Supply and Demand Shocks, Elasticities, and Consumer Behavior

Market Dynamics of Supply and Demand Shocks

• The market for agricultural products is characterized by supply curves that undergo frequent shifts due to external factors like weather conditions.

• A specific case study involves the vanilla market in Madagascar, which accounts for $80\%$ of global production. A cyclone in the region destroyed $30\%$ of the vanilla crop, effectively removing roughly one-quarter ($25\%$) of the world's vanilla supply.

• The supply of vanilla is represented as perfectly vertical in the short term. This is because harvests are seasonal and supply is fixed once the harvest is complete. Expanding production typically takes three to four years because producers must plant new orchids and wait for them to mature.

• A leftward shift in supply (from $S$ to $S_1$) creates an initial excess demand at the original equilibrium price ($p_0$). This excess demand is represented by the distance $q_1 q_0$.

• The pressure of excess demand causes the price to rise until a new equilibrium ($E_1$) is reached at price $p_1$ and quantity $q_1$, where the excess demand is eliminated.

The Role of Demand Slopes in Supply Shocks

• The magnitude of a price change resulting from a supply shift depends heavily on the slope of the demand curve.

• Steep Demand Curve ($D_1$): A decrease in supply results in a significant price increase (from $p_0$ to $p_1$).

• Flatter Demand Curve ($D_2$): The same decrease in supply leads to a much more limited price rise (from $p_0$ to $p_2$).

• The impact on farmer income (revenue) is also determined by the demand slope. Revenue equals price multiplied by quantity ($P \times Q$).

  • Before a shift, revenue is the sum of rectangles $A + B$.

  • After a shift with steep demand ($D_1$), the price rise more than compensates for the quantity decrease. New revenue is $B + C + F$. Additional revenue ($C + F$) outweighs the lost revenue ($A$), resulting in a net increase.

  • After a shift with flat demand ($D_2$), the price rise does not compensate for the quantity drop. New revenue is $B + C$. The additional revenue ($C$) is smaller than the lost revenue ($A$), resulting in a net decrease.

• On average, global supply shocks can benefit farmers if demand is sufficiently steep. Conversely, individual outcomes vary; a farmer whose plantation was destroyed is worse off, while a farmer with an unaffected plantation during a general crop failure is better off due to the market-wide price spike.

Supply Shocks from Production Costs

• While crop failures shift the supply curve along the horizontal axis, changes in production costs typically shift the intercept on the vertical axis.

• Cost Increase Scenario: Consider tomatoes grown in heated greenhouses. If heating costs rise, the supply curve shifts upward from $S$ to $S'$. A uniform shift suggests a consistent cost increase for every unit produced.

• Vertical Demand ($D_2$): Only a price effect occurs. The equilibrium quantity remains unchanged at point $B$. Producers pass the entire cost increase to consumers through higher prices.

• Horizontal Demand ($D_3$): No price increase occurs. The equilibrium shifts solely in terms of quantity to point $C$. Producers bear the entire cost increase, leading to significantly reduced net income.

• Typical Demand ($D_1$): The cost increase is shared between producers and consumers. The price rises to equilibrium $E_1$, but the quantity also falls.

• The ability of producers to pass on costs to consumers depends primarily on the slope of demand.

Demand Shocks and Price Volatility

• Raw materials such as aluminium, copper, lead, and zinc exhibit high price volatility compared to finished goods.

• In demand shocks, price and quantity move in the same direction, but the split between price and quantity changes depends on the supply curve.

• Raw Materials Supply: Typically have a steep supply curve ($S_{raw}$). Expanding supply (e.g., opening copper mines) is expensive, labour-intensive, and requires significant time. Reopening disused mines also requires substantial investment.

• Finished Goods Supply: Typically have a flatter supply curve ($S_{finished}$). Manufacturers can usually increase production in the short run more easily than raw material extractors.

• Economic Cycles: Shifts in demand curves ($D_0$ to $D_{boom}$ or $D_{bust}$) reflect cycles of growth or recession.

  • For raw materials, demand shocks lead to significant price fluctuations with minimal changes in quantity traded.

  • For finished products, demand shocks lead to minimal price changes but significant fluctuations in quantity.

• Seller revenues decline during recessions and increase during recoveries in both cases, but the driver (price vs. quantity) differs based on the product type.

Defining Price Elasticity of Demand

• The slope is an insufficient measure of price sensitivity because it is influenced by units of measurement (e.g., euros vs. yuan, litres vs. gallons) and the relative value of the good (e.g., a $€1$ increase on a $€3$ sandwich vs. a $€30,000$ car).

• Own Price Elasticity of Demand ($\epsilon_D$): Defined as the ratio of the percentage change in quantity demanded to the percentage change in the price of the good.

• Arc Elasticity: Measures response over a specific segment.

  • Formula: $\epsilon_D = \frac{\frac{\Delta D(p)}{D(p)}}{\frac{\Delta p}{p}} = \frac{\Delta D(p)}{\Delta p} \times \frac{p}{D(p)}$.

  • Drawback: Sensitivity depends on the direction of movement (e.g., point $A$ to $B$ vs. $B$ to $A$).

• Point Elasticity: Measures sensitivity at a specific point as the change becomes infinitely small.

  • Formula: $\epsilon_D = \frac{d D(p)}{d p} \times \frac{p}{D(p)}$.

• Special Cases:

  • Perfectly Inelastic Demand: Vertical line, $\epsilon_D = 0$. Quantity does not respond to price.

  • Perfectly Elastic Demand: Horizontal line, $\epsilon_D = -\infty$. Quantity response is infinite to any price change.

• For a linear demand curve, elasticity is not constant. It is $0$ at the horizontal intercept, $-\infty$ at the vertical intercept, and exactly $-1$ at the midpoint.

Elasticity and Revenue Relationships

• Total Revenue ($TR$) is defined as $TR(p) = p \times D(p)$.

• Inelastic Demand (|\epsilon_D| < 1): Price and revenue move in the same direction. A price increase leads to higher revenue because the drop in quantity is minimal.

• Elastic Demand (|\epsilon_D| > 1): Price and revenue move in opposite directions. A price increase leads to lower revenue because the quantity demanded falls significantly.

• Unitary Elasticity ($|\epsilon_D| = 1$): Occurs at the midpoint of a linear demand curve; revenue is maximized here.

Determinants and Categories of Consumption Goods

• Ordinary Goods: Goods where there is a negative relationship between price and demand. This is driven by two factors:

  • Substitution Effect: Consumers replace expensive goods with cheaper alternatives (e.g., switching from beef to chicken).

  • Income Effect: A price rise reduces purchasing power, effectively acting like a fall in income.

• Exceptions to the Law of Demand:

  • Giffen Goods: Goods where demand increases as price increases (an ascending demand curve).

  • Snob Goods: Goods that become more attractive at higher prices due to perceived status or as a signal of higher quality.

• Determinants of Elasticity:

  • Substitutability: More available substitutes lead to higher elasticity (e.g., brand-level soft drinks vs. soft drinks as a whole group).

  • Urgency: Life-saving medical products are more inelastic than furniture.

  • Time Frame: Long-term elasticity is higher than short-term elasticity because consumers have more time to find alternatives (e.g., developing fuel-efficient cars after the $1973$ oil crisis).

Empirical Own Price Elasticities (Belgian Data)

• Inelastic groups (|\epsilon_D| < 1):

  • Medical care ($-0.01$)

  • Communications ($-0.03$)

  • Water and soft drinks ($-0.15$)

  • Heating ($-0.15$)

  • Food ($-0.36$)

  • Rental ($0.01$ - note: small positive value likely within margin of error)

• Elastic groups (|\epsilon_D| > 1):

  • Tobacco ($-1.01$)

  • Vehicles ($-1.37$)

Own Price Elasticity of Supply

• Defined as the percentage change in quantity offered divided by the percentage change in price.

  • Formula: $\epsilon_S = \frac{d S(p)}{d p} \times \frac{p}{S(p)}$.

• Supply elasticity is typically positive as higher prices trigger higher quantities offered.

• Perfectly Inelastic Supply ($\epsilon_S = 0$): Vertical curve. Seen in seasonal, perishable agriculture where the harvest cannot be increased or stored.

• Perfectly Elastic Supply ($\epsilon_S = \infty$): Horizontal curve. Common in international trade analyses where small countries (like Belgium purchasing oil) are price takers and can buy any quantity at the world market price.

• Elasticity of supply is determined by production costs. If costs rise rapidly with additional production, supply is steep/inelastic. If production can expand easily, supply is elastic.

Income Elasticity and Engel Curves

• Income Elasticity ($\epsilon_y$): The ratio of the percentage change in quantity demanded to the percentage change in income.

  • Formula: $\epsilon_y = \frac{d D(y)}{d y} \times \frac{y}{D(y)}$.

• Engel Curve: The graphical representation of the relationship between quantity demanded and income.

• Classification of Goods:

  • Inferior Goods: Demand falls as income increases (\epsilon_y < 0).

  • Normal Goods: Demand increases as income increases (\epsilon_y > 0).

  • Necessity Goods: Income elasticity is between $0$ and $1$ (0 < \epsilon_y < 1). Budget share decreases as income rises.

  • Luxury Goods: Income elasticity is greater than $1$ (\epsilon_y > 1). Budget share increases as income rises.

• Budget Share ($w$): Defined as $w = \frac{p D(y)}{y}$. The relationship between the change in budget share and income depends on whether \epsilon_y  1.

• Engel's Law: Observed by Ernst Engel, stating that the budget share for food declines as a household becomes wealthier.

Historical Figures in Statistics

• Ernst Engel (1821-1896): Director of the Saxon Bureau of Statistics and a romantic liberal. He formulated Engel's Law based on Belgian data.

• Edouard Ducpétiaux (1804-1868): Belgian inspector general of prisons. He collected detailed household accounts for $1,000$ working-class households in $1853$. One of his striking findings was that a prison inmate in Belgium was materially better off than the poorest working-class households.

Cross-Price Elasticity of Demand

• Measures the percentage change in the quantity demanded of one good in response to a percentage change in the price of another good.

  • Formula: $\epsilon_{cross} = \frac{\Delta D(p_j)}{D(p_j)} \times \frac{p_i}{\Delta p_i}$.

• Substitutes: Cross-price elasticity is positive. For example, if the price of wine increases, the demand for beer increases.

• Complements: Cross-price elasticity is negative. For example, if the price of charging stations increases, the demand for electric cars decreases.

• Independent Goods: Cross-price elasticity is close to zero (e.g., cheese and shoes).

Case Study: US Soft Drink Market Elasticities

• Income Elasticities:

  • Mountain Dew: $1.83$ (Luxury good).

  • Coca-Cola: $1.18$ (Luxury good).

  • Pepsi: $0.75$ (Necessity good).

  • Sprite: $0.87$ (Necessity good).

• Own Price Elasticities (all elastic, |\epsilon_D| > 1):

  • Coca-Cola: $-3.79$

  • Pepsi: $-3.94$

  • Sprite: $-2.84$

  • Mountain Dew: $-4.39$

• Cross-Price relationships:

  • Coca-Cola and Pepsi are strong substitutes ($2.18$ and $2.34$ cross-elasticities respectively).

  • Coca-Cola and Sprite are effectively independent goods ($0.00$ or $0.15$).

  • Sprite and Mountain Dew appear as complements in this specific dataset ($-1.86$ and $-2.73$).