Module 4 and 5 Study Notes: Supply, Demand, and Elasticity

Markets and Competition

Market: Defined as a group of buyers and sellers of a particular good or service.
Competitive Market: A market environment containing many buyers and sellers such that each individual has a negligible (or no) impact on the prevailing market price.
Quantity Demanded ( $Q_d$ ): The specific amount of a good that buyers are both willing (desire the product) and able (possess the budget) to purchase at a given price.
Law of Demand: The claim that, with other things being equal, the quantity demanded of a good falls as the price of that good rises.
Demand Schedule: A structured table displaying the relationship between the price ( $P$ ) and the quantity demanded ( $Q_d$ ).
Demand Curve: A graphical representation showing the relationship between the price ( $P$ ) and quantity demanded ( $Q_d$ ).
Market Demand (Aggregate Demand): The sum of all individual demands for a specific good or service.

The Mechanics of Demand

Negative Relationship: Price and quantity demanded are negatively related. As $P \uparrow$ , $Q_d \downarrow$ .
Example Demand Schedule (Individual): * $P = 10 \implies Q_d = 0$ * $P = 9 \implies Q_d = 0.5$ * $P = 8 \implies Q_d = 1$ * $P = 7 \implies Q_d = 1.5$ * $P = 6 \implies Q_d = 2$ * $P = 5 \implies Q_d = 2.5$ * $P = 4 \implies Q_d = 3$ * $P = 3 \implies Q_d = 3.5$ * $P = 2 \implies Q_d = 4$ * $P = 1 \implies Q_d = 4.5$ * $P = 0 \implies Q_d = 5$
Aggregating Market Demand: * Market demand is calculated by summing individual consumer quantities at every price level. * Data Example: * At $P = 9$ : Consumer 1 ( $0.5$ ) + Consumer 2 ( $1.0$ ) = Market ( $1.5$ ). * At $P = 8$ : Consumer 1 ( $1.0$ ) + Consumer 2 ( $2.0$ ) = Market ( $3.0$ ). * At $P = 5$ : Consumer 1 ( $2.5$ ) + Consumer 2 ( $5.0$ ) = Market ( $7.5$ ). * At $P = 0$ : Consumer 1 ( $5.0$ ) + Consumer 2 ( $10.0$ ) = Market ( $15.0$ ).
Shifters of the Demand Curve: * Direction of Shift: An increase in demand shifts the curve to the right (higher quantity at any price). A decrease in demand shifts the curve to the left (lower quantity at any price). * Determinants of Demand: 1. Income: * Normal Good: Demand increases ( $D \uparrow$ ) when income increases ( $I \uparrow$ ). Change in income and demand move in the same direction. * Inferior Good: Demand decreases ( $D \downarrow$ ) when income increases ( $I \uparrow$ ). Change in income and demand move in opposite directions. 2. Prices of Related Goods: * Substitutes: If the price of MilkDuds falls, the demand for cupcakes falls (consumers switch to the cheaper substitute). If the price of MilkDuds rises, the demand for cupcakes rises. * Complements: If the price of coffee falls, demand for cupcakes increases (consumed together). If the price of coffee rises, demand for cupcakes decreases. 3. Tastes/Preferences: * Positive health news about a product increases demand. * Negative health impact reports decrease demand. 4. Expectations about the Future Income: * If an individual expects an increase in future income, they may increase demand for normal goods today, acting as if they already possess the funds. 5. Number of Buyers: An increase in population or the number of participants in the market increases overall demand.

The Mechanics of Supply

Quantity Supplied ( $Q_s$ ): The amount of a good or service that sellers are willing and able to supply at a given price.
Law of Supply: The claim that, other things being equal, the quantity supplied of a good rises when the price of the good rises ( $P \uparrow \implies Q_s \uparrow$ ).
Aggregating Market Supply: * Market supply is the sum of quantities offered by all firms at each price point. * Data Example: * At $P = 5$ : Firm 1 ( $5$ ) + Firm 2 ( $10$ ) = Market Supply ( $15$ ). * At $P = 15$ : Firm 1 ( $15$ ) + Firm 2 ( $30$ ) = Market Supply ( $45$ ). * At $P = 30$ : Firm 1 ( $30$ ) + Firm 2 ( $60$ ) = Market Supply ( $90$ ).
Shifters of the Supply Curve: 1. Input Prices: If the price of an input (e.g., cupcake liners) increases, supply decreases ( $S \downarrow$ ). If input prices decrease, supply increases ( $S \uparrow$ ). 2. Technology: Advances in technology (e.g., a faster oven) increase supply ( $S \uparrow$ ). Government restrictions on technology can decrease supply. 3. Expectations: If sellers expect the price of cupcakes to rise in the near future, they may hold back products today to sell them later for higher profit, thereby decreasing supply ( $S \downarrow$ ) today. 4. Number of Sellers: An increase in the number of sellers in the market increases supply ( $S \uparrow$ ), while a decrease in sellers decreases supply ( $S \downarrow$ ).

Market Equilibrium and Disequilibrium

Equilibrium: A state where the price reaches a level where quantity supplied equals quantity demanded ( $Q_s = Q_d$ ).
Market Dynamics Table: * $P = 10 \implies Q_d = 0, Q_s = 5 \implies ext{Surplus of } 5$ * $P = 8 \implies Q_d = 1, Q_s = 4 \implies ext{Surplus of } 3$ * $P = 6 \implies Q_d = 2, Q_s = 3 \implies ext{Surplus of } 1$ * Equilibrium ( $P=5$ ): $Q_d = 2.5, Q_s = 2.5$ . * $P = 2 \implies Q_d = 4, Q_s = 1 \implies ext{Shortage of } 3$ * $P = 0 \implies Q_d = 5, Q_s = 0 \implies ext{Shortage of } 5$
Surplus: A situation where Q_s > Q_d. Markets tend to lower prices to reach equilibrium.
Shortage: A situation where Q_d > Q_s. Markets tend to raise prices to reach equilibrium.
Comparative Statics (Single Curve Shifts): * Decrease in Demand ( $D \downarrow$ ) $o P \downarrow, Q \downarrow$ * Increase in Demand ( $D \uparrow$ ) $o P \uparrow, Q \uparrow$ * Decrease in Supply ( $S \downarrow$ ) $o P \uparrow, Q \downarrow$ * Increase in Supply ( $S \uparrow$ ) $o P \downarrow, Q \uparrow$
Ambiguous Outcomes (Simultaneous Shifts): * If both Demand and Supply change and the magnitude of the shifts is unknown, either the price or the quantity will have an ambiguous effect.

Elasticity and Its Applications

Elasticity: A general measure of responsiveness.
Price Elasticity of Demand ( $\epsilon_d$ ): A measure of how much the quantity demanded of a good responds to a change in the price of that good. * Formula: $\epsilon_d = rac{\text{percentage change in } Q_d}{\text{percentage change in } P}$ . * Absolute Values: Because demand curves are downward-sloping, elasticities are negative, but are reported as absolute values ( $|\epsilon_d|$ ).
Determinants of Demand Elasticity: 1. Availability of Close Substitutes: More substitutes lead to higher elasticity. 2. Necessities vs. Luxuries: Necessities (e.g., insulin, water) are inelastic; luxuries (e.g., boats) are elastic. 3. Market Definition: Narrowly defined markets (e.g., blue felt pens) are more elastic than broad markets (e.g., toilet paper) due to easier substitution. 4. Time Horizon: Goods tend to be more elastic over longer time horizons as consumers have time to adjust.
Calculation Methods: * Midpoint Method (Average): $\epsilon_d = \frac{\Delta Q_d}{Q_{avg}} \div \frac{\Delta P}{P_{avg}} = \frac{Q_2 - Q_1}{(\frac{Q_1 + Q_2}{2})} \div \frac{P_2 - P_1}{(\frac{P_1 + P_2}{2})}$ .
Classification of Elasticity: * Elastic: |\epsilon_d| > 1 ( $Q_d$ is very responsive). * Inelastic: |\epsilon_d| < 1 ( $Q_d$ is not very responsive). * Unit Elastic: $|\epsilon_d| = 1$ . * Perfectly Inelastic: Vertical demand curve. * Perfectly Elastic: Horizontal demand curve.
Total Revenue (TR) and Elasticity: * $TR = P \times Q$ . * Elastic Demand: Price and Total Revenue move in opposite directions ( $P \uparrow, TR \downarrow$ ; $P \downarrow, TR \uparrow$ ). The quantity effect dominates. * Inelastic Demand: Price and Total Revenue move in the same direction ( $P \uparrow, TR \uparrow$ ; $P \downarrow, TR \downarrow$ ). The price effect dominates. * Unit Elastic: Total revenue remains unchanged when price changes.
Example Calculation (UNI Tuition): * Tuition increases by $18.5\%$ , enrollment drops by $1\%$ . * $\epsilon_d = \frac{-1\%}{18.5\%} = -0.05$ . This is price inelastic (|\epsilon_d| < 1).
Elasticity vs. Slope: Slope is constant for a linear demand curve, but elasticity is not. A single demand curve can have elastic, unit elastic, and inelastic regions.
Other Elasticities: * Income Elasticity ( $\epsilon_i$ ): $\frac{\% \Delta Q_d}{\% \Delta \text{Income}}$ . * Normal good: \epsilon_i > 0. * Inferior good: \epsilon_i < 0. * Cross-Price Elasticity ( $\epsilon_{ab}$ ): $\frac{\% \Delta Q_d(\text{good A})}{\% \Delta P(\text{good B})}$ . * Substitutes: \epsilon_{ab} > 0. * Complements: \epsilon_{ab} < 0.
Price Elasticity of Supply ( $\epsilon_s$ ): $\frac{\% \Delta Q_s}{\% \Delta P}$ . * Steeper supply curves are more inelastic; flatter ones are more elastic.

Government Policies: Price Controls and Taxes

Price Ceiling: A legal maximum on the price at which a good or service can be sold.
Price Floor: A legal minimum on the price at which a good or service can be sold (e.g., Minimum Wage).
Tax Incidence: The study of how the burden of a tax is shared among market participants.
Tax on Buyers: 1. Decreases Willingness to Pay (WTP). 2. Demand curve shifts down/left by the size of the tax.
Tax on Sellers: 1. Increases cost to sellers. 2. Supply curve shifts up/left by the size of the tax.
Mathematical Example ( $D: P = 30 - Q$ , $S: P = 2Q$ ): * Initial Equilibrium: $30 - Q = 2Q \implies Q^* = 10, P^* = 20$ . * With a $3$ tax (either side): * New Quantity ( $Q_t$ ) = $9$ . * Price buyers pay ( $P_b$ ) = $21$ . * Price sellers receive ( $P_s$ ) = $18$ . * Buyers' Burden: P_b - P^* = 21 - 20 = $1. * Sellers' Burden: P^* - P_s = 20 - 18 = $2.
General Tax Conclusions: * Taxes discourage market activity (quantity traded decreases). * Both buyers and sellers share the burden, regardless of which party the tax is levied upon. * Elasticity and Tax Burden: The less flexible (more inelastic) party bears the greater burden of the tax.

Market Efficiency

Consumer Surplus (CS): A buyer's willingness to pay minus the amount the buyer actually pays. Graphically, the area under the demand curve and above the market price.
Producer Surplus (PS): The amount a seller is paid minus the seller's cost. Graphically, the area above the supply curve and below the market price.
Total Surplus (TS): Also called Total Welfare. $TS = CS + PS$ .
Efficiency: An allocation of resources that maximizes the Total Surplus received by all members of society.
Equity: The fairness of the distribution of well-being among society members.
Free Market Insights: * Supply is allocated to buyers who value the goods most (highest WTP). * Demand is allocated to sellers who produce at the lowest cost. * Markets produce the quantity that maximizes surplus (Efficiency).

Costs of Taxation: Deadweight Loss

Deadweight Loss (DWL): The fall in total surplus that results from a market distortion, such as a tax. It represents the loss to buyers and sellers that exceeds the revenue raised by the government.
Welfare Analysis of Tax: * $CS$ changes by $-(B + C)$ . * $PS$ changes by $-(D + E)$ . * $\text{Tax Revenue}$ = $(P_b - P_s) \times Q_t$ (Areas $B + D$ ). * $DWL = C + E$ .
Determinants of DWL: * Tax size: As tax size increases, DWL increases at an increasing rate. * Elasticity: DWL increases as the price elasticity of supply or demand increases. More elastic markets result in larger DWL.
Tax Revenue Dynamics: * As tax size increases, tax revenue first increases, then decreases (Laffer Curve concept). * The "Ideal" tax maximizes revenue while minimizing DWL, which involves a difficult trade-off found through economic modeling and trial-and-error.
Numerical Problem Case Study: * Given $D: P = 80 - 4Q$ and $S: P = Q$ . * Pre-tax: $Q^* = 16, P^* = 16$ . $CS = 512, PS = 128, TS = 640$ . * With $10$ tax on suppliers: $Q_t = 14, P_b = 24, P_s = 14$ . * Post-tax outcomes: $CS = 392, PS = 98, \text{Tax Revenue} = 140, TS \text{ (with revenue)} = 630$ . * $DWL = 640 - 630 = 10$ . (Calculated as $\frac{1}{2} \times (16 - 14) \times 10 = 10$ ).