Notes@HKU by Jax

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=pP=p

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

  1. Shortage
  2. Reduction of Product Quality (S↑S\uparrow because lowered COGS, D↓D\downarrow because of lower quality)
  3. Bribery and Wasteful Lines
  4. Loss of Gains from Trade (DWL)
  5. Misallocation of Resources
Q1=Intersect(P=p,D)Q2=Intersect(P=p,S)Shortage=Q2−Q1\begin{aligned} Q_1 &= \text{Intersect}(P=p, D)\\ Q_2 &= \text{Intersect}(P=p, S)\\ \text{Shortage} &= Q_2 - Q_1\\ \end{aligned}

Allocation of limited supply

There are three ways to allocate the limited supply:

  1. Bibery
  2. Waiting in line
  3. Highest valued customers The three ways affect the welfare loss and customer surplus differently.
Bribe equilibriumBEq=y(Intersect(x=x(Q1),D))−pLetV=BEq×Q1Total value of bribery=Vwhen allocating by briberyWelfare loss={DWLbribery or highest-valuedDWL+Vwaiting in lineCustomer surplus={CS+Vhighest-valuedCSbribery or waiting in line\begin{aligned} \text{Bribe equilibrium} BEq &= y(\text{Intersect}(x = x(Q_1), D)) - p\\ \text{Let} V &= BEq \times Q_1\\ \text{Total value of bribery} & = V \text{when allocating by bribery}\\ \text{Welfare loss} &= \begin{cases} DWL & \text{bribery or highest-valued}\\ DWL + V & \text{waiting in line} \end{cases}\\ \text{Customer surplus} &= \begin{cases} CS + V & \text{highest-valued}\\ CS & \text{bribery or waiting in line}\\ \end{cases} \end{aligned}
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