Individual and Market Demand, Consumer Choice, and Competitive Supply

Individual Demand and Consumer Choice

• Derivation of Individual Demand Curves

  • Individual demand curves relate the quantity of a good that a single consumer will buy to its price, derived directly from utility-maximizing choices under budget constraints.

  • Consumption choices are determined by budget lines and indifference curves. In a two-good setup featuring food and clothing, income is fixed at $20$ and the price of clothing is fixed at $2.00\,/\text{unit}$.

  • Price Changes and the Price-Consumption Curve

  • Initial state: Price of food = $1.00\,/\text{unit}$. The utility-maximizing market basket is $B$ (12 units of food, 4 units of clothing), achieving utility level $U_2$.

  • Food price increase: Price of food rises to $2.00\,/\text{unit}$. The budget line rotates inward about the vertical intercept, becoming twice as steep. The utility-maximizing point shifts to $A$ (4 units of food, 6 units of clothing) on a lower indifference curve $U_1$, reflecting decreased purchasing power.

  • Food price decrease: Price of food falls to $0.50\,/\text{unit}$. The budget line rotates outward. The consumer reaches point $D$ (20 units of food, 5 units of clothing) on a higher indifference curve $U_3$

  • Price-Consumption Curve: Curve tracing the utility-maximizing combinations of two goods as the price of one good changes. As the price of food falls, attainable utility increases and food consumption expands.

  • Depending on individual preferences, clothing consumption can either increase or decrease when the price of food falls, as the price drop enhances overall purchasing power for both goods.

• Properties of the Individual Demand Curve

  • Changing Utility Along the Demand Curve: The level of utility that can be attained changes continuously along the demand curve. Lower product prices correspond to higher attainable indifference curves and higher purchasing power.

  • Optimality and the Marginal Rate of Substitution (MRS): At every point on the demand curve, the consumer maximizes utility by satisfying the condition that the marginal rate of substitution of food for clothing equals the price ratio of the two goods:

    $MRS = \frac{P_{food}}{P_{clothing}}$

• As the price of food falls, the price ratio decreases, causing the $MRS$ to decline down the demand curve:

  • At point $E$ (price = $2.00$), the price ratio is $1$ ($2.00/2.00$), so $MRS = 1$. The marginal benefit of an additional unit of food is $2.00$.

  • At point $G$ (price = $1.00$), the price ratio is $\frac{1}{2}$ ($1.00/2.00$), so $MRS = 0.5$. The marginal benefit is $1.00$.

  • At point $H$ (price = $0.50$), the price ratio is $\frac{1}{4}$ ($0.50/2.00$), so $MRS = 0.25$. The marginal benefit is $0.50$

  • Income Changes and the Income-Consumption Curve

• Income changes shift the budget line parallel to its original position while keeping its slope constant (since relative prices remain unchanged at $P_{food} = 1.00$ and $P_{clothing} = 2.00$).

• Income = $10$: Maximizing point $A$ (4 food, 3 clothing) on $U_1$, plotted as point $E$ on demand curve $D_1$

• Income = $20$: Maximizing point $B$ (10 food, 5 clothing) on $U_2$, plotted as point $G$ on demand curve $D_2$

• Income = $30$: Maximizing point $D$ (16 food, 7 clothing) on $U_3$, plotted as point $H$ on demand curve $D_3$

• Income-Consumption Curve: Curve tracing the utility-maximizing combinations of two goods as a consumer's income changes.

• An upward-sloping income-consumption curve implies that an increase in income shifts the individual demand curve to the right (from $D_1$ to $D_2$ to $D_3$).

• Normal versus Inferior Goods

  • Normal Good: A good for which the quantity demanded increases as income increases. The income elasticity of demand is positive ($E_I > 0$

  • Inferior Good: A good for which the quantity demanded decreases as income increases. The income elasticity of demand is negative ($E_I < 0$

  • Relationship dynamics: Hamburger can be a normal good at low income levels (consumption rises from 5 to 10 units as income increases from $10$ to $20$). However, as income increases further to $30$, hamburger becomes an inferior good as consumers substitute toward steak (hamburger consumption drops from 10 to 8 units), causing the income-consumption curve to bend backward.

• Engel Curves

  • Engel Curve: Curve relating the quantity of a good consumed to an individual's income.

  • Normal Good Engel Curve: Slopes upward across all income ranges (e.g. food consumption increases from 4 to 10 to 16 units as income grows from $10$ to $20$ to $30$

  • Inferior Good Engel Curve: Slopes upward for lower income ranges, but bends backward/downward once income exceeds the threshold where the good becomes inferior (e.g. hamburger Engel curve bends backward above $20$ income per month).

• Empirical Household Spending: Consumer Expenditures in the United States

  • Source: U.S. Department of Labor, Bureau of Labor Statistics, "Consumer Expenditure Survey, Annual Report 2010". Data presented in 2009 dollars across income groups:

  • Income Groups: Less than $10,000$, $10,000-19,999$, $20,000-29,999$, $30,000-39,999$, $40,000-49,999$, $50,000-69,999$, $70,000\text{ and above}$.

  • Entertainment Expenditures ($):$1,041$,$1,025$,$1,504$,$1,970$,$2,008$,$2,611$,$4,733 (High income elasticity; nearly 5-fold expansion).\n\n * Owned Dwelling Expenditures (): $1,880$, $2,083$, $3,117$, $4,038$, $4,847$, $6,473$, $12,306$ (High income elasticity; over 6-fold expansion).

  • Rented Dwelling Expenditures ($):$3,172$,$3,359$,$3,228$,$3,296$,$3,295$,$2,977$,$2,098$(Inferior good for incomes above$30,000\n\n * Health Care Expenditures (): $1,222$, $1,917$, $2,536$, $2,684$, $2,937$, $3,454$, $4,393$ (Normal good with positive elasticity).

  • Food Expenditures ($):$3,429$,$3,529$,$4,415$,$4,737$,$5,384$,$6,420$,$9,761 (Normal good with positive elasticity).\n\n * Clothing Expenditures (): $799$, $927$, $1,080$, $1,225$, $1,336$, $1,608$, $2,850$ (Normal good with positive elasticity).

• Substitutes and Complements

  • Substitutes: Two goods for which an increase in the price of one leads to an increase in the quantity demanded of the other.

  • Complements: Two goods for which an increase in the price of one leads to a decrease in the quantity demanded of the other.

  • Independent Goods: Two goods for which a change in the price of one has no effect on the quantity demanded of the other.

  • Identification via Price-Consumption Curve: On a downward-sloping portion of a price-consumption curve, two goods are substitutes. On an upward-sloping portion, they are complements.

Income and Substitution Effects

• Decomposition of a Price Change

  • A fall in the price of a good produces two distinct economic effects simultaneously:

  • Substitution Effect: Change in consumption of a good associated with a change in its price, with the level of utility held constant.

  • Income Effect: Change in consumption of a good resulting from an increase in real purchasing power, holding relative prices constant.

  • Total Effect Equation:

    $\text{Total Effect } (F_1 F_2) = \text{Substitution Effect } (F_1 E) + \text{Income Effect } (E F_2)$

• The Substitution Effect

  • Captures the change in consumption resulting purely from relative price changes.

  • Graphical derivation: Constructed by drawing an imaginary budget line parallel to the new budget line $RT$ (reflecting lower relative prices), but tangent to the original indifference curve $U_1$ (holding satisfaction constant).

  • Directionality: The substitution effect ALWAYS leads to an increase in quantity demanded when price decreases, due to the convex shape of indifference curves.

• The Income Effect

  • Reflects the movement from one indifference curve to another as purchasing power changes.

  • Normal Good: The income effect is positive ($E F_2 > 0$). The income effect reinforces the substitution effect, expanding consumption further.

  • Inferior Good: The income effect is negative ($E F_2 < 0$). As purchasing power increases, consumption of the inferior good decreases. However, as long as the substitution effect exceeds the negative income effect, total quantity demanded still increases when price falls.

• Special Case: The Giffen Good

  • Giffen Good: A good whose demand curve slopes upward because the negative income effect is larger than the substitution effect.

  • Requires a exceptionally large negative income effect; rarely observed in real-world markets because individual goods typically represent a small share of a consumer's overall expenditure budget.

• Policy Application: Analysis of a Gasoline Tax with a Rebate

  • Objective: Evaluate a federal policy raising gasoline tax by $0.50\,/\text{gallon}$ combined with an equal per-capita tax rebate program.

  • Initial Baseline: Low-income consumer with income = $9000$, gasoline price = $1.00\,/\text{gallon}$, buying 1200 gallons of gasoline and spending $7800$ on other goods (Point $C$ on budget line $AB$

  • Price Elasticity of Demand for gasoline = $-0.5$; Income Elasticity of Demand = $0.3$

  • Tax Implementation: A $0.50$ tax increases price by $50\%$. Without rebate, consumption drops by $25\%$ ($-0.5 \times 50\%$

  • Rebate Implementation: Tax proceeds generate a $450$ rebate ($900 \text{ gallons} \times 0.50$

  • Net Effect: Income rises by $5\%$ ($450/9000$), increasing gasoline consumption by $1.5\%$ ($0.3 \times 5\%$

  • Final Consumption: Reaches $913.5\text{ gallons}$ at point $H$. Overall gasoline consumption decreases by $286.5\text{ gallons}$ ($1200 - 913.5$

  • Welfare Impact: The consumer is left slightly worse off because final consumption point $H$ lies on an indifference curve below initial curve $U_2$

Market Demand and Elasticity

• Derivation of the Market Demand Curve

  • Market Demand Curve: Curve relating the quantity of a good that all consumers in a market will buy to its price.

  • Aggregation procedure: Obtained by summing individual consumer demand curves horizontally at each price level.

  • Horizontal Aggregation Example (Three-Consumer Market for Coffee):

  • Price = $5.00$: Consumer A = 0, B = 2, C = 4 -> Market Demand = 6 units.

  • Price = $4.00$: Consumer A = 0, B = 4, C = 7 -> Market Demand = 11 units.

  • Price = $3.00$: Consumer A = 2, B = 6, C = 10 -> Market Demand = 18 units.

  • Price = $2.00$: Consumer A = 4, B = 8, C = 13 -> Market Demand = 25 units.

  • Price = $1.00$: Consumer A = 6, B = 10, C = 16 -> Market Demand = 32 units.

  • Structural Properties: The market demand curve shifts right as new consumers enter. Market demand curves can be kinked if some consumers enter the market only below specific threshold prices.

• Price Elasticity of Demand and Consumer Expenditures

  • Elasticity Formula:

    $E_P = \frac{\Delta Q / Q}{\Delta P / P} = \left(\frac{P}{Q}\right)\left(\frac{\Delta Q}{\Delta P}\right)$

• Elasticity Categories:

  • Inelastic Demand ($|E_P| < 1$): Quantity demanded is unresponsive. Price increases lead to increases in total consumer expenditure / seller revenue.

  • Elastic Demand ($|E_P| > 1$): Quantity demanded is highly responsive. Price increases lead to decreases in total consumer expenditure / seller revenue.

  • Unit-Elastic Demand ($|E_P| = 1$): Total expenditure remains constant across price changes.

  • Isoelastic Demand Curve: A demand curve with a constant price elasticity along its entire length.

• Expenditure Summary Matrix:

  • Inelastic Demand: If price increases, expenditures increase; if price decreases, expenditures decrease.

  • Unit Elastic Demand: If price increases or decreases, expenditures are unchanged.

  • Elastic Demand: If price increases, expenditures decrease; if price decreases, expenditures increase.

  • Empirical Market Demand: The Aggregate Demand for Wheat

• Domestic Demand: $Q_{DD} = 1430 - 55P$ (Price elasticity $\approx -0.2\text{ to }-0.3$

• Export Demand: $Q_{DE} = 1470 - 70P$ (Price elasticity $\approx -0.4$

• Aggregation Mechanics:

  • For $P > 21.00\,/\text{bushel}$: Export demand $Q_{DE} \le 0$. Aggregate world demand equals domestic demand ($Q = 1430 - 55P$

  • For $P \le 21.00\,/\text{bushel}$: Aggregate demand $Q = Q_{DD} + Q_{DE} = (1430 - 55P) + (1470 - 70P) = 2900 - 125P$

  • The resulting total world demand curve is kinked at $P = 21.00\,/\text{bushel}$.

  • Speculative Demand and Asset Bubbles

• Speculative Demand: Demand driven not by direct consumption benefits, but by expectations that the price of a good will increase.

• Bubble: A price increase driven not by demand fundamentals, but by the belief that prices will keep rising. Bubbles lead to severe financial dislocations when they burst.

  • Demographic Housing Demand Parameters

• Housing represents $25\%$ of average household budgets; bottom $20\%$ income renters spend $55\%$ of income on housing vs $2.8\%$ overall.

• Demographic Elasticities (Table 4.4):

  • Single individuals: Price elasticity = $-0.10$, Income elasticity = $0.21$

  • Married, head age < 30, 1 child: Price elasticity = $-0.25$, Income elasticity = $0.06$

  • Married, head age 30-39, 2+ children: Price elasticity = $-0.15$, Income elasticity = $0.12$

  • Married, head age 50+, 1 child: Price elasticity = $-0.08$, Income elasticity = $0.19$

• Income Elasticity by Wealth Bracket: Bottom 10th percentile income elasticity = $0.09$; top 10th percentile = $0.54$

  • Long-Run International Gasoline Demand

• Cross-country comparisons reveal long-run price elasticity of gasoline demand $\approx -1.4$

• High-tax nations (Germany, France, UK, Norway) exhibit prices of $6.00-8.00\,/\text{gallon}$ and low consumption ($< 200\text{ gallons/capita/year}$), compared to the US ($2.50-4.00\,/\text{gallon}$ and $> 400\text{ gallons/capita/year}$.

Consumer Surplus and Market Valuation

• Individual and Aggregate Consumer Surplus

  • Consumer Surplus: Difference between the maximum amount a consumer is willing to pay for a good and the amount actually paid.

  • Individual Valuation Example (Rock Concert Tickets at $14.00\,/\text{ticket}$):

  • 1st ticket: Willingness to pay = $20.00$, Surplus = $6.00$

  • 2nd ticket: Willingness to pay = $19.00$, Surplus = $5.00$

  • 3rd ticket: Willingness to pay = $18.00$, Surplus = $4.00$

  • 4th ticket: Willingness to pay = $17.00$, Surplus = $3.00$

  • 5th ticket: Willingness to pay = $16.00$, Surplus = $2.00$

  • 6th ticket: Willingness to pay = $15.00$, Surplus = $1.00$

  • Total individual consumer surplus = $6 + 5 + 4 + 3 + 2 + 1 = 21.00$

  • Aggregate Market Calculation: Area below the continuous linear market demand curve and above the price line.

  • Market ticket expenditure = $6500 \text{ tickets} \times 14.00 = 91,000$

  • Aggregate consumer surplus = $\frac{1}{2} \times (20.00 - 14.00) \times 6500 = 19,500$

• Environmental Valuation: Valuation of Clean Air

  • Non-market valuation via housing price differentials in Boston and Los Angeles.

  • Demand for nitrogen oxide ($\text{NO}_x$) reduction at $1000\,/\text{pphm}$:

  • Family achieves a $5\text{ pphm}$ pollution reduction, paying $5000$

  • Consumer surplus triangle height = $2000 - 1000 = 1000$; base = $5\text{ pphm}$.

  • Consumer surplus = $\frac{1}{2} \times 1000 \times 5 = 2500\,/\text{household}$.

  • Suspended Particulates Valuation: $1\text{ mg/m}^3$ reduction valued at $2400\,/\text{household}$.

Network Externalities

• Network Externality Principles

  • Network Externality: Situation in which each individual's demand depends on the purchases/usage of other individuals.

  • Positive Network Externality: Quantity of a good demanded by a consumer increases in response to the growth in purchases by other consumers.

  • Negative Network Externality: Quantity of a good demanded decreases in response to the growth in purchases by other consumers.

• Positive Network Externalities and the Bandwagon Effect

  • Bandwagon Effect: Positive network externality in which a consumer wishes to possess a good in part because others do (e.g. social networking sites, word processing software).

  • Demand Curve Elasticity Impact: Positive network externalities make market demand significantly MORE elastic than individual demand curves without externalities.

  • Mechanics of Price Drop from $30$ to $20$:

  • Pure price effect (without externality): Quantity expands from $40,000$ to $48,000$ on curve $D_{40}$.

  • Externality effect: Growth in users shifts demand curve to $D_{80}$, expanding quantity demanded further to $80,000$

• Negative Network Externalities and the Snob Effect

  • Snob Effect: Negative network externality in which a consumer wishes to own an exclusive or unique good (e.g. rare artwork, custom sports cars, exclusive watches).

  • Demand Curve Elasticity Impact: Makes market demand significantly LESS elastic.

  • Mechanics of Price Drop from $30,000$ to $15,000$:

  • Pure price effect: Quantity demanded expands from $2,000$ to $14,000$ on curve $D_2$

  • Snob effect: Increased total ownership reduces exclusivity, shifting demand curve left to $D_6$, cutting demand by $8,000$ units and resulting in a net quantity of only $6,000$

• Empirical Case: Facebook Network Growth

  • Growth trajectory illustrating positive network externalities (Table 4.5):

  • 2004: 1 million users

  • 2005: 5.5 million users

  • 2006: 12 million users (<1 hour/user/month)

  • 2007: 50 million users (2 hours/user/month)

  • 2008: 100 million users (3 hours/user/month)

  • 2009: 350 million users (5.5 hours/user/month)

  • 2010: 500 million users (7 hours/user/month)

Empirical Estimation of Demand

• Statistical Methods and Demand Estimation

  • Least-squares linear demand specification: $Q = a - bP + cI$

  • Raspberry Market Data (Table 4.6):

  • 2004: Q = 4, P = 24, I = 10

  • 2005: Q = 7, P = 20, I = 10

  • 2006: Q = 8, P = 17, I = 10

  • 2007: Q = 13, P = 17, I = 17

  • 2008: Q = 16, P = 10, I = 27

  • 2009: Q = 15, P = 15, I = 27

  • 2010: Q = 19, P = 12, I = 20

  • 2011: Q = 20, P = 9, I = 20

  • 2012: Q = 22, P = 5, I = 20

  • Regression result: $Q = 8.08 - 0.49P + 0.81I$

  • Elasticity along linear curve: $E_P = -b \left(\frac{P}{Q}\right)$. In 1999 ($Q=16, P=10$), $E_P = -0.31$; in 2003 ($Q=22, P=5$), $E_P = -0.11$

• Log-Linear Demand Formats

  • Log-linear / Isoelastic equation:

    $\log(Q) = a - b \log(P) + c \log(I)$

• Constant price elasticity = $-b$; constant income elasticity = $c$

• Cross-price elasticity integration: $\log(Q) = a - b \log(P) + b_2 \log(P_2) + c \log(I)$. Positive $b_2$ denotes substitutes; negative $b_2$ denotes complements.

  • Empirical Application: Ready-to-Eat Cereal Market

• Estimated demand for Grape Nuts:

    $\log(Q_{GN}) = 1.998 - 2.085 \log(P_{GN}) + 0.62 \log(I) + 0.14 \log(P_{SW})$

• Parameter interpretations: Own-price elasticity = $-2.085$ (elastic); Income elasticity = $0.62$; Cross-price elasticity with Shredded Wheat = $0.14$ (weak substitutes).

Mathematical Treatment of Demand Theory

• Constrained Utility Maximization

  • Optimization problem: Maximize $U(X, Y)$ subject to budget constraint $P_X X + P_Y Y = I$

  • Marginal utilities: $MU_X = \frac{\partial U}{\partial X}$ and $MU_Y = \frac{\partial U}{\partial Y}$

• Method of Lagrange Multipliers

  • Lagrangian Function:

    $\mathcal{L} = U(X, Y) - \lambda(P_X X + P_Y Y - I)$

• First-Order Necessary Conditions:

    $\frac{\partial \mathcal{L}}{\partial X} = MU_X(X, Y) - \lambda P_X = 0$

    $\frac{\partial \mathcal{L}}{\partial Y} = MU_Y(X, Y) - \lambda P_Y = 0$

    $\frac{\partial \mathcal{L}}{\partial \lambda} = I - P_X X - P_Y Y = 0$

• The Equal Marginal Principle and MRS

  • Lagrange multiplier equality:

    $\lambda = \frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}$

    $\frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}$

• Tangency condition with indifference curves:

    $MU_X dX + MU_Y dY = dU^* = 0 \implies -\frac{dY}{dX} = \frac{MU_X}{MU_Y} = MRS_{XY} = \frac{P_X}{P_Y}$

• Marginal Utility of Income

  • Total differentiation yields $\frac{dU}{dI} = \lambda$. The multiplier $\lambda$ represents the extra utility obtained from an additional dollar of income.

• Cobb-Douglas Demand Derivation

  • Utility Function: $U(X, Y) = a \log(X) + (1-a)\log(Y)$

  • First-order conditions yield $P_X X = \frac{a}{\lambda}$ and $P_Y Y = \frac{1-a}{\lambda}$. Substituting into the budget constraint yields $\lambda = \frac{1}{I}$.

  • Explicit Demand Functions:

    $X = \left(\frac{a}{P_X}\right) I$

    $Y = \left(\frac{1-a}{P_Y}\right) I$

• Numerical evaluation ($a = 0.5, P_X = 1, P_Y = 2, I = 100$): Optimal choices $X = 50, Y = 25, \lambda = 0.01$. Increasing income to $101$ yields $X = 50.5, Y = 25.25$, raising utility from $3.565$ to $3.575$ (an increase of $0.01$

  • Duality in Consumer Theory

• Dual problem: Minimize expenditure $P_X X + P_Y Y$ subject to achieving utility $U(X, Y) = U^*$

• Lagrangian: $\mathcal{L} = P_X X + P_Y Y - \mu(U(X, Y) - U^*)$

• Multiplier relationship: $\mu = \frac{1}{\lambda} = \frac{P_X}{MU_X} = \frac{P_Y}{MU_Y}$, yielding identical demand functions as direct utility maximization.

  • Slutsky Equation and Hicksian Decomposition

• Slutsky Equation:

    $\frac{dX}{dP_X} = \left. \frac{\partial X}{\partial P_X} \right|_{U=U^*} - X \left(\frac{\partial X}{\partial I}\right)$

• Hicksian Substitution Effect: Constructed using compensated budget line $R'T'$ parallel to new budget line $RT$ and intersecting initial budget line $RS$ at point $B$. Revealed preference proves that compensated basket lies on $BT'$, establishing a strictly negative substitution effect without assuming indifference curve convexity.

Perfectly Competitive Markets and Profit Maximization

• Three Basic Assumptions of Perfect Competition

  • Price Taking: Individual firms sell a small fraction of industry output and have no influence on market price; they take price as given. Consumers are also price takers.

  • Product Homogeneity: Outputs of all firms are perfect substitutes (commodities like agricultural goods, metals, oil). Ensures a uniform market price.

  • Free Entry and Exit: No special costs restricting new firms from entering or existing firms from leaving the market.

• Market Structure vs Competitive Conduct

  • Numerical presence of many firms is neither necessary nor sufficient for competitive behavior. Highly elastic demand facing individual firms can induce competitive pricing even in markets with few firms.

• The Profit Maximization Assumption

  • Microeconomic models assume firms maximize long-run profit. While manager-shareholder principal-agent conflicts exist in large corporations, competitive market forces mandate profit-maximizing behavior for long-term firm survival.

• Alternative Organizational Forms

  • Cooperative: Association of businesses or individuals jointly owned/operated by members for mutual benefit (e.g. agricultural co-ops, food co-ops, housing co-ops).

  • Condominium: Housing unit individually owned while common facilities are controlled jointly by an owners' association.

  • Condos vs Co-ops in NYC: Nationally, condos outnumber co-ops 10:1; in NYC, co-ops outnumber condos 4:1. Condo units sell for a $15.5\%$ valuation premium over equivalent co-ops due to resale freedom and simplified governance.

Short-Run Output and Competitive Supply

• Profit Maximization Rule for Any Firm

  • Profit equation: $\pi(q) = R(q) - C(q)$

  • Maximization condition: $\frac{d\pi}{dq} = \frac{dR}{dq} - \frac{dC}{dq} = 0 \implies MR(q) = MC(q)$

  • Output Rule: Profit is maximized where $MR = MC$ on the rising portion of the marginal cost curve.

• Demand and Marginal Revenue for the Competitive Firm

  • The competitive firm faces a horizontal demand curve $d$ at market price $P$

  • Average revenue ($AR$) and marginal revenue ($MR$) equal market price:

    $d = AR = MR = P$

• Competitive Output Condition: Choose output $q^*$ such that:

    $MC(q) = P$

• Short-Run Profitability and Shutdown Rules

  • Profit level = Rectangle $ABCD = (P - ATC) \times q^*$

  • Positive Economic Profit: Occurs when $P > ATC$

  • Short-Run Loss Minimization: When $AVC < P < ATC$, the firm incurs losses ($ABCD = (ATC - P) \times q^*$), but continues operating because revenue covers variable costs and partially offsets fixed costs.

  • Shutdown Rule: If market price falls below minimum Average Variable Cost ($P < AVC$), the firm shuts down production immediately to limit losses to fixed costs.

• Empirical Production: Aluminum Smelting Plant Short-Run Output

  • Short-run marginal cost structure:

  • $MC = 1140\,/\text{ton}$ up to $600\text{ tons/day}$ (2 regular shifts).

  • $MC = 1300\,/\text{ton}$ between $600\text{ and } 900\text{ tons/day}$ (3 shifts including overtime).

  • Operational decisions:

  • Price $P_1 = 1250\,/\text{ton}$: Produce $600\text{ tons/day}$ (2 shifts).

  • Price $P_2 = 1360\,/\text{ton}$: Produce $900\text{ tons/day}$ (3 shifts).

  • Price $P < 1140\,/\text{ton}$: Halt production completely.

• Managerial Guidelines for Marginal Cost Estimation

  • Do not use AVC as a proxy for MC when costs rise steeply (Overtime example: 80 units regular shift -> $AVC = MC = 38\,/\text{unit}$; 100 units with overtime -> $AVC = 42\,/\text{unit}$, but overtime $MC = 58\,/\text{unit}$).

  • Account for non-variable accounting components (e.g. required union severance pay lowers saved MC upon layoff).

  • Incorporate all opportunity costs into MC (e.g. store floor space opportunity cost of $90\,/\text{sq ft/day}$).

Short-Run Industry Supply and Producer Surplus

• The Competitive Firm's Short-Run Supply Curve

  • The firm's short-run supply curve is the portion of the marginal cost curve $MC$ above minimum $AVC$

  • Upward slope stems from diminishing marginal returns to variable inputs.

  • Input Price Shifts: An increase in an input price shifts the $MC$ curve upward from $MC_1$ to $MC_2$, causing profit-maximizing output to fall from $q_1$ to $q_2$

• Refinery Processing: Short-Run Production of Petroleum Products

  • Stepped marginal cost curve $SMC$ caused by discrete capacity limits across thermal crackers ($9,700\text{ barrels/day}$ capacity) and secondary units ($10,700\text{ barrels/day}$ capacity).

  • Output rules: $P = 73\,/\text{barrel}$ -> 0 production; $P = 74-75\,/\text{barrel}$ -> $9,700\text{ barrels/day}$; $P > 75\,/\text{barrel}$ -> expand toward $10,700\text{ barrels/day}$.

• Short-Run Market Supply Curve

  • Obtained by summing individual firm supply curves horizontally.

  • Input Price Effects: Industry-wide expansion increases input demand, raising input prices, shifting individual $MC$ curves upward, and making market supply less elastic.

  • Price Elasticity of Short-Run Supply: $E_S = \frac{\Delta Q / Q}{\Delta P / P}$. Always positive.

• Short-Run World Supply of Copper

  • Country-by-Country Operating Marginal Costs (2010 Data):

  • Russia: Capacity = $750\text{ thousand metric tons}$, $MC = 1.30\,/\text{lb}$

  • Zambia: Capacity = $770\text{ thousand metric tons}$, $MC = 1.50\,/\text{lb}$

  • Chile: Capacity = $5,520\text{ thousand metric tons}$, $MC = 1.60\,/\text{lb}$

  • Peru: Capacity = $1,285\text{ thousand metric tons}$, $MC = 1.70\,/\text{lb}$

  • United States: Capacity = $1,120\text{ thousand metric tons}$, $MC = 1.70\,/\text{lb}$

  • Indonesia: Capacity = $840\text{ thousand metric tons}$, $MC = 1.80\,/\text{lb}$

  • Australia: Capacity = $900\text{ thousand metric tons}$, $MC = 2.30\,/\text{lb}$

  • Poland: Capacity = $430\text{ thousand metric tons}$, $MC = 2.40\,/\text{lb}$

  • Canada: Capacity = $480\text{ thousand metric tons}$, $MC = 2.60\,/\text{lb}$

  • Elasticity profile: Highly elastic at prices between $1.30$ and $1.80\,/\text{lb}$; becomes highly inelastic above $2.40\,/\text{lb}$ as producers reach physical capacity.

• Producer Surplus in the Short Run

  • Definition: Sum over all units produced of the difference between market price and marginal cost of production.

  • Mathematical Formulation:

    $\text{Producer Surplus } (PS) = R - VC$

• Producer Surplus vs Profit:

    $\text{Profit } (\pi) = R - VC - FC = PS - FC$

• In the short run with positive fixed costs, $PS > \pi$

• Market Producer Surplus: Area below market price line and above market supply curve between 0 and output $Q^*$

Long-Run Output and Industry Supply

• Long-Run Profit Maximization

  • All inputs variable. The firm chooses output where long-run marginal cost equals price:

    $LMC = P$

• Expansion from short run ($q_1$) to long run ($q_3$) increases profit rectangle from $ABCD$ to $EFGD$

  • Long-Run Competitive Equilibrium

• Three required equilibrium conditions:

  1. All firms maximize profit ($LMC = P$).

  2. Zero economic profit for all firms ($P = LAC_{min}$), leaving no incentive for entry or exit.

  3. Market price equates total quantity supplied to total quantity demanded ($Q_S = Q_D$).

  • Accounting Profit versus Economic Profit

• Accounting Profit = Revenue - Cash Costs - Depreciation.

• Economic Profit: $\pi = R - wL - rK$, where $rK$ is the user cost of capital.

• Zero Economic Profit: The firm earns a normal, competitive return on investment equal to its opportunity cost of capital.

  • Economic Rent

• Economic Rent: Amount firms are willing to pay for an input less the minimum amount necessary to obtain it.

• In the long run, positive accounting profits earned by firms with scarce inputs (patents, prime land, unique location) represent economic rent. When the opportunity cost of scarce inputs is included, economic profit equals zero.

• In competitive markets, long-run producer surplus equals total economic rent generated by scarce inputs.

  • Long-Run Industry Supply Configurations

• Constant-Cost Industry: Input prices remain constant as industry output expands. Long-run industry supply curve $S_L$ is horizontal at minimum $LAC$

• Increasing-Cost Industry: Input prices rise as industry output expands. Long-run industry supply curve $S_L$ is upward sloping.

• Decreasing-Cost Industry: Input prices fall as industry output expands (external economies of scale). Long-run industry supply curve $S_L$ is downward sloping.

  • Empirical Industry Classification

• Coffee: Constant-cost industry (abundant land, constant tree care costs).

• Oil: Increasing-cost industry (depletion of accessible fields forces drilling in costlier reserves).

• Automobiles: Decreasing-cost industry (volume expansion lowers component supply costs).

  • Effects of an Output Tax

• Individual Firm Tax $t$: Shifts firm $MC$ upward to $MC + t$, reducing output from $q_1$ to $q_2$

• Industry-wide Tax $t$: Shifts industry supply curve upward by $t$ ($S_2 = S_1 + t$), raising market price from $P_1$ to $P_2$ and lowering industry output from $Q_1$ to $Q_2$

  • New York Taxicab Supply Analysis

• Driver Financial Breakdown: 3,600 hours worked/year, 2,400 paid miles, 4,800 trips/year at $15.00\,/\text{trip}$ average -> $72,000$ gross revenue. Gas/maintenance $10,000$, medallion lease $33,000$ ($110\,/\text{shift} \times 300\text{ shifts}$) -> $29,000$ net annual income.

• Price Sensitivity: Fare drop to $10.00$ cuts net income to $5,000$; fare increase to $20.00$ raises net income to $53,000$

• Medallion Restriction: Number of medallions capped at 13,150 (issued in 1937). Unrestricted supply curve $S$ is highly elastic, but the medallion cap makes supply curve $S'$ vertical at 13,150 cabs.

• Long-Run Housing Supply Elasticity

  • Owner-occupied suburban housing: Constant-cost industry with near-horizontal supply curve.

  • Urban rental housing: Increasing-cost industry due to land scarcity and zoning laws; long-run elasticity of supply = $0.36$