Question

The supply of coffee is given by q= 100+p, while the demand is given by q= 120−4p. The government imposes a price-ceiling at p= 2. Find the dead-weight loss.

(a) 2.5 (b) 15 (c) 2 (d) 0.5

Answer 1

Option (a).

In equilibrium, quantity demanded equals quantity supplied.

100 + p = 120 - 4p

5p = 20

p = 4

q = 100 + 4 = 104

When p = 2,

Quantity demanded (Qd) = 120 - (4 x 2) = 120 - 8 = 112

Quantity supplied (Qs) = 100 + 2 = 102

Since consumers can buy only what producers will sell, market quantity is 102.

When q = 102, from demand function,

102 = 120 - 4p

4p = 18

p = 4.5 (Demand price)

Deadweight loss = (1/2) x (Demand price - Ceiling price) x Change in quantity = (1/2) x (4.5 - 2) x (104 - 102)

= (1/2) x 2.5 x 2 = 2.5