5.4 Price Elasticity of Supply of Supply and Putting It All Together

Definition: The price elasticity of supply (e_S) measures the responsiveness of the quantity supplied of a good or service to a change in its price, assuming all other factors remain constant.
Calculation: It is the ratio of the percentage change in quantity supplied to the percentage change in price:
eS = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}} = \frac{\%\Delta QS}{\%\Delta P}
Direction: The price elasticity of supply is generally positive because price and quantity supplied typically move in the same direction (due to the law of supply).
Responsiveness: A larger eS indicates that firms are more responsive to price changes; a smaller eS indicates less responsiveness.

Inelastic Supply: If the price elasticity of supply is between 0 and 1.0 (0 < e_S < 1.0), supply is considered inelastic. This means the percentage change in quantity supplied is less than the percentage change in price.
Elastic Supply: If the price elasticity of supply is greater than 1.0 (e_S > 1.0), supply is considered elastic. This means the percentage change in quantity supplied is greater than the percentage change in price.
Unit Elastic Supply: If the price elasticity of supply equals 1.0 (e_S = 1.0), supply is unit elastic. The percentage change in quantity supplied is equal to the percentage change in price.
Perfectly Inelastic Supply: A vertical supply curve represents perfectly inelastic supply, where e_S = 0. This means the quantity supplied does not change at all, regardless of price changes.
- Example: The supply of new Beatles' songs is perfectly inelastic because the band members John Lennon and George Harrison are no longer alive to create new music.
Perfectly Elastic Supply: A horizontal supply curve represents perfectly elastic supply, where e_S = \infty (infinity). Suppliers are willing to provide any amount at a specific price, but none at a lower price.

The elasticity of supply depends on how quickly production costs increase when producers try to expand output.
- Elastic Supply: If costs do not rise much when output expands (e.g., software downloads, toothpicks), supply will be more elastic. A small price increase leads to a significant increase in quantity supplied.
- Inelastic Supply: If costs increase rapidly when output expands (e.g., farmers trying to plant more corn late in the season, needing to use less fertile land or more resources), supply will be more inelastic. Even a large price increase leads to only a small increase in quantity supplied.

The length of the time horizon under consideration significantly impacts supply elasticity.
- Short Run: In the short run, producers have limited options to adjust production. Supply tends to be more inelastic.
  - Example: A corn farmer cannot quickly plant significantly more corn in the middle of a growing season, even if prices spike.
- Long Run: Over a longer time horizon, producers have more flexibility to adjust production (e.g., converting land from other crops, investing in new machinery). Supply tends to become more elastic.
  - Example: The same corn farmer can plan to devote more acreage to corn next year if prices remain high.

The concept of supply elasticity can be applied to labor supply, where individuals supply their labor services to employers.
Typical Upward-Sloping Labor Supply (Positive Elasticity):
- In most cases, higher wages increase the opportunity cost of leisure, motivating people to work more hours.
- Example: A small pay raise or a promotion to a higher-paying management position often leads to a willingness to work longer hours.
Backward-Bending Labor Supply Curve (Negative Elasticity):
- At very high wage levels, individuals may reach a point where further wage increases lead them to work less rather than more, opting for more leisure time (e.g., early retirement, fewer shifts).
- Example: Professional golfers, once they achieve very high earnings per event, may choose to enter fewer tournaments in favor of other activities.

Elasticity helps explain why prices for some goods are volatile while others are stable when demand or supply shifts.

When demand is inelastic (e.g., oil), a shift in supply (e.g., a decrease) causes a large change in price and a small change in quantity.
When demand is elastic (e.g., computers), an equivalent shift in supply causes a small change in price and a large change in quantity.
- Conclusion: Inelastic demand contributes to greater price volatility when supply shifts.

When supply is inelastic (e.g., avocados during a growing season), a shift in demand (e.g., an increase) results in a large change in price and a small change in quantity, as producers cannot easily expand output.
When supply is elastic (e.g., jeans), an equivalent shift in demand causes a small change in price and a large change in quantity, as producers can easily accommodate the change in demand by making more.
- Conclusion: Inelastic supply contributes to greater price volatility when demand shifts.

Context: The coronavirus pandemic led to a sudden surge in demand for consumer-grade toilet paper due to panic buying and a shift in consumption patterns (more use at home).
Reasons for Inelastic Supply:
- Just-in-Time Production: Toilet paper sales are typically predictable, so producers optimized supply chains for just-in-time manufacturing, minimizing excess capacity and storage costs.
- Input Constraints: Most consumer-grade toilet paper uses fast-growing eucalyptus trees from Brazil. In the short run, the supply of this key input was relatively fixed, causing pulp costs to skyrocket for producers.
- Production Capacity: Factories typically run at high capacity (around 92%). While producers increased this to 99.8% by speeding lines and adding shifts, this only resulted in about an 8% production increase, far less than the surge in demand.
- Unwarranted Long-Term Expansion: Installing new production lines is extremely costly (around 300 \text{ million} per line) and not justified for a temporary demand spike, as post-pandemic demand is expected to return to normal levels.
Outcome: The extremely inelastic supply, combined with a large increase in demand and price control measures (anti-gouging statutes), led to persistent shortages rather than large price increases that would clear the market.