C9

Income Elasticity, Supply Elasticity, and Economic Surplus

Course Logistics and Announcements

  • Seminar Rescheduling:

    • The seminar originally scheduled for next Friday has been postponed to the end of the month (the last Friday of the month).

    • Next Friday will instead be a standard lecture class.

    • An official announcement and message regarding this change will be posted on the course Moodle page.

Refinement of Income Elasticity of Demand

Income elasticity measures the sensitivity of the quantity demanded to changes in consumer income.

  • Definition: Income elasticity is defined as the percentage change in the quantity demanded divided by the percentage change in the income (Revenue\text{Revenue}) of the consumer.

    • Formula: Income Elasticity=%Change in Qd%Change in Income\text{Income Elasticity} = \frac{\% \text{Change in } Q_d}{\% \text{Change in Income}}

  • Significance of the Sign:

    • Positive Sign (>0): Indicates a Normal Good. The change in demand moves in the same direction as the change in income (e.g., income increases, demand increases). This applies to the majority of goods consumed.

    • Negative Sign (<0): Indicates an Inferior Good. When income increases, the demand for these goods declines.

      • Examples: Rice, potatoes, junk food, and public transportation.

      • Behavioral Note: If income declines, the demand for these inferior goods will increase (opposite direction).

Categorization of Goods by Income Elasticity

Among normal goods (>0), we distinguish between two sub-groups based on the magnitude of the elasticity:

  • Luxury Goods:

    • Elasticity Condition: Income elasticity is greater than one (>1).

    • Characteristic: The percentage change in quantity demanded is larger than the percentage change in income.

    • Expenditure Share: The share of total expenditure spent on luxury goods increases as income rises. The wealthier a consumer becomes, the larger the portion of their budget they allocate to these items.

    • Examples: Trips, holidays, healthcare, high-quality food, and meats.

  • Necessity Goods:

    • Elasticity Condition: Income elasticity is between zero and one (0 < \text{Elasticity} < 1).

    • Characteristic: The percentage change in quantity demanded is lower than the percentage change in income.

    • Expenditure Share: The share of total expenditure allocated to necessity goods declines as income increases, even though the absolute demand might still rise.

  • Special Case: Housing:

    • Historically, housing was observed to have an income elasticity approximately equal to one (11), meaning a 10%10\% increase in income led to a 10%10\% increase in housing expenditure.

    • More recent observations categorize housing as a necessity good (elasticity <1), where its weight in the total expenditure budget declines as income grows.

Price Elasticity of Supply

Price elasticity of supply measures the responsiveness of the quantity supplied to a change in the price of the good.

  • Definition: The ratio between the percentage change in units supplied and the percentage change in the price.

    • Formula: Price Elasticity of Supply=%Change in Qs%Change in Price\text{Price Elasticity of Supply} = \frac{\% \text{Change in } Q_s}{\% \text{Change in Price}}

  • General Rule: Unlike demand, we primarily focus on price elasticity for supply. While elasticity can be calculated between any two related variables, price is the standard metric here.

Determinants of Supply Elasticity

  • Inventories and Stocks: If a seller has accumulated a stock or inventory of the good, the supply is more elastic (responsive) to price changes.

  • Access to Factors of Production: If it is easy and cost-effective for a producer to hire more workers or access raw materials/inputs, the supply will be more reactive to price increases.

  • Time Horizon:

    • Short-Term: The supply curve is often inelastic (steep) as it is difficult to adjust production capacity or input levels immediately.

    • Long-Term: The supply curve is more elastic as producers have time to adjust to price changes, build new facilities, or acquire more inputs.

Extreme Cases in Supply Elasticity

  • Perfectly Inelastic Supply:

    • Visual: A vertical supply curve.

    • Elasticity: Equal to zero (00).

    • Interpretation: The quantity supplied remains constant regardless of the price.

    • Real-World Example: The historical Tokyo Fish Market (perishable goods). Fishermen must sell everything caught during the night by the end of the morning at any price because the fish cannot be stored and will spoil.

  • Perfectly Elastic Supply:

    • Visual: A horizontal line.

    • Elasticity: Equal to infinity (∞\infty).

    • Interpretation: Consumers can buy any quantity at the market price, but nothing at a price even slightly higher. This is the supply curve perceived by an individual buyer in a perfectly competitive market (e.g., a bakery or grocery store where you accept the displayed price without bargaining).

  • Unit Elastic Supply:

    • Visual: Any supply curve originating from the graph's origin (0,00,0).

    • Elasticity: Equal to one (11). A 1%1\% increase in price leads to a 1%1\% increase in quantity supplied.

Economics as a Method: The Drug Market Model

This example illustrates how economics simplifies reality through models and hypotheses to analyze moral or social issues objectively.

  • Hypotheses Proposed:

    1. Demand Side: Relatively price inelastic (steep curve). Illegal drugs create addiction, so consumers are less sensitive to price changes.

    2. Supply Side: Relatively price elastic (flatter curve). Individual dealers often act as price takers on the market.

  • Implication for Policy: By structuring the analysis this way, governments can model the outcomes of addressing the supply side (e.g., seizing drugs) versus the demand side (e.g., rehabilitation/education) to determine the impact on market prices and related crimes.

Introduction to Consumer and Producer Surplus

Surplus is a vital tool used to measure the economic well-being (welfare) of buyers and sellers and the impact of shocks or policy interventions.

  • Consumer Surplus (CS): The difference between what a buyer is willing to pay (their maximum value for the good) and the actual market price.

    • CS=Willingness to Pay−Market Price\text{CS} = \text{Willingness to Pay} - \text{Market Price}

  • Producer Surplus (PS): The difference between the market price and the seller's willingness to sell (linked to the cost of production).

    • PS=Market Price−Willingness to Sell\text{PS} = \text{Market Price} - \text{Willingness to Sell}

  • Market Efficiency: In a perfectly competitive market, the total surplus (CS+PS\text{CS} + \text{PS}) is maximized, representing an efficient allocation that cannot be improved upon under certain strict conditions.

Detailed Mechanics of Consumer Surplus

  • The Downward Sloping Demand Curve: Slopes downward for two reasons:

    1. Intensive Margin: Individuals want to buy more units of a good as the price drops.

    2. Extensive Margin: More people enter the market and become willing to buy the good as the price drops.

  • Newspaper vs. Soda Case Study:

    • Soda Cans: Dispensers give one item per coin because an extra soda provides additional marginal utility/well-being (intensive margin).

    • Newspapers: Dispensers often open for the consumer to take any number of copies. This exists because one copy is sufficient; a second copy of the same news adds zero utility. Therefore, the downward slope is driven by the extensive margin (more unique readers at lower prices).

  • Graphical Measurement:

    • The aggregate consumer surplus is the area below the demand curve and above the market price.

    • For a linear demand curve, CS is the area of a triangle: Area=Base×Height2\text{Area} = \frac{\text{Base} \times \text{Height}}{2}.

    • Units are measured in monetary terms (e.g., Dollars, Francs).

  • Manga Market Example (Discrete Data):

    • Buyer A: WTP = 1818, Price = 1010, Surplus = 88

    • Buyer B: WTP = 1414, Price = 1010, Surplus = 44

    • Buyer C: WTP = 1010, Price = 1010, Surplus = 00 (Indifferent buyer)

    • Buyer D: WTP = 88, Price = 1010, Surplus = −2-2 (Will not participate voluntarily)

    • Total CS: 8+4+0=128 + 4 + 0 = 12

  • Impact of Price Increases:

    • When price rises from P0P_0 to P1P_1, CS declines (represented by a trapezoidal area). This reduction consists of:

      1. Foregone Surplus: Losses from buyers who leave the market because the price exceeds their WTP.

      2. Reduced Surplus: Losses from buyers who stay in the market but now pay more for the units they consume.

Detailed Mechanics of Producer Surplus

  • WTS and Cost of Production: The willingness to sell (WTS) is fundamentally linked to the cost of production. A seller will only participate if the price covers their costs.

  • Graphical Measurement:

    • The aggregate producer surplus is the area above the supply curve and below the market price.

    • Total Revenue: The total area (Price×Quantity\text{Price} \times \text{Quantity}).

    • Cost of Production: The area below the supply curve.

    • PS Calculation: Total Revenue−Cost of Production=Producer Surplus\text{Total Revenue} - \text{Cost of Production} = \text{Producer Surplus}.

  • Impact of Price Changes: Similar to consumers, price changes allow policy makers to calculate exactly how much seller well-being is affected in monetary units.