Question

Show the work:

1. Suppose the market demand and supply curves are given by Q^d = 20 – 3P and Q^s = P, respectively. Suppose the government imposes a price ceiling of $2:

1. Calculate the magnitude of the resulting shortage.

2. Calculate the resulting full economic price. That is, the maximum price consumers are willing to pay to avoid waiting in line.

Answer 1

Quantity demanded, Qd = 20 - 3P

Quantity supplied, Qs = P

At equilibrium demand will be equal to supply. Equate demand to supply

20 - 3P = P

=> 4P = 20

=> P = $ 5 per unit

Equilibrium quantity, Q = 20 - 3 × 5 = 5 units

When a price ceiling of $ 2 is imposed then the quantity demanded will be equal to

Qd = 20 - 3 × 2 = 14 units.

Quantity supplied, Qs = 2 units.

Shortage = Qd - Qs = 14 - 2 = 12 units.

A. Resulting shortage = 12 units.

B. The price consumers are willing to pay in order to avoid the waiting line will be equal to

2 = 20 - 3P

=> 3P = 20 - 2

=> 3P = 18

=> P = $ 6 per unit.

Maximum price consumers are willing to pay to avoid waiting in line = $ 6 per unit.

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