Welfare, Efficiency, and Deadweight Loss in Market Outcomes

Welfare Criteria and Efficiency in Markets

Defining Welfare and Efficiency

• Welfare Criteria: In this course, market outcomes are measured by the total surplus they generate.

  • Total Surplus ($TS$): The sum of consumer surplus ($CS$) and producer surplus ($PS$) at a given outcome.

• Efficiency: An outcome is defined as efficient if:

  • It has higher total surplus than any other possible outcome in the market.

  • It maximizes total surplus out of all possible outcomes.

  • A key property is that it is impossible to make one person better off without making another person worse off. For instance, you cannot increase $CS$ without simultaneously lowering $PS$, and vice versa.

• Outcome Definition: An outcome constitutes a specific price, quantity supplied, and quantity demanded.

Market Equilibrium and Efficiency

• Key Finding: The equilibrium outcome in a market is inherently efficient.

  • The market equilibrium maximizes the total feasible surplus.

  • It is also the only outcome that maximizes total surplus; any other outcome would yield a lower total surplus.

Impact of Non-Equilibrium Prices: Price Above Equilibrium

• Scenario: Let's consider a price ($P$) above the equilibrium price, for example, $P = ext{300}$ (equilibrium was $P = ext{200}$, $Q = ext{30 million}$).

• Quantity Effects:

  • Quantity demanded ($Q_D$) would be $20 ext{ million}$.

  • Quantity supplied ($Q_S$) would be $45 ext{ million}$.

  • There is excess supply (QS > QD).

  • Only $20 ext{ million}$ units will be sold, as sellers cannot sell more than what buyers are willing to buy.

• Total Surplus ($TS$) Changes:

  • $TS$ decreases significantly compared to equilibrium.

  • $10 ext{ million}$ units (from $20 ext{ million}$ to $30 ext{ million}$) that were sold in equilibrium are no longer sold.

  • The surplus from these lost transactions is not generated, leading to an overall reduction in $TS$. The total surplus becomes a trapezium bounded by the demand and supply curves up to $20 ext{ million}$ units, which is smaller than the equilibrium triangle.

• Consumer Surplus ($CS$) Changes:

  • $CS$ decreases in two ways:

    1. Lost Transactions: Buyers lose the surplus from the $10 ext{ million}$ units no longer sold.

    2. Surplus Transfer: For the $20 ext{ million}$ units still sold, consumers pay a higher price, transferring some of their surplus to producers. This means the $CS$ triangle (Area 1) is smaller than the original equilibrium $CS$ triangle.

• Producer Surplus ($PS$) Changes:

  • Producers lose surplus from the $10 ext{ million}$ lost transactions.

  • However, producers gain surplus (Area 2) from consumers on the $20 ext{ million}$ units sold due to the higher price.

  • Therefore, $PS$ may go up or down depending on the relative magnitudes of the lost surplus from fewer transactions and the gained surplus from the higher price per unit sold.

• Deadweight Loss ($DWL$):

  • The lost surplus from the transactions that no longer happen (the gray area, labeled Area 4 plus Area 5 in the diagrams) is called deadweight loss.

  • $DWL$ explicitly measures how much less total surplus there is compared to the equilibrium outcome.

  • For prices above equilibrium, $TS$ is strictly less than under the equilibrium outcome.

Impact of Non-Equilibrium Prices: Price Below Equilibrium

• Scenario: Let's consider a price below the equilibrium price, for example, $P = ext{100}$.

• Quantity Effects:

  • Quantity supplied ($Q_S$) would be $15 ext{ million}$.

  • Quantity demanded ($Q_D$) would be $40 ext{ million}$.

  • There is excess demand (QD > QS).

  • Only $15 ext{ million}$ units will be sold, as buyers cannot purchase more than what suppliers are willing to sell.

• Total Surplus ($TS$) Changes:

  • $TS$ decreases compared to equilibrium because $15 ext{ million}$ units (from $15 ext{ million}$ to $30 ext{ million}$) that were sold in equilibrium are no longer sold.

  • The total surplus becomes a trapezium, again smaller than the equilibrium triangle.

• Consumer Surplus ($CS$) Changes:

  • Consumers lose surplus from the $15 ext{ million}$ units no longer sold (Area 4).

  • However, for the $15 ext{ million}$ units still sold, consumers pay a lower price, transferring some surplus from producers to them (Area 2).

  • Therefore, $CS$ may go up or down depending on the relative sizes of lost transactions and gained surplus per unit.

• Producer Surplus ($PS$) Changes:

  • Producers unambiguously lose surplus because they sell fewer units at a lower price. Their $PS$ becomes a smaller triangle (Area 3), a strict subset of their equilibrium $PS$.

• Deadweight Loss ($DWL$):

  • The lost surplus from the units not being sold (Area 4 plus Area 5 in the diagrams) represents the $DWL$.

  • Prices below equilibrium also lead to a strictly lower total surplus.

Why Equilibrium Maximizes Total Surplus

• Total Surplus Formula: $TS = CS + PS$ which can also be expressed as the sum of (willingness to pay ($WTP$) of consumers - willingness to supply ($WTS$) of producers) for all units traded.

• Quantities Below Equilibrium:

  • If the quantity sold is below the equilibrium quantity (e.g., $15 ext{ million}$ units where equilibrium is $30 ext{ million}$), there are still units between $15 ext{ million}$ and $30 ext{ million}$ where WTP > WTS.

  • For each of these units, selling them would generate positive additional total surplus.

  • By not selling these units, the market imposes a deadweight loss, meaning there are