Question

Consider a competitive market characterized by the following supply and demand formulas: Demand: P = 105 - 0.25QD Supply: P = 0.275QS

(c) With the aid of a diagram, carefully explain what would happen in this market if the government were to impose a price ceiling of $30 per unit in this market. As part of your answer calculate the size of the deadweight loss associated with this price control.

Answer 1

Sol 1 : Demand = P : 105 - 0.25Qd

Supply = P : 0.275Qs

Equilibrium = 105 - 0.25Qd = 0.275Qs

105 = 0.275Qs + 0.25Qd

105 = 0.525Qd ........... (Qd = Qs , at equilibrium)

105/0.525 = Qd

200 = Qd = Qs

P= 0.275 x 200 = $55

(C) If , the government imposes a price ceiling of $30 per unit , then there will be the following effects on the market.

• As, price decreases in the market , demand increases and supply increases.
• It creates a shortage in the market due to excess demand over the supply.
• So , there will be rationing of the product because of limited supply.

Deadweigh loss is the loss of trade due to policy of the government. (Price ceiling)

So, supply when price is $30 ,

Qs = 30/0.275 = 109

Demand when price is $30

Qd = 300

And, price when quantity is 109 units

P = 105 - 0.25 (109)

P = $77.75

So , deadweigh loss is equal to the triangle Shaded in the diagram .

Area of deadweigh loss =

1/2 × base(price) x height(quantity)

1/2 × 47.75 x 91

= 2172.625