Examkin

Question

Difficulty: Very hardPrice Controls: Ceilings and Floors

The market demand and supply functions for locally produced rice in a region are given as Qd=1500−20PQ_d = 1500 - 20P and Qs=300+10PQ_s = 300 + 10P, where PP is price per bag (in hundreds of Naira) and QQ is quantity (in thousands of bags). If the government enforces a maximum price ceiling of 25 hundred Naira per bag and an informal black market emerges that absorbs all supplied output, what is the resulting black market price per bag?

  1. 47.50 hundred NairaAnswer
  2. B
    40.00 hundred Naira
  3. C
    70.00 hundred Naira
  4. D
    22.50 hundred Naira

Answer

The black market price per bag is 47.50 hundred Naira.
At the government-imposed price ceiling of Pc=25P_c = 25 hundred Naira, producers only supply Qs=300+10(25)=550Q_s = 300 + 10(25) = 550 thousand bags. In an un-rationed black market, consumers compete for these 550 thousand bags. Substituting Qd=550Q_d = 550 into the demand function 550=1500−20P550 = 1500 - 20P gives 20P=95020P = 950, resulting in a black market price of 47.5047.50 hundred Naira.

Step-by-Step Solution

1
Calculate the quantity supplied at the official price ceiling.
Substitute Pc=25P_c = 25 into the supply equation: Qs=300+10(25)=550Q_s = 300 + 10(25) = 550 thousand bags.
Because the price ceiling is set below equilibrium (Pe=40P_e = 40), suppliers restrict output to 550 thousand bags.
2
Determine the black market price along the demand curve for the restricted quantity.
Set Qd=550Q_d = 550 in the demand equation: 550=1500−20Pbm  ⟹  20Pbm=950  ⟹  Pbm=47.50550 = 1500 - 20P_{bm} \implies 20P_{bm} = 950 \implies P_{bm} = 47.50 hundred Naira.
In an un-rationed black market, consumers compete for the limited quantity supplied (550), bidding the price up to the maximum willingness-to-pay on the demand curve.

Key Concept

Black Market Price Determination under Price Ceilings
Rate this question

Topics

Price Controls: Ceilings and Floors

More questions from this topic