Price ceilings and floors

Policy makers often intervene in markets to achieve a desired outcome. Two common forms of intervention are price ceilings and price floors.

Price ceilings

Price ceilings

P=p

Limited price that a good can be sold. A price ceiling is ineffective if set above $P_eq$ . The following are the effects of a price ceiling:

Shortage
Reduction of Product Quality ( $S\uparrow$ because lowered COGS, $D\downarrow$ because of lower quality)
Bribery and Wasteful Lines
Loss of Gains from Trade (DWL)
Misallocation of Resources

\begin{aligned} Q_D &= \text{Intersect}(P=p, D)\\ Q_S &= \text{Intersect}(P=p, S)\\ \text{Shortage} &= Q_D - Q_S\\ \end{aligned}

Allocation of limited supply

There are three ways to allocate the limited supply:

Bibery
Waiting in line
Highest valued customers The three ways affect the welfare loss and customer surplus differently.

\begin{aligned} \text{Bribe equilibrium } BEq &= y(\text{Intersect}(x = x(Q_S), D)) - p\\ \text{Let } V &= BEq \times Q_S\\ \text{Total value of bribery } & = V \text{when (1)}\\ \text{Welfare loss} &= \begin{cases} DWL & \text{(1) or (3)}\\ DWL + V & \text{(2)} \end{cases}\\ \text{Customer surplus} &= \begin{cases} CS + V & \text{(3)}\\ CS & \text{(1) or (2)}\\ \end{cases} \end{aligned}

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