C4

Introduction to Market Analysis: Demand, Supply, and Aggregation Dynamics

Analysis of the Demand Curve and Experimental Data

• Auction Experiment Recap:

  • The lecturer references a classroom experiment involving bidding on a candy bag.

  • The highest bid recorded in a previous iteration (two years ago) was $500 \times 10^6\,Swiss\,francs$ ($500\,million\,CHF$).

  • The second-highest bid was $10 \times 10^6\,Swiss\,francs$ ($10\,million\,CHF$).

  • On a logarithmic scale, these represent values of $8.7$ and $7$ respectively.

• Interpreting the Curve:

  • The vertical axis represents the log of the price ($P$).

  • The curve tracks how many individuals are willing to pay that specific price or a higher one.

  • There is an inverse relationship between the bid/price and the number of people willing to purchase.

  • As the price increases, the number of willing buyers declines.

• Defining the Demand Curve:

  • The demand curve indicates the number of units consumers demand as a functional relationship to the price on the vertical axis.

  • Example: If the price reaches a certain point (represented as a log scale index), $20$ people may demand the good. If the price drops significantly, demand may increase to $70$ units.

  • This inverse relationship dictates that as price ($P$) increases, quantity demanded ($Q_D$) decreases.

Market Demand and Aggregation

• Market Level vs. Individual Level:

  • The negative relationship between price and quantity holds for both market demand curves and individual demand curves.

  • A market is defined by one supplier (or group of suppliers) and a group of buyers.

• Horizontal Summation:

  • The market demand curve is obtained through the horizontal aggregation of individual demand curves.

  • At any given price, the units demanded by every individual are summed to determine the total market demand.

  • Individual demand curves are heterogeneous; they differ across people due to variations in tastes, preferences, and income.

• Example Calculation of Horizontal Addition:

  • Consider two individuals with linear demand curves:

    • Individual 1: At price $P = 6$, demands $10$ units; at $P = 3$, demands $20$ units; at $P = 0$, demands $30$ units.

    • Individual 2: At price $P = 6$, demands $0$ units; at $P = 3$, demands $30$ units; at $P = 0$, demands $50$ units.

  • Market Summation ($Q_{Total} = Q_1 + Q_2$):

    • For $P > 6$: Neither individual demands units, so aggregate demand is $0$.

    • At $P = 6$: Total demand is $10 + 0 = 10$.

    • At $P = 3$: Total demand is $20 + 30 = 50$.

    • At $P = 0$: Total demand is $30 + 50 = 80$.

  • The resulting market demand curve is "flatter" than individual curves because it is more elastic at every price point where multiple consumers enter the market.

Factors Affecting Demand: Movements vs. Shifts

• Determinants of Demand Heterogeneity:

  • Necessity: Some individuals have a greater physical or practical need for a specific good.

  • Income/Wealth: Differences in financial resources affect purchasing power.

  • Tastes and Preferences: Subjective liking for a product (e.g., candy) varies significantly.

• Exogenous Factors (Contextual Shocks):

  • Demand is influenced by factors other than price, including marketing, advertising, and information shocks.

  • Example: Attending a medical lecture on the dangers of sugar/processed food might cause a consumer to lower their bid for candy, regardless of the price.

  • Example: A time constraint (e.g., being locked in a room for 5 hours without food) may increase a consumer's willingness to pay ($WTP$).

• Distinguishing Movement and Shifts:

  • Movement Along the Curve: Caused exclusively by a change in the unit price of the good itself.

  • Shift of the Curve: Caused by a change in "other factors" (the context or circumstances) while the price remains constant.

    • Shift to the Left: Occurs if consumers demand fewer units at every price point (e.g., discovery of cheaper substitutes nearby).

    • Shift to the Right: Occurs if consumers demand more units at every price point (e.g., increase in necessity or income).

Nature of Goods: Substitutes, Complements, and Income Effects

• Related Goods:

  • Substitutes: Goods that can replace one another. If the price of Good A increases, the demand for Good B (the substitute) increases.

    • Scenario: A $CO_2$ tax makes car driving more expensive. This causes the demand for electric bikes ($e-bikes$) to shift to the right.

  • Complements: Goods consumed together. If the price of Good A increases, the demand for Good B (the complement) decreases.

    • Scenario: A $CO_2$ tax increases the price of flights. This causes the demand for holidays in faraway islands (which require flights) to shift to the left.

• Income Effects:

  • Normal Goods: Demand increases when consumer income ($R$) increases.

  • Inferior Goods: Demand increases when consumer income ($R$) decreases.

    • Examples: Public transportation (bus tickets), low-quality/junk food, second-hand goods, old editions of books, or older technology.

Mathematical Formalization of Demand

• Implicit Demand Function:

  • Represented as $Q_D = F(P)$, or more specifically $Q_D = F(P, R, P_C, P_S, \pi)$.

  • The notation ($-$) or ($+$) is often used above variables to indicate inverse or direct relationships.

• Linear Demand Hypothesis:

  • A common simplification in economic modeling: $Q_D = A - BP$.

  • $A$ and $B$ are positive parameters estimated from empirical data.

• The Indirect Demand Function (Marshallian Convention):

  • Economist Alfred Marshall established the convention of placing Price ($P$) on the vertical axis and Quantity ($Q$) on the horizontal axis.

  • To graph this, one must solve for $P$:

  • $P = \frac{A}{B} - \frac{1}{B} \times Q_D$

  • The slope of the linear demand curve is $-\frac{1}{B}$.

• General Linear Form with Multiple Variables:

  • $Q_D = A - B_1 P + B_2 R - B_3 P_C + B_4 P_S$

  • The signs of the coefficients ($B_1, B_2, B_3, B_4$) define the nature of the good (Normal vs. Inferior, Substitute vs. Complement).

Characteristics of the Supply Curve

• Smartphone Sale Experiment:

  • A survey on the willingness of students to sell their personal smartphones.

  • At $CHF\,10$, almost no one is willing to sell.

  • At $CHF\,200$, demand for selling increases to several individuals.

  • At $CHF\,50,000$, virtually every student would sell their phone.

• The Law of Supply:

  • There is a positive (direct) relationship between price and quantity supplied ($Q_S$).

  • As the unit price rises, the number of units offered by sellers increases.

• Horizontal Summation of Supply:

  • The market supply curve is the horizontal sum of individual supply curves.

  • Example: If Producer 1 (Chevron) supplies $4$ units and Producer 2 (ExxonMobil) supplies $6$ units at $P = 25$, the market supply is $10$.

Factors Affecting Supply

• Movement vs. Shift (Supply):

  • Movement Along the Curve: Caused by a change in the market price of the good.

  • Shift of the Curve: Caused by changes in the production context.

    • Costs of Inputs: If the price of lithium (an input for smartphones) increases, production costs rise, shifting the supply curve to the left (less supplied at any given price).

    • Technology ($\tau$): An improvement in production technology reduces costs and makes production easier, shifting the supply curve to the right.

    • Expectations: Anticipated future crises or changes in buyer purchasing power can influence current supply levels.

    • Number of Sellers: More firms entering the market shifts the total supply curve to the right.

• Mathematical Representation of Supply:

  • Implicit Function: $Q_S = G(P)$.

  • Linear Hypothesis: $Q_S = C + MP$, where $M > 0$.

  • $M$ is the coefficient in front of the price, indicating the positive slope.

  • $C$ (the intercept) can be positive, negative, or zero, determining the starting point of the supply curve on the axis.

Questions & Discussion

• Question (Student): Regarding the aggregation of demand curves, why is the resulting market curve flatter?

• Answer (Lecturer): It is flatter because you are adding up the quantities of several individual demand curves at every single price point, which essentially makes the total quantity more sensitive (elastic) to price changes.

• Question (Student): Does the intercept $C$ in the supply equation mean you supply even if the price is zero?

• Answer (Lecturer): Exactly. Depending on the sign of $C$, it affects the starting point. We will discuss specific cases where this happens later in the course.

• Question (Student): Regarding the shift in demand for bikes vs. holidays, why might someone think demand for faraway holidays wouldn't shift left?

• Answer (Lecturer): While an individual's income might not have changed, if the price of a complement (the flight) rises due to the $CO_2$ tax, it is highly unlikely that market demand would increase; it will almost certainly decline.

• Classroom Management Note: The lecturer addressed complaints regarding noise levels in the room and urged students to be quiet out of respect for their colleagues' interest in the material.