Comprehensive Study Notes: ECON 1B03 Units 5-8

Unit 5: Elasticity

• Foundational Concept of Elasticity:

  • Elasticity quantifies how strongly economic buyers and sellers respond to changes in price, income, or the price of related goods.

  • It standardizes economic responsiveness into a unit-free numerical metric by evaluating the ratio of percentage changes rather than absolute changes or slopes.

• What Elasticity Measures:

  • Demand Curve Fundamentals: A demand curve plots quantity demanded ($Q$) on the horizontal axis against price ($P$) on the vertical axis. Following the law of demand, it slopes downward: as price declines, quantity demanded increases.

  • Change in Quantity Demanded vs. Change in Demand:

  • Change in Quantity Demanded: Movement along a single demand curve caused exclusively by a change in the good's own price.

  • Change in Demand: A shift of the entire demand curve ($D$ to $D'$) caused by external factors such as changes in consumer income, tastes, expectations, or prices of related goods.

  • Curvature of Real-World Curves: Linear demand curves are frequently drawn for pedagogical simplicity, but real-world demand curves frequently bend. Elasticity measures must therefore operate consistently on both linear and non-linear demand schedules.

• Slope versus Elasticity`:

  • The slope of a demand curve is defined by units of measurement (e.g., measuring quantity in grams versus kilograms, single units versus dozens; measuring price in dollars versus cents alters the numerical slope value by orders of magnitude).

  • Percentage changes are entirely independent of units: a $10\%$ increase in soda consumption remains a $10\%$ increase regardless of physical packaging.

  • Slope does not equal elasticity, although the two values are mathematically interrelated.

• Empirical Application of Elasticity Beyond Prices:

  • In a Danish DNA database empirical investigation, a $1\%$ increase in the probability of apprehending an offender reduced crime by more than $2\%$, representing an elasticity of crime with respect to detection likelihood of approximately $-2$.

• Governing Rules and Formulas:     $\text{Elasticity} = \frac{\%\,\Delta \text{ in quantity demanded}}{\%\,\Delta \text{ in factor being examined}}$     $\text{Price Elasticity of Demand} = \frac{\%\,\Delta \text{ in quantity demanded}}{\%\,\Delta \text{ in price}}$

• Worked Examples:

  • Cheerios: If a $10\%$ price increase causes boxes demanded to fall by $25\%$, price elasticity of demand is:       $\frac{-25\%}{10\%} = -2.5$

  • Rye Grain Bushels (Units Invariance): Price falls from \\$3 to \\$2 ($\Delta P = -\$1$), while sales increase from $8\text{ million}$ to $12\text{ million bushels}$ ($\Delta Q = 4\text{ million}$).

    • Measured in single bushels: $\frac{\Delta Q}{\Delta P} = \frac{4{,}000{,}000}{-1} = -4{,}000{,}000$ .

    • Measured in millions of bushels: $\frac{\Delta Q}{\Delta P} = \frac{4}{-1} = -4$.

    • In both cases, the percentage change in quantity is $40\%$, the percentage change in price is $-40\%$, and the price elasticity of demand is precisely $-1$.

  • Soda Tax Metric Scaling: A price increase of \\$1 on soda decreases sales from $10.2\text{ million}$ to $10.1\text{ million bottles}$. The slope ratio is $-0.1$ in dollars and millions of bottles, $-0.001$ in cents and millions, $-100$ in dollars and thousands, and $-1$ in cents and thousands, yet elasticity remains identical.

• Analytical Traps and Warnings:

  • Quantity is placed in the numerator and price in the denominator. Inverting them yields $-0.4$ instead of $-2.5$.

  • Stating "elasticity equals the slope of the demand curve" is c Dategorically false.

  • Using the phrasing "percent change in demand from a $1\%$ price change" is inaccurate; the correct economic term is "change in quantity demanded."

• Direct Applications and Checks:

  • If price falls by $20\%$ and quantity demanded rises by $10\%$, price elasticity of demand is $\frac{10\%}{-20\%} = -0.5$.

  • Re-measuring price in cents instead of dollars alters the slope by a factor of $100$, but leaves elasticity unchanged.

  • Economists reject slope as a measure of responsiveness because slope is sensitive to arbitrary units of measurement.

  • The Midpoint Formula:

• The Inherent Flaw in Simple Percentage Calculations:

  • Standard percentage changes depend on the chosen base value.

  • Moving from \\$1.50 to \\$1.35 is a $-10\%$ change ($\frac{-0.15}{1.50}$), but moving from \\$1.35 to \\$1.50 is an $11.1\%$ change ($\frac{+0.15}{1.35}$).

  • The midpoint formula averages starting and ending values to guarantee a single, invariant elasticity measure across any two points regardless of direction.

• Mathematical Formulation:     $\text{Price Elasticity of Demand} = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$

• Worked Example (Retail Bottled Coca-Cola):

  • Baseline daily sales: $1000\text{ bottles}$ of 2-litre Coca-Cola at \\$1.50. Proposed price cut to \\$1.35.

  • Demand Curve $D_1$: Sales rise to $1200\text{ bottles}$.       $\%\,\Delta Q = \frac{1200 - 1000}{(1000 + 1200)/2} = \frac{200}{1100} \approx 18.18\%$       $\%\,\Delta P = \frac{1.35 - 1.50}{(1.50 + 1.35)/2} = \frac{-0.15}{1.425} \approx -10.53\%$       $\text{Elasticity} = \frac{18.18\%}{-10.53\%} \approx -1.73 \quad (\text{Elastic})$

  • Demand Curve $D_2$: Sales rise only to $1050\text{ bottles}$.       $\%\,\Delta Q = \frac{1050 - 1000}{(1000 + 1050)/2} = \frac{50}{1025} \approx 4.88\%$       $\text{Elasticity} = \frac{4.88\%}{-10.53\%} \approx -0.46 \quad (\text{Inelastic})$

  • Method Comparison on $D_1$:

    • Simple percentage cutting price: $\frac{+20.00\%}{-10.00\%} = -2.00$.

    • Simple percentage raising price: $\frac{-16.67\%}{+11.11\%} = -1.50$.

    • Midpoint method: $\frac{+18.18\%}{-10.53\%} = -1.73$.

• Analytical Traps and Warnings:

  • Never divide by the initial value; always divide by the average of the two endpoints.

  • Ensure index matching: if $Q_2$ represents the new quantity, $P_2$ must represent the new price. A positive calculated price elasticity of demand indicates index misalignment.

• Direct Applications and Checks:

  • If price drops from \\$1.50 to \\$1.30 and sales rise from $2000$ to $2500$:       $\%\,\Delta Q = \frac{500}{2250} \approx 22.22\%$       $\%\,\Delta P = \frac{-0.20}{1.40} \approx -14.29\%$       $\text{Elasticity} = \frac{22.22\%}{-14.29\%} \approx -1.56$

  • Hot dog stand selling $30$ at \\$3 cuts price to \\$2 and sells $60$:       $\%\,\Delta Q = \frac{30}{45} = 66.67\%$       $\%\,\Delta P = \frac{-1}{2.50} = -40\%$       $\text{Elasticity} = \frac{66.67\%}{-40\%} \approx -1.67$       If it sells only $40$:       $\%\,\Delta Q = \frac{10}{35} \approx 28.57\%$       $\text{Elasticity} = \frac{28.57\%}{-40\%} \approx -0.71$

  • Classification of Price Elasticity of Demand:

• Classification Thresholds:

  • Inelastic: Absolute value between $0$ and $1$ ($0 > E > -1$). The percentage change in quantity demanded is smaller than the percentage change in price.

  • Unit Elastic: Absolute value exactly equal to $1$ ($E = -1$). Percentage change in quantity equals percentage change in price.

  • Elastic: Absolute value strictly greater than $1$ ($E < -1$). Percentage change in quantity is greater than the percentage change in price.

• Sign Convention and Terminology:

  • Because price and quantity demanded move in opposite directions, price elasticity of demand is fundamentally negative.

  • Economists frequently drop the negative sign and communicate in absolute terms: "an elasticity of $3$" represents $-3$.

  • "More elastic" or "larger elasticity" refers to values further away from zero ($-3$ is more elastic than $-2$).

• Worked Comparative Example ($10\%$ Price Cut Across Goods):

  • Bagels: $-10\%\, P$, $+20\%\, Q \implies E = -2.00$ (Elastic).

  • Good X: $-10\%\, P$, $+10\%\, Q \implies E = -1.00$ (Unit elastic).

  • Wheat: $-10\%\, P$, $+5\%\, Q \implies E = -0.50$ (Inelastic).

• Analytical Traps and Warnings:

  • Inelastic demand does not mean quantity demanded is static; consumers still purchased $5\%$ more wheat, but reacted less than the price fell.

• Direct Applications and Checks:

  • Comparing $-1.5$ and $-0.8$, $-1.5$ is more elastic ($|-1.5| > |-0.8|$).

  • If a $10\%$ price rise cuts soda consumption in Chile by $13.7\%$, elasticity is $\frac{-13.7\%}{10\%} = -1.37$, which is elastic.

  • If elasticity is $-0.3$ and price rises, quantity falls by a smaller percentage than price rose.

  • Elasticity Changes Along a Linear Demand Curve:

• Mechanical Principle: Along any linear, downward-sloping demand curve, the slope ($\frac{\Delta P}{\Delta Q}$) is constant, but elasticity is not.

• Upper Region: High prices and low quantities mean that a given absolute price reduction represents a small percentage change in price, while the corresponding absolute quantity increase represents a large percentage change in quantity. Hence, $|E| > 1$ (Elastic).

• Lower Region: Low prices and large quantities mean that the same absolute price reduction represents a large percentage change in price, while the quantity increase represents a small percentage change in quantity. Hence, $|E| < 1$ (Inelastic).

• Midpoint: Exactly midway along a linear demand curve running from axis to axis, demand is unit elastic ($|E| = 1$).

• Intersecting Curves Rule: When two demand curves intersect at a common coordinate, the flatter curve (smaller slope in absolute value) is more elastic at that intersection point than the steeper curve.

• Worked Numerical Example ($P = 100 - 2Q_D$):

  • Coordinate derivation: $Q = \frac{100 - P}{2}$.

    • At P = \\$80, $Q = 10$. At P = \\$76, $Q = 12$.

    • At P = \\$52, $Q = 24$. At P = \\$48, $Q = 26$.

    • At P = \\$30, $Q = 35$. At P = \\$26, $Q = 37$.

  • Range \80 \rightarrow \$76$: $\frac{2/11}{-4/78} = \frac{18.18\%}{-5.13\%} = -3.54$ (Elastic).

  • Range \52 \rightarrow \$48$: $\frac{2/25}{-4/50} = \frac{8.00\%}{-8.00\%} = -1.00$ (Unit elastic).

  • Range \30 \rightarrow \$26$: $\frac{2/36}{-4/28} = \frac{5.56\%}{-14.29\%} = -0.39$ (Inelastic).

  • Exact midpoint: P = \\$50, $Q = 25$.

• Direct Applications and Checks:

  • For $P = 260 - 3Q$ between \\$170 and \\$155: Quantities are $30$ and $35$. Midpoint elasticity evaluates to elastic.

  • For $P = 260 - 3Q$ between \\$50 and \\$35: Quantities are $70$ and $75$. Midpoint elasticity evaluates to inelastic.

  • On $P = 100 - 2Q$, the unit elastic point occurs where P = \\$50 and $Q = 25$.

  • Non-Plug-and-Play Elasticity Problems:

• Algebraic Manipulations:     $\%\,\Delta Q = \text{Elasticity} \times \%\,\Delta P$     $\%\,\Delta P = \frac{\%\,\Delta Q}{\text{Elasticity}}$

• "Times as Many" Multipliers: Selling $6.5\text{ times as many}$ means output increased from an index of $1$ to $6.5$. This constitutes an increase of $5.5$, or a $+550\%$ change, not $+650\%$.

• Ceteris Paribus Requirements:

  • Elasticity calculations mandate moving along an unshifted demand curve.

  • If market demand shifts concurrently (e.g., Valentine's Day roses, income changes, promotional advertising), quantity changes cannot isolate price responsiveness.

• Worked Example (Gasoline Tax Policy):

  • Parameters: Long-run price elasticity of demand = $-0.55$. Baseline price = \\$3.00, baseline annual sales = $140\text{ billion gallons}$. A \\$1.00 per-gallon tax raises the consumer pump price by \\$0.70 to \\$3.70.

  • Step 1: Percentage change in price:       $\%\,\Delta P = \frac{0.70}{(3.00 + 3.70)/2} = \frac{0.70}{3.35} \approx 20.9\%$

  • Step 2: Percentage change in quantity demanded:       $\%\,\Delta Q = -0.55 \times 20.9\% \approx -11.5\% \quad (\text{or } -0.11\text{ rounded})$

  • Step 3: Solve for $Q_2$ via midpoint formula:       $\frac{Q_2 - 140}{(140 + Q_2)/2} = -0.11$       $Q_2 - 140 = -0.055(140 + Q_2) = -7.7 - 0.055Q_2$       $1.055Q_2 = 132.3 \implies Q_2 \approx 125.4\text{ billion gallons}$

  • Step 4: Calculate total tax revenue:       $\text{Tax Revenue} = \\$1.00 \times 125.4\text{ billion} = \\$125.4\text{ billion}$

• Direct Applications and Checks:

  • Cigarette demand elasticity is $-0.25$ with $360\text{ billion}$ units bought annually. A tax raising price by $50\%$ causes quantity demanded to change by $-0.25 \times 50\% = -12.5\%$.

  • In the short run, gasoline elasticity is $-0.02$. Cutting quantity demanded by $1\%$ requires a price increase of $\frac{-1\%}{-0.02} = 50\%$.

  • Determinants of Price Elasticity of Demand:

• Availability of Close Substitutes: The single most critical determinant. Readily available substitutes increase buyer sensitivity ($|E|$ is larger). Absence of substitutes leaves consumers captive ($|E|$ closer to $0$).

• Passage of Time: Consumers require time to adjust behavior, reconfigure capital, or adopt alternatives. Demand is substantially more elastic over long horizons than short horizons.

• Luxuries versus Necessities: Necessities (e.g., home water, whole milk, bread) exhibit highly inelastic demand; luxuries (e.g., vacation travel, concert tickets) exhibit elastic demand.

• Definition of the Market: Broadly defined markets (e.g., food, all soft drinks) have virtually no substitutes and are highly inelastic. Narrowly defined markets (e.g., Coca-Cola, Post Raisin Bran) have extensive substitutes and are highly elastic.

• Share of the Consumer Budget: Goods consuming a large fraction of income (e.g., automobiles, housing) provoke intense price scrutiny and are elastic. Goods consuming an insignificant fraction (e.g., table salt) are highly inelastic.

• Empirical Estimates Table (Short-Run US Data):

  • Inelastic: Whole milk ($-0.04$), Gasoline ($-0.06$), Cigarettes ($-0.25$), Beer ($-0.29$), Chicken ($-0.37$), Water for home use ($-0.38$), Bread ($-0.40$), Uber in 4 cities ($-0.50$), Books from Amazon ($-0.60$), Health insurance for low income ($-0.65$), Skim milk ($-0.69$), Soda all brands ($-0.70$).

  • Elastic: Butter ($-1.13$), Grapes ($-1.18$), Coca-Cola ($-1.22$), E-cigarettes ($-1.28$), Beef ($-1.79$), New automobiles ($-1.95$), Post Raisin Bran ($-2.50$), Prego pasta sauce ($-2.90$), Tide liquid detergent ($-3.92$), Books from Barnes & Noble ($-4.00$).

• Case Application (Tesla): When competing automakers launched alternative electric vehicles, consumers gained close substitutes, demand for Tesla vehicles became more elastic, and Tesla implemented a $14\%$ price reduction on the Model 3 in early 2023.

  • Elasticity and Total Revenue:

• Total Revenue Definition: Total revenue ($TR$) equals price multiplied by quantity sold ($TR = P \times Q$). Graphically, it is the area of a rectangle of height $P$ and width $Q$ under the demand curve.

• Opposing Price Effects: A price cut lowers revenue per unit sold across existing sales, but expands the total volume of units sold.

• Mathematical Coordination Rules:

  • Elastic Demand ($|E| > 1$): Price and total revenue move in opposite directions. A price cut increases total revenue ($P \downarrow \implies TR \uparrow$).

  • Inelastic Demand ($|E| < 1$): Price and total revenue move in the same direction. A price rise increases total revenue ($P \uparrow \implies TR \uparrow$).

  • Unit Elastic Demand ($|E| = 1$): Total revenue is maximized; marginal changes in price leave total revenue unchanged.

• Worked Numerical Example ($P = 100 - 2Q$):

  • At $P = \\$80, Q = 10 \implies TR = \\$800$.

  • Price cut to P = \\$76, Q = 12 (Elastic, $E = -3.54$): Revenue lost on existing units = 10 \times \\$4 = \\$40. Revenue gained on new units = 2 \times \\$76 = \\$152. Net revenue increases to \\$912.

  • At $P = \\$30, Q = 35 \implies TR = \\$1050$.

  • Price cut to P = \\$26, Q = 37 (Inelastic, $E = -0.39$): Revenue lost on existing units = 35 \times \\$4 = \\$140. Revenue gained on new units = 2 \times \\$26 = \\$52. Net revenue falls to \\$962.

• Traps: Revenue is not profit. Profit accounts for production costs, whereas revenue completely ignores costs.

  • Real-World Revenue Applications (Taxes, Fines, and Corporate Strategy):

• Bethlehem, Pennsylvania Parking Fines: The city considered raising expired parking meter fines from \\$10 to \\$15, forecasting revenue to rise from \\$5.5\text{ million} to \\$5.9\text{ million}. This projection assumes inelastic demand. However, discouraging illegal parking requires elastic demand, whereas maximizing city revenue requires inelastic demand; these two objectives conflict.

• Municipal Soda Taxes:

  • Philadelphia implemented a tax of $1.5\text{ cents per ounce}$; San Francisco levied $2\text{ cents per ounce}$.

  • Newfoundland and Labrador instituted a tax of $20\text{ cents per litre}$ on September 1, 2022, projecting \\$10\text{ million} annually on $50\text{ million litres}$.

  • Cook County (Chicago) repealed its soda tax in 2017 after revenue fell short of projections because consumers possessed close geographic substitutes outside county borders.

• Market Symmetry of Taxes:

  • Imposing a \\$0.75 tax on a baseline market ($90{,}000\text{ units}$ at \\$1.75):

    • Inelastic demand: Price rises to \\$2.25, sales contract to $80{,}000$, tax yield = \\$60{,}000\text{ daily}.

    • Elastic demand: Price rises to \\$2.00, sales contract to $70{,}000$, tax yield = \\$52{,}500\text{ daily}.

• Corporate Pricing Decisions:

  • Apple iPhone: Sales volumes declined while total iPhone revenue increased, confirming demand was inelastic in that price corridor.

  • Walt Disney Parks: Theme park attendance fell by $17\%$ following price increases, yet theme park revenues hit record highs, proving inelastic demand.

  • Semiconductor Shortage in Automotive: Vehicle sales dropped by $15\%$ or more while automaker revenue increased, indicating inelastic demand during the supply contraction.

  • Procter & Gamble: Raised prices on Pampers and Bounty; because competitor brands concurrently raised prices, cross-brand substitution diminished, keeping demand inelastic.

  • Extreme Polar Cases of Demand:

• Perfectly Inelastic Demand:

  • Demand curve is vertical ($E = 0$). Quantity demanded is completely unresponsive to price changes.

  • Example: Insulin doses for diabetics or life-saving pharmaceuticals over relevant price ranges.

  • Revenue changes in direct, exact lockstep with price changes.

• Perfectly Elastic Demand (Infinitely Elastic):

  • Demand curve is horizontal ($E = \infty$).

  • Consumers purchase unlimited quantities at the market price ($P_1$), but if price increases by a fraction of a cent, quantity demanded collapses instantly to zero.

  • Income Elasticity of Demand:

• Formula and Definition: Measures the percentage change in quantity demanded relative to a percentage change in consumer income ($I$):     $E_I = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{I_2 - I_1}{(I_1 + I_2)/2}}$

• Classification of Goods:

  • Normal Good: $E_I > 0$ (quantity demanded increases with income).

    • Luxury Good: $E_I > 1$ (expenditure share rises; quantity changes faster than income).

    • Necessity Good: $0 < E_I \le 1$ (expenditure share falls; quantity changes slower than income).

  • Inferior Good: $E_I < 0$ (quantity demanded decreases with rising income; e.g., instant noodles, canned tuna, long-distance bus trips).

• Worked Example (Income Increases from \\$40{,}000 to \\$60{,}000 , $\%\,\Delta I = 40\%$):

  • Restaurant meals: $10 \rightarrow 20\text{ per month}$ ($+66.67\% \implies E_I = +1.67$, Luxury).

  • Bread: $10 \rightarrow 11\text{ loaves per month}$ ($+9.52\% \implies E_I = +0.24$, Necessity).

  • Instant noodles: $20 \rightarrow 14\text{ packs per month}$ ($-35.29\% \implies E_I = -0.88$, Inferior).

  • Cross-Price Elasticity of Demand:

• Formula and Definition: Evaluates the responsiveness of quantity demanded for Good A following a price change in Good B:     $E_{AB} = \frac{\%\,\Delta Q_A}{\%\,\Delta P_B} = \frac{\frac{Q_{2,A} - Q_{1,A}}{(Q_{1,A} + Q_{2,A})/2}}{\frac{P_{2,B} - P_{1,B}}{(P_{1,B} + P_{2,B})/2}}$

• Relational Classifications:

  • Substitutes: $E_{AB} > 0$. A price increase in B diverts purchasing toward A (e.g., Coke and Pepsi, beef and chicken).

  • Complements: $E_{AB} < 0$. A price increase in B depresses demand for both products (e.g., hot dogs and buns, smartphones and software apps).

  • Unrelated (Independent): $E_{AB} = 0$.

• Empirical Beverage Scanner Data:

  • Beer own-price elasticity: $-0.30$ (Inelastic).

  • Beer cross-price with wine: $-0.83$ (Complements in consumer scanner baskets).

  • Beer cross-price with spirits: $-0.50$ (Complements).

  • Beer income elasticity: $+0.09$ (Normal necessity).

  • Case Study: The Disappearing Family Farm:

• Historical Trajectory in Canada: In 1931, Canada possessed $728{,}623\text{ farms}$ representing $31.7\%$ of the population. By 2021, the farm count contracted to $189{,}874$, housing approximately $2\%$ of the population.

• The Economic Paradox:

  • Massive productivity advances and mechanization shifted wheat market supply aggressively to the right.

  • Agricultural food products exhibit a low income elasticity of demand (demand shifts right only minutely as population wealth grows).

  • Agricultural food products exhibit highly inelastic price elasticity of demand.

  • The massive supply shift coupled with inelastic demand forces a catastrophic plunge in commodity prices ($14\text{ million tonnes}$ at inflation-adjusted \\$535/\text{tonne} in 1960 vs. $35\text{ million tonnes}$ at \\$298/\text{tonne} in 2024).

  • Total farm revenues fall, forcing all but the largest, most technologically efficient operations into consolidation or insolvency.

  • Price Elasticity of Supply:

• Definition and Mechanics: Measures the percentage change in quantity supplied relative to the percentage change in product price:     $E_S = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$

• Supply Curve Elasticity Dynamics: Price elasticity of supply is positive due to upward-sloping supply curves. Along a standard upward-sloping supply schedule, the lower segment is elastic ($E_S > 1$), transitioning through unit elasticity ($E_S = 1$) to an inelastic upper segment ($E_S < 1$ ) as capacity constraints take hold.

• Worked Example (Commercial Bakery Loaves per Day):

  • Price range $\\$2 \rightarrow \\$4$, $Q_S$ expands $100 \rightarrow 300$: $\frac{100.00\%}{66.67\%} = 1.50$ (Elastic).

  • Price range $\\$4 \rightarrow \\$6$, $Q_S$ expands $300 \rightarrow 450$: $\frac{40.00\%}{40.00\%} = 1.00$ (Unit elastic).

  • Price range $\\$6 \rightarrow \\$8$, $Q_S$ expands $450 \rightarrow 500$: $\frac{10.53\%}{28.57\%} = 0.37$ (Inelastic).

• Determinants of Supply Elasticity:

  • Availability of Inputs: Readily accessible inputs permit rapid output expansions (elastic); scarce or fixed inputs create inelastic supply.

  • Passage of Time: The primary determinant. In the immediate run, capacity is fixed. Over longer horizons, facilities expand, equipment is procured, and supply becomes highly elastic.

• Global Commodity Dynamics (Crude Oil Swings):

  • Both the short-run demand and short-run supply of crude oil are extraordinarily inelastic (no immediate substitutes; years required to locate and drill new fields).

  • 2009–2011: Global demand increased by less than $5\%$ ($85\text{ to } 89\text{ million barrels/day}$), driving prices up by $175\%$ from \\$40 to \\$110.

  • 2011–2019: Hydraulic fracturing (fracking) in the US and Canada raised US output from $5.6\text{ to } 12.3\text{ million barrels/day}$, expanding supply to $102\text{ million barrels/day}$ and plunging price from \\$110 to \\$56.

  • Inelastic curves turn minor quantity shocks into immense price volatility ($\$64$ in Jan 2020 down to \\$18 in April 2020; up to \\$122 in June 2022 following the Russian invasion of Ukraine, down to \\$80 by early 2023).

Unit 6: Consumer Choice

• Foundations of Consumer Value and Budgets:

  • The Fundamental Economic Assertion: Rational consumers select the specific bundle of commodities that maximizes total satisfaction subject to the limits of an available budget constraint.

  • Determinants of Willingness to Purchase:

  • Natural Desire: The personal affinity for a commodity; the most critical factor.

  • Relative Value: Valuation compared to all competing consumer goods.

  • Available Income: The ultimate constraint dictating purchasing limits.

  • Components of the Available Budget:

  • Current earnings from labor, investments, or gifts.

  • Accumulated savings (dissaving allows spending to exceed current income).

  • Borrowing capacity (creates legal debt obligations requiring future consumption to sit below income).

  • Duality of Economic Value:

  • Subjective: Valuations vary fundamentally across unique individuals (explains downward slope of demand curves as lower-valuing buyers enter at lower prices).

  • Relative: Value depends on current asset holdings and the array of alternative goods available.

• Theory of Utility:

  • Utilitarian Roots: Utility denotes the subjective pleasure, satisfaction, or benefit acquired from consumption, conceptualized by philosophers Jeremy Bentham and John Stuart Mill. Though early economists postulated a cardinal metric termed "utils," utility is inherently non-measurable and cannot be compared across individuals.

  • Marginal Utility ($MU$): The additional utility derived from consuming exactly one more unit of a good:     $MU = \frac{\Delta TU}{\Delta Q} = \text{slope of the total utility curve } u(Q)$

  • Law of Diminishing Marginal Utility: As an individual consumes more units of a specific good during a given period, the additional satisfaction received from each subsequent unit diminishes.

  • Point of Satiation ($Q_S$): The quantity at which total utility attains its absolute maximum ($U_{\max}$) and $MU = 0$. Past satiation, marginal utility becomes negative ($MU < 0$) and total utility drops (e.g., overeating to the point of illness).

  • Worked Numerical Example (Grey Cup Pizza Slices):

  • 0 slices: $TU = 0, MU = -$

  • 1 slice: $TU = 20, MU = 20$

  • 2 slices: $TU = 36, MU = 16$

  • 3 slices: $TU = 46, MU = 10$

  • 4 slices: $TU = 52, MU = 6$

  • 5 slices: $TU = 54, MU = 2$

  • 6 slices: $TU = 51, MU = -3$

  • Total utility maximizes at 5 slices ($54\text{ utils}$); the 6th slice produces negative marginal utility.

• Equimarginal Principle: Equal Marginal Utility per Dollar:

  • Optimization Rule: A consumer maximizes total utility across goods by equalizing the marginal utility per dollar spent across all purchases, while fully exhausting the allocated budget:     $\frac{MU_X}{P_X} = \frac{MU_Y}{P_Y} \quad \text{subject to} \quad P_X X + P_Y Y = M$

  • Adjustment Mechanics: If $\frac{MU_X}{P_X} > \frac{MU_Y}{P_Y}$, reallocation of expenditures toward Good X increases total utility. As more X is purchased, $MU_X$ falls due to diminishing marginal utility; as less Y is consumed, $MU_Y$ rises, bringing the ratios into equilibrium.

  • Worked Example (George's $\$100$ Recreation Budget):

  • Movie tickets (P_M = \\$10), Bowling sessions (P_B = \\$20).

  • Option evaluation spending \\$100:

    • 0 Bowling, 10 Movies: $TU = 0 + 207 = 207$

    • 1 Bowling, 8 Movies: $TU = 75 + 207 = 282$

    • 2 Bowling, 6 Movies: $TU = 130 + 205 = 335$

    • 3 Bowling, 4 Movies: $TU = 170 + 190 = 360$

    • 4 Bowling, 2 Movies: $TU = 185 + 130 = 315$

    • 5 Bowling, 0 Movies: $TU = 190 + 0 = 190$

  • Verification via marginal utility per dollar at optimal bundle (3 Bowling, 4 Movies):       \frac{MU_B}{P_B} = \frac{40}{\\20} = 2 \quad \text{and} \quad \frac{MU_M}{P_M} = \frac{20}{\\10} = 2

  • Both ratios equal $2\text{ utils/dollar}$, and the total budget of \\$100 is fully exhausted.

  • Exam Time Budget Allocation:

  • Six available study hours allocated across Economics and Psychology exams.

  • With equal point weights, equalize additional points per hour. The optimal bundle is 4 hours of Economics and 2 hours of Psychology, both yielding 5 marginal points.

  • If Psychology points are weighted three times higher, triple the marginal psychology point scale; optimal allocation shifts to 2 hours of Economics and 4 hours of Psychology.

• Indifference Curve Theory:

  • Definition and Properties: An indifference curve plots all consumption bundles of Good X (horizontal axis) and Good Y (vertical axis) that yield the exact same level of total utility.

  • Downward sloping: Consuming more X mandates giving up Y to preserve identical utility.

  • Higher curves represent higher utility: Due to non-satiation (more is preferred to less).

  • Curves cannot intersect: Intersecting indifference curves violate the mathematical axiom of transitivity ($a \equiv b$ and $a \equiv c \implies b \equiv c$, impossible if bundle $c$ has more of both goods than $b$).

  • Marginal Rate of Substitution ($MRS$):

  • The rate at which a consumer is willing to trade Good Y for Good X while maintaining constant utility:       $MRS = \frac{MU_X}{MU_Y}$

  • The slope of the indifference curve at any given coordinate is $-MRS$.

  • Curves bow inward (diminishing $MRS$): As a consumer possesses abundant X and scarce Y, $MU_X$ is small and $MU_Y$ is large, yielding a low $MRS$ (flat curve). Conversely, scarce X and abundant Y produces a high $MRS$ (steep curve).

• The Budget Constraint:

  • Algebraic Derivation:     $P_X X + P_Y Y \le M \implies Y = \frac{M}{P_Y} - \left(\frac{P_X}{P_Y}\right)X$

  • Vertical Intercept: $\frac{M}{P_Y}$

  • Horizontal Intercept: $\frac{M}{P_X}$

  • Slope of the Budget Line: $-\frac{P_X}{P_Y}$ (the market's economic exchange rate between the two goods).

  • Opportunity Set: The triangular area bounded by the budget line and coordinate axes; represents all financially attainable consumption bundles.

• Optimal Consumer Equilibrium (Tangency Condition):

  • Graphical Tangency: The consumer attains the highest reachable indifference curve at the point where the budget line is tangent to an indifference curve.

  • Mathematical Equivalences:     $\text{Slope of Indifference Curve} = \text{Slope of Budget Line}$     $-MRS = -\frac{P_X}{P_Y} \implies \frac{MU_X}{MU_Y} = \frac{P_X}{P_Y} \implies \frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}$

  • The Non-Tangency Lens: Any indifference curve intersecting the budget line twice forms an internal lens-shaped region containing superior, reachable bundles with higher utility.

• Shifts in Income and Price:

  • Income Alterations: Changes in $M$ generate parallel shifts of the budget line (slope $-\frac{P_X}{P_Y}$ remains invariant). Higher income expands the opportunity set outward; lower income contracts it inward.

  • Price Alterations: A change in $P_X$ pivots the budget line around the static vertical intercept ($\frac{M}{P_Y}$). An increase in $P_X$ rotates the line inward and steepens the slope; a decrease rotates the line outward and flattens the slope.

  • Income and Substitution Effects of a Price Change:

  • Substitution Effect: The adjustment in quantity demanded caused purely by the change in the relative price of the good, holding consumer purchasing power (real utility) constant. Always pushes in the direction opposite to the price change.

  • Income Effect: The adjustment in quantity demanded resulting from the change in purchasing power caused by the price change, holding nominal income constant.

  • Interaction Matrix (Evaluating Impact on Non-Price-Changed Good Y):

    • If $P_X \uparrow \implies X \downarrow, Y \uparrow$: Substitution effect dominates $\implies$ Substitutes.

    • If $P_X \uparrow \implies X \downarrow, Y \downarrow$: Income effect dominates $\implies$ Complements.

    • If $P_X \downarrow \implies X \uparrow, Y \downarrow$: Substitution effect dominates $\implies$ Substitutes.

    • If $P_X \downarrow \implies X \uparrow, Y \uparrow$: Income effect dominates $\implies$ Complements.

• Extreme Preference Configurations:

  • Perfect Complements:

  • Goods consumed exclusively in fixed proportions (e.g., 1 computer printer to 1 printer cable; 1 bicycle frame to 2 bicycle tires).

  • Indifference curves form rigid $90^\circ$ right angles.

  • Possesses zero substitution effect following a price change; quantity changes stem entirely from the income effect.

  • Perfect Substitutes:

  • Goods viewed by the consumer as entirely interchangeable (e.g., identical brands of paper towels).

  • Indifference curves are straight lines with constant slope and constant $MRS$.

  • Generates corner solutions: the consumer spends their entire budget on whichever good offers the lower unit price.

• Derivation of Market Demand and Giffen Goods:

  • Horizontal Aggregation: Market demand is derived by horizontally summing the individual quantities demanded by every consumer at each discrete market price.

  • Giffen Goods:

  • An extreme theoretical exception where an increase in price causes an increase in quantity demanded (upward-sloping demand curve).

  • Requires a good to be strongly inferior, with an income effect so overwhelmingly powerful that it exceeds the negative substitution effect, and it must absorb a massive fraction of consumer income.

  • Empirical Confirmation: Robert Jensen and Nolan Miller (2006) proved the existence of Giffen goods among impoverished households in China: subsidized vouchers lowering the price of dietary staples led households to consume less rice in Hunan and less wheat (noodles/buns) in Gansu, shifting purchasing toward pork and meat.

• Behavioral Economics and Cognitive Imperfections:

  • Neoclassical versus Behavioral Framework: Neoclassical models assume economic agents exhibit perfect rationality, stable preferences, flawless mathematical calculation, and absolute willpower. Behavioral economics incorporates bounded rationality, cognitive shortcuts, shifting preferences, and systematic decision errors.

  • Systematic Cognitive Biases:

  • Confirmation Bias: Selectively assimilating information that reinforces preexisting beliefs while discarding contradictory evidence.

  • Self-Serving Bias: Attributing personal successes to internal competence while blaming external factors for personal failures.

  • Overconfidence Effect: Systematically overestimating the accuracy of one's personal knowledge or forecasts.

  • Hindsight Bias: Believing after an outcome occurs that one accurately predicted it beforehand.

  • Availability Heuristic: Evaluating probabilities based on how readily vivid examples come to mind (e.g., plane crash coverage distorting commercial flight risk perceptions).

  • Planning Fallacy: Systematically underestimating task completion durations despite prior experiential evidence.

  • Framing Effect: Arriving at divergent conclusions based entirely on how information is contextualized (e.g., "90% fat-free" outselling "10% fat").

  • Risk Orientations:

  • Risk-Averse: Avoids uncertainty; requires a risk premium to undertake gambles.

  • Risk-Neutral: Decides purely based on expected monetary value ($\text{Expected Benefit} \ge \text{Cost}$).

  • Risk-Loving: Accepts gambles where the expected value is below the financial cost.

  • Critical Behavioral Anomalies:

  • Endowment Effect (Richard Thaler): Placing higher value on an object simply because one possesses property rights over it. (Alan Krueger Super Bowl lottery study: 94% of winners refused to buy a ticket for \\$3000, yet 92% refused to sell their won ticket for \\$3000).

  • Sunk Cost Fallacy: Failing to ignore unrecoverable past expenditures when making forward-looking marginal choices (Kahneman and Tversky play ticket study).

  • Anchoring: Basing valuation estimates on arbitrary, irrelevant numerical benchmarks (Tversky and Kahneman spinning wheel experiment: arbitrary numbers 10 and 65 anchored subsequent guesses of African UN membership at 25% and 45%, respectively).

  • Nudges: Low-cost behavioral architecture adjustments preserving free choice (e.g., automatic RRSP enrollment defaults; Wellth app requiring medication selfies to preserve financial deposits).

• Social Dynamics, Network Externalities, and Experimental Fairness:

  • Bed Bath & Beyond Case Analysis: CEO Mark Tritton (March 2019) disrupted customer social shopping habits by eliminating signature 20%-off mailer coupons, reducing variety, and swapping national brand names for private labels. Operating losses reached \\$1.5\text{ billion} (2019–2022), leading to corporate bankruptcy and liquidation.

  • Network Externalities: Value to an individual user expands as total user volume expands (e.g., smartphones, tablet operating systems). Can produce path dependence and switching costs, potentially locking markets into legacy standards (e.g., QWERTY keyboard designs, VHS over Betamax, Windows over Mac; though economists Stan Leibowitz and Stephen Margolis argue historical alternatives were not conclusively superior).

  • Experimental Economics on Fairness:

  • Ultimatum Game (Werner Güth): Allocator divides \\$20. Economic self-interest predicts offering \\$0.01 and recipient accepting. In practice, allocators offer $40\text{ to } 50\%$, and recipients reject offers below $10\text{ to } 20\%$, willingly destroying wealth to punish unfairness.

  • Dictator Game (Kahneman, Knetsch, Thaler): Recipient cannot reject. 122 out of 161 Cornell student allocators still opted for an equal \\$10/\\$10 split, confirming intrinsic preferences for fairness.

  • High-Stakes Testing in India (Andersen et al.): Raising stakes to $20{,}000\text{ rupees}$ (200 days' wages) lowered average offers to $12\%$ and dropped rejections to $4\%$, proving fairness concerns diminish as personal opportunity costs escalate.

  • Fairness in Pricing: Ticket scalping and pricing constraints for high-demand events (Hamilton on Broadway, Taylor Swift Toronto Eras tour, Toronto Maple Leafs). Firms restrict price hikes during demand spikes because consumers interpret cost-justified price increases as fair, but demand-driven surges as price gouging.

Unit 7: Production and Costs

• Capital Acquisition and Legal Structures of Business:

  • Financing Modalities:

  • Debt Financing: Bank loans, mortgages, corporate bonds, credit lines. Demands scheduled contractual interest payments and compulsory principal repayment regardless of profitability.

  • Equity Financing: Issuance of corporate shares. Surrenders residual ownership rights; does not require repayment, but investors anticipate future dividends and capital gains.

  • Comparative Legal Business Organizations:

  • Sole Proprietorship: Single owner/manager; simple setup, profits taxed once at personal rates; exposed to unlimited personal liability; strictly constrained equity capital.

  • Partnership: Two or more owners; governed by a legal partnership agreement; profits taxed at individual rates; general partners face unlimited personal liability (limited partners possess limited liability but cannot manage); modest equity pool.

  • Corporation: Separate legal entity; managed by a board of directors; owners enjoy limited liability; exposed to dual taxation (corporate profit tax and personal dividend tax); vast equity raising potential.

  • Rate of Return on Invested Capital:     $\text{Rate of Return} = \frac{\text{Accounting Profit}}{\text{Invested Capital}} \times 100\%$

• Accounting Profit versus Economic Profit:

  • Accounting Profit: Total revenue minus explicit monetary operating costs (wages, material inputs, utility bills, rent, depreciation).

  • Economic Profit ($\pi$): Accounting profit minus the opportunity cost of invested capital (the risk-adjusted return capital could have secured in alternative endeavors):     $\pi = \text{Total Revenue} - \text{Explicit Costs} - \text{Implicit Costs}$     $\pi = \text{Total Revenue} - \text{Total Cost}$

  • Economic Benchmark Interpretation:

  • $\pi > 0$: Supernormal profit; capital yields more than its opportunity cost; attracts capital entry.

  • $\pi = 0$: Normal profit; capital yields exactly its required opportunity cost; investors are fully satisfied; accounting profit remains positive.

  • $\pi < 0$: Economic loss; capital yields less than alternative ventures of comparable risk; signals long-run exit.

  • Worked Numerical Example (The Specialized Café):

  • Explicit input costs = \\$170{,}000. Invested capital = \\$100{,}000. Required hurdle rate of return = $12\%$ (\text{Expected return} = \\$12{,}000 ).

  • At Revenue = \\$190{,}000: Accounting Profit = \\$20{,}000; \pi = \\$20{,}000 - \\$12{,}000 = +\\$8{,}000 (Supernormal).

  • At Revenue = \\$182{,}000: Accounting Profit = \\$12{,}000; \pi = \\$12{,}000 - \\$12{,}000 = \\$0 (Normal profit; successful business).

  • At Revenue = \\$180{,}000: Accounting Profit = \\$10{,}000; \pi = \\$10{,}000 - \\$12{,}000 = -\\$2{,}000 (Economic loss despite accounting profit).

  • Implicit Costs (Ebba Kantzen's Pizza Enterprise):

  • Explicit costs: \\$108{,}000 (ingredients, oven loan interest, wages, utilities, lease).

  • Implicit costs: Foregone corporate salary (\\$30{,}000), foregone bank interest on personal savings (\\$3{,}000), economic depreciation of machinery (\\$50{,}000 - \\$40{,}000 = \\$10{,}000). Total implicit costs = \\$43{,}000. Economic cost = \\$151{,}000.

• Production Functions and Horizons:

  • The Production Function: Shows the maximum physical quantity of output ($q$) attainable from given input combinations of Capital ($K$) and Labor ($L$):     $q = f(K, L)$

  • Input Classifications:

  • Fixed Inputs: Physical plant, heavy machinery, salaried executive administration; volume remains invariant regardless of short-run output changes.

  • Variable Inputs: Hourly production labor, raw materials, process electricity, operating fuel; scale directly with production volumes.

  • Time Horizons:

  • Short Run: Operating horizon in which at least one input ($K$) is physically fixed; output adjusts exclusively via variable inputs ($L$).

  • Long Run: Planning horizon in which all inputs ($K$ and $L$) are fully variable; plant capacity can be adjusted.

  • Very Long Run: Technological horizon in which the production function itself undergoes structural modification via technological progress.

• Labor Productivity Metrics:

  • Average Product of Labor ($AP_L$): Output per unit of labor employed:     $AP_L = \frac{q}{L}$

  • Marginal Product of Labor ($MP_L$): Additional output generated by employing one additional unit of labor:     $MP_L = \frac{\Delta q}{\Delta L}$

  • Productivity Cycles and Specialization:

  • Increasing Marginal Returns: Initial additions of labor permit division of labor and specialized tasks (Adam Smith's pin factory: 18 distinct operations generated 4,800 pins per worker daily compared to 20 pins in isolation).

  • Law of Diminishing Marginal Returns: Adding more of a variable input to a fixed input eventually causes the marginal product of the variable input to decline.

  • The Marginal-Average Mathematical Relationship:

  • When $MP_L > AP_L \implies AP_L$ is rising.

  • When $MP_L < AP_L \implies AP_L$ is falling.

  • $MP_L = AP_L$ precisely at the maximum peak of $AP_L$.

  • Worked Master Schedule (Labor and Output):

  • $L = 8\text{ hrs}, q = 104 \implies AP_L = 13.0, MP_L = -$

  • $L = 10\text{ hrs}, q = 160 \implies AP_L = 16.0, MP_L = \frac{56}{2} = 28.0$

  • $L = 15\text{ hrs}, q = 204 \implies AP_L = 13.6, MP_L = \frac{44}{5} = 8.8$

  • $L = 20\text{ hrs}, q = 234 \implies AP_L = 11.7, MP_L = \frac{30}{5} = 6.0$

  • $L = 30\text{ hrs}, q = 270 \implies AP_L = 9.0, MP_L = \frac{36}{10} = 3.6$

  • $L = 45\text{ hrs}, q = 315 \implies AP_L = 7.0, MP_L = \frac{45}{15} = 3.0$

  • $AP_L$ peaks at $L = 10$ ($16.0$), immediately after $MP_L$ achieves its maximum ($28.0$).

• Short-Run Cost Structures:

  • Total Formulations:     $TC = FC + VC$     $VC = (w \times L) + (m \times q)$

  • Where $w$ represents hourly wage, $L$ represents labor hours, and $m$ represents unit raw material cost.

  • Fixed costs ($FC$) remain constant at all output levels including zero; variable costs ($VC$) start at zero and expand with output.

  • Per-Unit Formulations:     $ATC = \frac{TC}{q} = AFC + AVC$     $AFC = \frac{FC}{q}$     $AVC = \frac{VC}{q}$     $MC = \frac{\Delta TC}{\Delta q} = \frac{\Delta VC}{\Delta q}$

  • Mirror Linkage to Labor Productivity:     $MC = \frac{w}{MP_L} + m$

  • When $MP_L$ is rising, marginal cost is falling. When $MP_L$ reaches its peak, $MC$ hits its minimum. When $MP_L$ diminishes, $MC$ rises.

  • Short-Run Cost Curve Geometric Properties:

  • $AFC$ continuously declines toward the horizontal axis as output expands ("spreading the overhead").

  • The vertical distance between $ATC$ and $AVC$ equals $AFC$, meaning the curves converge continuously.

  • The marginal cost curve ($MC$) cuts $AVC$ at its minimum point, and cuts $ATC$ at its minimum point ($ATC_{\min}$, the short-run minimum efficient scale).

  • The minimum of $ATC$ always lies to the right of the minimum of $AVC$ because declining $AFC$ pulls $ATC$ downward even after $AVC$ has started rising.

• Comprehensive Cost Table Synthesis:

  • Master parameters: FC = \\$400, w = \\$20/\text{hr}, m = \\$50/\text{unit}, P = \\$55/\text{unit}.

  • $q = 104$: $FC = 400$, $VC = 5360$, $TC = 5760$, $MC = -$, $AFC = 3.85$, $AVC = 51.54$, $ATC = 55.38$, $\pi = -40$.

  • $q = 160$: $FC = 400$, $VC = 8200$, $TC = 8600$, $MC = 50.71$, $AFC = 2.50$, $AVC = 51.25$, $ATC = 53.75$, $\pi = +200$.

  • $q = 204$: $FC = 400$, $VC = 10500$, $TC = 10900$, $MC = 52.27$, $AFC = 1.96$, $AVC = 51.47$, $ATC = 53.43$, $\pi = +320$.

  • $q = 234$: $FC = 400$, $VC = 12100$, $TC = 12500$, $MC = 53.33$, $AFC = 1.71$, $AVC = 51.71$, $ATC = 53.42$, $\pi = +370$.

  • $q = 270$: $FC = 400$, $VC = 14100$, $TC = 14500$, $MC = 55.56$, $AFC = 1.48$, $AVC = 52.22$, $ATC = 53.70$, $\pi = +350$.

  • $q = 315$: $FC = 400$, $VC = 16650$, $TC = 17050$, $MC = 56.67$, $AFC = 1.27$, $AVC = 52.86$, $ATC = 54.13$, $\pi = +275$.

  • Empirical observations:

  • Minimum $AVC$ occurs at $q = 160$ ($\$51.25$).

  • Minimum $ATC$ occurs at $q = 234$ ($\$53.42$).

  • Profit maximizes at $q = 234$ (\pi = \\$370), where price ($\$55$) still exceeds $MC$ ($\$53.33$), before $MC$ exceeds price at $q = 270$ ($\$55.56$).

• Cost Curve Shifts:

  • Change in Fixed Costs: Shifts $AFC$ and $ATC$ vertically. Has no impact on $MC$ or $AVC$.

  • Change in Variable Costs: Shifts $MC$, $AVC$, and $ATC$ vertically. Has no impact on $AFC$.

  • AI and Digital Technology Shifting Dynamics: A flat software subscription license increases $FC$ (shifting $AFC$ upward), but reduces needed labor hours per client, reducing $VC$ (shifting $MC$ and $AVC$ downward) and ultimately reducing overall $ATC$.

• Long-Run Cost Theory and Technical Efficiency:

  • Long-Run Envelope Property: In the long run, all inputs are variable; $FC = 0$ and $TC = VC$. Long-Run Average Total Cost ($LATC$) represents the lower envelope of all potential Short-Run Average Total Cost ($SATC$) curves, meaning $LATC \le SATC$ everywhere.

  • Long-Run Scale Classifications:

  • Economies of Scale: $LATC$ declines as output expands (due to specialization, engineering scaling rules, bulk purchasing discounts).

  • Constant Returns to Scale: $LATC$ is horizontal across output changes.

  • Diseconomies of Scale: $LATC$ rises as output expands (due to managerial coordination breakdowns, bureaucratic bottlenecks; e.g., Ford's historical 75,000-worker River Rouge complex).

  • Additional Efficiency Channels:

  • Economies of Scope: Cost savings derived from producing multiple related goods simultaneously using shared overhead (e.g., fast-food outlets selling burgers, chicken, and ice cream).

  • Learning-by-Doing: Labor productivity gains derived purely from cumulative repetition and task familiarity.

• Isoquant and Isocost Theory:

  • Isoquants: Curves mapping all combinations of capital ($K$) and labor ($L$) yielding an identical physical output volume ($q$).

  • Slope of Isoquant = $-MRTS$ (Marginal Rate of Technical Substitution).     $MRTS = \frac{MP_L}{MP_K}$

  • Diminishing $MRTS$ yields convex, bowed-in curves toward the origin.

  • Isocosts: Lines collecting all input combinations of $K$ and $L$ that cost the exact same total expenditure ($C$):     $C = wL + rK \implies K = \frac{C}{r} - \left(\frac{w}{r}\right)L$

  • Slope of Isocost = $-\frac{w}{r}$

  • Vertical Intercept = $\frac{C}{r}$; Horizontal Intercept = $\frac{C}{w}$.

  • Cost Minimization Tangency:     $\text{Slope of Isoquant} = \text{Slope of Isocost} \implies MRTS = \frac{w}{r} \implies \frac{MP_L}{MP_K} = \frac{w}{r}$     $\frac{MP_L}{w} = \frac{MP_K}{r}$

  • Cost minimization mandates equalizing marginal product per dollar across all inputs.

  • Wage Increase Impact (Substitution and Scale Effects):

  • When the wage ($w$) increases, the isocost line rotates inward around the vertical capital intercept ($\frac{C}{r}$), becoming steeper.

  • Substitution Effect: To produce the same output, the firm substitutes away from expensive labor toward capital (movement along the isoquant to a higher capital-labor ratio).

  • Scale Effect: The overall increase in production costs prompts the firm to reduce total output, contracting both capital and labor use.

  • Cross-Country Production Differences: Nissan utilizes advanced industrial robotics in Japan (steep isocost due to high relative wages), but relies on manual labor in India (flat isocost due to low relative wages); both firms optimize costs efficiently given local input price ratios.

Unit 8: Perfect Competition

• The Profit Maximization Rule ($MR = MC$):

  • Marginal Principles: Profit ($\pi = TR - TC$) is maximized where the revenue of the last unit produced equals the cost of making it ($MR = MC$).

  • Marginal Revenue: The change in total revenue from selling one additional unit ($MR = \frac{\Delta TR}{\Delta q}$).

  • Decision Process: If $MR > MC$, the unit adds to total profit; if $MR < MC$, producing the unit reduces total profit.

• The Five Strict Conditions of Perfect Competition:

  • 1. Many Small Buyers and Sellers: Every market participant is infinitesimally small relative to market volume; no individual agent can alter the market price.

  • 2. Homogeneous (Standardized) Good: Products are identical across all competing sellers, rendering them perfect substitutes.

  • 3. Perfect Information: All market participants possess complete price and quality knowledge across all suppliers.

  • 4. Zero Transaction Costs: No contractual penalties, administrative fees, or structural frictions impede buying or selling.

  • 5. Free Entry and Exit: Capital faces no legal, financial, or technological barriers to entering or vacating the industry.

• Comparative Market Structures Spectrum:

  • Perfect Competition: Infinite firms, identical products, high ease of entry (e.g., agricultural commodities, foreign exchange).

  • Monopolistic Competition: Many firms, differentiated products, high ease of entry (e.g., casual restaurants, clothing retail).

  • Oligopoly: Few large firms, identical or differentiated products, low ease of entry (e.g., automotive manufacturing, cell carrier networks).

  • Monopoly: Single seller, unique product with no substitutes, blocked entry (e.g., municipal tap water, postal delivery).

• The Perfectly Competitive Firm's Demand Curve:

  • Price Taker Identity: The firm cannot establish its own price; it inherits the equilibrium price ($P^*$) determined by market supply and demand.

  • Horizontal Elasticity: The individual firm's demand curve ($d$) is a horizontal line at the market price ($P^*$). The firm can sell any desired quantity at $P^*$, but charging a penny more reduces sales to zero.

  • Mathematical Identity:     $d = P = MR = AR$

  • Total Revenue Trajectory: Total revenue ($TR = P \times q$) is a linear upward-sloping ray emerging from the origin with a constant slope equal to $P$.

• Short-Run Output Determination and Profit Measurements:

  • Output Optimization Rule:     $P = MC \quad (\text{on the upward-sloping segment of } MC)$

  • Geometry of Profit and Loss:     $\text{Profit per Unit} = P - ATC$     $\text{Total Profit} = (P - ATC) \times q^*$

  • Three Financial Regimes:

  • Supernormal Profit: $P > ATC$ at $q^*$. A profit rectangle of height $(P - ATC)$ and width $q^*$ sits above $ATC$.

  • Breakeven: $P = ATC$ at $q^*$. Economic profit is zero; price touches the minimum of $ATC$.

  • Operating Loss: $P < ATC$ at $q^*$. An operating loss rectangle of height $(ATC - P)$ and width $q^*$ sits above price.

  • Worked Numerical Example (Andy's Basketball Enterprise):

  • Fixed costs = \\$10.

  • Case 1: Market price P = \\$12.50. Marginal cost matches price at $q^* = 6$ (MC = \\$12.50, ATC = \\$9.25).       $\pi = (12.50 - 9.25) \times 6 = \\$3.25 \times 6 = +\\$19.50 \quad (\text{Profit})$

  • Case 2: Market price drops to P = \\$6.00. Marginal cost matches price at $q^* = 4$ (MC = \\$6.00, ATC = \\$8.50).       $\pi = (6.00 - 8.50) \times 4 = -\\$2.50 \times 4 = -\\$10.00 \quad (\text{Loss})$

• The Short-Run Shutdown Decision:

  • Operating versus Halting Production:

  • Operate: Collects revenue ($TR$), pays variable costs ($VC$), loses $\text{Loss} = TC - TR = (FC + VC) - TR$.

  • Shut Down: Produces zero output, pays zero variable costs, collects zero revenue, but must still pay fixed costs: $\text{Loss} = FC$.

  • The Shutdown Test:

  • If $TR > VC \implies P > AVC$: Operate in the short run. Revenue fully covers variable costs and contributes toward offsetting fixed costs, minimizing loss.

  • If $TR < VC \implies P < AVC$: Shut down immediately. Continuing to operate adds operating losses on top of fixed costs.

  • If $TR = VC \implies P = AVC$: Indifferent between operating and shutting down; total loss equals $FC$ in both scenarios.

  • Sunk Cost Principle: Sunk fixed costs cannot be recovered in the short run and must be entirely disregarded when choosing whether to produce.

  • The Short-Run Supply Curve:

  • The individual firm's short-run supply curve is its marginal cost ($MC$) curve lying strictly above the minimum of the average variable cost ($AVC$) curve.

  • At prices below minimum $AVC$, quantity supplied collapses to zero.

• Long-Run Dynamics: Entry, Exit, and Normal Profit:

  • Market Adjustment Chains:

  • Economic Profits ($P > ATC$): Attracts outside capital; new firms enter the industry; market supply shifts right; market price falls; each individual firm contracts output along its $MC$ curve until $P = \text{minimum } ATC$ and $\pi = 0$.

  • Economic Losses ($P < ATC$): Distressed firms exit the industry; market supply shifts left; market price rises; remaining firms expand output along their $MC$ curve until $P = \text{minimum } ATC$ and $\pi = 0$.

  • Long-Run Competitive Equilibrium Condition:     $P = MR = MC = \text{minimum } ATC$

  • All firms earn zero economic profit ($\pi = 0$), which represents a normal accounting profit compensating investors for the opportunity cost of capital.

  • Case Application (Cage-Free Egg Industry): Premium pricing in 2015 produced supernormal profits, enticing widespread entry across the US egg market. Supply expanded dramatically, driving market price down toward the minimum average cost of production and eliminating supernormal returns.

• Long-Run Industry Supply Curves:

  • Constant-Cost Industry: Expanding industry output does not change input prices for typical firms. The long-run industry supply curve ($S_{LR}$) is perfectly horizontal at minimum $ATC$.

  • Increasing-Cost Industry: Industry expansion bids up the prices of specialized, scarce inputs (e.g., prime vineyard land, specialized mining equipment). Minimum $ATC$ shifts upward, yielding an upward-sloping $S_{LR}$.

  • Decreasing-Cost Industry: Industry expansion generates systemic external economies or enables input suppliers to realize major internal scale economies (e.g., early microchip and synthetic shoe sole manufacturing). Minimum $ATC$ shifts downward, yielding a downward-sloping $S_{LR}$.

• Producer Surplus and Market Efficiency:

  • Producer Surplus ($PS$):

  • The area below the market price line and above the supply ($MC$) curve from zero to $q^*$.

  • Represents total revenue minus total variable cost ($PS = TR - VC$); also termed gross profit.

  • Linkage to Economic Profit: $\pi = PS - FC$.

  • In long-run competitive equilibrium where $\pi = 0$, producer surplus exactly equals fixed cost ($PS = FC$).

  • Social Efficiency Dualities:

  • Productive Efficiency: Goods are manufactured at the lowest achievable unit cost ($P = \text{minimum } ATC$).

  • Allocative Efficiency: Production matches consumer marginal valuation. Price represents marginal benefit ($MB$), and firms produce to $P = MC$, guaranteeing $MB = MC$ for the terminal unit and maximizing total social surplus ($CS + PS$).