C5

Equilibrium of the Competitive Market and Intro to Elasticity

Administrative Information and Course Structure

• Seminar and Tutorial Schedule

  • There will be no regular class on Friday. Instead, students will attend the first seminar with the assistant.

  • The seminar focus is on the first problem set. Students are advised to try solving exercises in advance rather than listening passively to solutions.

  • Group work is strongly encouraged. Tutorials (held on Mondays) are designated times for students to work through exercises together and ask assistants questions.

  • The seminar time is confirmed for 12:00 or 12:15 in the designated room.

• Recording Policy

  • Lectures and seminars are recorded.

  • Tutorials are not recorded. This is intended as an incentive for active participation, ensuring students feel free to speak, discuss, and ask questions without being on camera.

• Course Metaphor

  • The professor conceptualizes the course as a "factory" or a "company." Every component—the lectures, the seminars, and the tutorials—contributes to the final outcome. Responsibility for specific types of questions is split between the professor (theory) and assistants (applications/exercises).

Review of Linear Demand and Supply Equations

• The Linear Hypothesis

  • The course builds upon mathematical examples of demand and supply under the linear hypothesis.

  • Demand Equation Form: The transcript references a specific linear form for the demand of coffee: $Q_d = f(P_{\text{coffee}}, P_{\text{other goods}}, \text{Revenue}, \dots)$.

  • Supply Equation Form: The supply curve for coffee rests on functions of price, the cost of raw materials ($P_{\text{raw materials}}$), and wages ($W$).

  • Coefficients in these equations are derived from empirical analysis, typically provided by statisticians or economists.

• Movement vs. Shift

  • Movement along the curve: Triggered solely by a change in the price of the good itself ($P$).

  • Shift of the curve: Triggered by changes in variables other than the good's price (e.g., changes in wages, raw material costs, or consumer revenue).

Defining Market Equilibrium

• The Market Defined

  • A market consists of a group of sellers (suppliers) and buyers (demanders) interested in a specific good.

• Definition of Equilibrium

  • A market is at equilibrium when all buyers and sellers agree on a price ($P$) at which they will exchange units of a good.

  • At this point, the quantity supplied ($Q_s$) matches the quantity demanded ($Q_d$).

  • The Incentive Property: Equilibrium is a state where no agent has an incentive to change their decision. Everyone willing to buy at that price receives the good, and everyone willing to sell at that price sells the good.

• The Bargaining Process

  • Equilibrium is often reached through a process of negotiation or bargaining.

  • Example (Second-hand Car): A buyer and seller negotiate. If they agree on a price, the car is exchanged; if not, the car remains with the seller. In a massive market, this bargaining happens at an aggregate level until a single price clears the market.

Mechanisms of Market Adjustment

In order to understand equilibrium, one must understand disequilibrium states: shortages and leftovers (surpluses).

• Shortage (Excess Demand)

  • Definition: Occurs when $Q_d > Q_s$ at the current price.

  • Market Signal: The shortage acts as a message to producers that production is too low and prices can be raised.

  • Adjustment Mechanism: Consumers begin competing for limited units. They start bidding against one another, offering higher prices to secure the good. This drives the market price ($P$) upward toward equilibrium.

• Leftovers (Excess Supply/Surplus)

  • Definition: Occurs when $Q_s > Q_d$ at the current price.

  • Market Signal: Goods pile up in warehouses (inventory accumulation). This signals to producers that production is too high and prices must fall.

  • Adjustment Mechanism: Sellers start competing for buyers by lowering prices to attract customers. This downward pressure continues until the price reaches equilibrium.

Principles of Trade in Competitive Markets

• Voluntary Exchange

  • All exchanges are voluntary. No one can be forced to sell below their willingness to sell, nor can anyone be forced to buy above their willingness to pay.

• The Short Side of the Market Prevails

  • In any disequilibrium situation, the actual quantity traded is determined by the "short side" (the smaller value between $Q_d$ and $Q_s$).

  • If there is excess supply ($P > P^*$), the quantity exchanged is determined by demand.

  • If there is excess demand ($P < P^*$), the quantity exchanged is determined by supply.

Comparative Statics: Analyzing Shocks

Market shocks cause shifts in the curves, leading to a new equilibrium.

• Positive Supply Shock

  • Example: Technical innovation in oil extraction (e.g., fracking).

  • Graphical Result: Supply curve ($S$) shifts to the right ($S'$).

  • Immediate Effect: At the old equilibrium price, there is now an excess supply.

  • Final Outcome: Price ($P$) decreases and equilibrium quantity ($Q$) increases.

• Demand Shock

  • Example: An increase in consumer revenue ($R$).

  • Graphical Result: Demand curve ($D$) shifts to the right ($D'$).

  • Final Outcome: Both price ($P$) and quantity ($Q$) increase.

• Simultaneous Shocks

  • When both curves shift at once, the effect on one variable (either $P$ or $Q$) will be certain, while the other will be "ambiguous" or "uncertain," depending on the relative magnitude of the shifts.

  • Case 1: Both shift in the same direction (e.g., $D$ and $S$ shift right).

    • Quantity ($Q$) increases unambiguously.

    • Price ($P$) is uncertain (it may increase, decrease, or stay constant depending on which shift is larger).

  • Case 2: Curves shift in opposite directions (e.g., $S$ shifts left, $D$ shifts right).

    • Price ($P$) increases unambiguously.

    • Quantity ($Q$) is uncertain.

Mathematical Identification of equilibrium

To find equilibrium analytically, one must solve a system of two equations with two unknowns ($P$ and $Q$).

• Example Equations:

  • $Q_d = a - bP$

  • $Q_s = c + dP$

• Solution Method: Use substitution. Set $Q_d = Q_s$ and solve for the unique price ($P^*$). Once $P^*$ is found, substitute it back into either equation to find the equilibrium quantity ($Q^*$).

Real-World Applications and Case Studies

• The Oil Market: Historical data shows periods where price declines while quantity increases. Using market logic, this is identified as a positive supply shock.

• 9/11 Terrorist Attacks (2001): Observed data showed that both office space pricing and occupancy in Manhattan decreased simultaneously. This indicates a massive negative demand shock.

• Copper Consumption: High consumption increases with constant prices imply that both demand and supply shifted right at roughly the same rate.

• COVID-19 Housing Market:

  • City Centers: Experienced a sharp decline in price and demand (Negative Demand Shock).

  • Countryside/Suburbs: Experienced a massive increase in demand and price (Positive Demand Shock).

Introduction to Elasticity

• The Concept of Sensitivity

  • Elasticity measures the sensitivity of the quantity demanded (or supplied) to a change in price ($P$).

• The Total Revenue Problem

  • Total Revenue ($TR$) Formula: $TR = P \times Q$

  • The "Olive Oil" Example: If a producer (not in a perfectly competitive market) increases the price ($P$), two opposing forces act on $TR$:

    1. Price Effect: $TR$ tends to increase because each unit is sold for more.

    2. Quantity Effect: $TR$ tends to decrease because the quantity sold ($Q$) drops due to the law of demand.

  • Conclusion: Whether $TR$ increases, decreases, or stays the same depends entirely on the elasticity of the demand curve. The elasticity explains which effect (Price or Quantity) is dominant.

Questions & Discussion

• Question: Are the seminars recorded?

• Response: Yes, seminars are recorded to ensure students can review the correction of problem sets. However, tutorials remain unrecorded to foster an environment where students feel comfortable discussing among themselves without pressure.

• Question: Regarding the volume of the microphone.

• Response: The microphone is at the maximum level. Students are asked to remain quiet to ensure the recording and the lecture are audible, as noise makes it difficult for everyone to hear.