Buyback Programs:

  • A city government (e.g., Washington, D.C.) offers $\$84$ to buy back old firearms, shifting local demand rightward.

  • Because guns flow easily across city borders, local supply is perfectly elastic.

  • Result: Quantity traded increases from $1,000$ to $6,000$ guns, but local gun prices and street quantities remain unaffected, rendering local buybacks ineffective unless executed on a national level.

• Ethiopian Food Aid Policy Example:

  • Western aid agencies promise to donate $500\,\text{tons}$ of grain next year.

  • Expected future supply increases, lowering anticipated market price ($P' < P$).

  • Anticipating lower market prices, domestic Ethiopian farmers reduce seed planting today, decreasing domestic grain supply and producer surplus.

  • Domestic producers oppose food donations, while domestic consumers support them.

• Hong Kong Taxi Regulation Analysis:

  • Taxi fares $P$ and medallion quantities ($18,138$ licenses capped since 1994) are fixed by government regulation.

  • Recession ($D_1$): Regulated fare creates excess supply. Drivers queue for hours at the airport and offer illicit fare rebates.

  • Economic Boom ($D_2$): Regulated fare creates excess demand (shortage). Taxis are difficult to hail, and driver service quality deteriorates.

• Tradable Immigration Vouchers (Gary Becker Proposal):

  • To manage immigration costs without arbitrary quotas, governments can issue tradable immigration vouchers or levy fees.

  • Assigning vouchers to residents allows citizens to sell vouchers at market prices $P$, allocating immigration rights to non-residents with the highest Willingness to Pay ($\text{WTP}$).

Comparative Statics: Shifts in Demand and Supply

• Summary Rules for Single Curve Shifts:

  • Demand Shift Only:

  • Demand Increase ($D \uparrow$) $\implies P^* \uparrow, Q^* \uparrow$

  • Demand Decrease ($D \downarrow$) $\implies P^* \downarrow, Q^* \downarrow$

  • Supply Shift Only:

  • Supply Increase ($S \uparrow$) $\implies P^* \downarrow, Q^* \uparrow$

  • Supply Decrease ($S \downarrow$) $\implies P^* \uparrow, Q^* \downarrow$

• Simultaneous Curve Shifts:

• Inference Rules from Market Observations:

  • Observing $P \uparrow$ and $Q \downarrow$ $\implies$ Infer a leftward Supply Shift ($S \downarrow$).

  • Observing $P \uparrow$ and $Q \uparrow$ $\implies$ Infer a rightward Demand Shift ($D \uparrow$).

Empirical Estimation and Mathematical Formulations

• Quick Prediction Formulas for Price Changes:

  • Price Change from a Demand Shift (Magnitude $\%\Delta Q_{\text{shift}}$):     $\%\Delta P = \frac{\%\Delta Q_{\text{shift}}}{\eta_s + |\eta_d|}$

  • Price Change from a Supply Shift (Magnitude $\%\Delta Q_{\text{shift}}$):     $\%\Delta P = -\frac{\%\Delta Q_{\text{shift}}}{\eta_s + |\eta_d|}$

• Worked Exam Problem (2020 Fall Final Exam):

  • Given Parameters:

  • Price elasticity of demand $\eta_d = -0.6$

  • Price elasticity of supply $\eta_s = 1.79$

  • Demand shifts leftward by $3\%$ ($\%\Delta Q_{\text{shift}} = -3\%$

  • Step 1: Calculate Percentage Change in Equilibrium Price:     $\%\Delta P^* = \frac{-3\%}{1.79 + |-0.6|} = \frac{-3\%}{2.39} = -1.255\%$

  • Step 2: Calculate Percentage Change in Equilibrium Quantity:     $\%\Delta Q^* = \eta_s \times \%\Delta P^* = 1.79 \times (-1.255\%) = -2.246\%$

  • Final Result: Equilibrium price decreases by $1.255\%$, and equilibrium quantity decreases by $2.246\%$.