Question

Q3) Suppose that the market demand and supply curve in a competitive market are Q"-15 - 2P and QS-P. For each of the following policies, calculate the price and quantity that will be traded and the value of the deadweight loss. a) An excise tax of S1 per unit, paid by producers. b) A subsidy of $2 per unit, paid to consumers. c) A price floor of S7. d) A price ceiling of S4. e) A production quota of 3 units.

Answer 1

Answer : Demand : Q = 15 - 2P

=> 2P = 15 - Q

=> P = (15 - Q) / 2

=> P = 7.5 - 0.5Q

Supply : Q = P

=> P = Q

At equilibrium condition, demand = supply.

=>7.5 - 0.5Q = Q

=> 7.5 = Q + 0.5Q

=> 1.5Q = 7.5

=> Q = 7.5 / 1.5

=> Q = 5

From demand function we get,

P = 7.5 - (0.5 * 5)

=> P = 5

Therefore, the initial market quantity is, Q = 5 and price is, P = $5.

a) After imposing excise tax of $1 on producer, the supply function becomes,

P - 1 = Q

=> P = Q + 1

Now, at new equilibrium,

7.5 - 0.5Q = Q + 1

=> 7.5 - 1 = Q + 0.5Q

=> 6.5 = 1.5Q

=> Q = 6.5 / 1.5

=> Q = 4.3

From demand function we get,

P = 7.5 - (0.5 * 4.3)

=> P = 7.5 - 2.2

=> P = 5.3

Therefore, the price level is, P = $5.3 and quantity is, Q = 4.3 .

Deadweight loss = 0.5 * tax amount * $\Delta$Q

=> Deadweight loss = 0.5 * 1 * (5 - 4.3)

=> Deadweight loss = 0.35

Therefore, here the deadweight loss is $0.35.

b) After subsidy of $2 on consumers the demand demand function becomes,

P - 2 = 7.5 - 0.5Q

=> P = 7.5 + 2 - 0.5Q

=> P = 9.5 - 0.5Q

At new equilibrium,

9.5 - 0.5Q = Q

=> 9.5 = Q + 0.5Q

=> 1.5Q = 9.5

=> Q = 9.5 / 1.5

=> Q = 6.3

From demand function we get,

P = 9.5 - (0.5 * 6.3)

=> P = 9.5 - 3.2

=> P = 6.3

Therefore, the price level is, P = $6.3 and quantity is, Q = 6.3 .

Deadweight loss = 0.5 * subsidy amount * $\Delta$Q

=> Deadweght loss = 0.5 * 2 * (6.3 - 5)

=> Deadweight loss = 1.3

Therefore, the deadweight loss is $1.3.

c) When P = $7,

QD = 15 - (2 * 7)

=> QD = 1

QS = P

=> QS = 7

As QD = 1 which is less than QS, hence market Q = 1.

Therefore, the price is, P = $7 and quantity is, Q = 1.

Deadweight loss = 0.5 * $\Delta$P * $\Delta$Q

=> Deadweight loss = 0.5 * (7 - 5) * (5 - 1)

=> Deadweight loss = 4

Therefore, the deadweight loss is $4.

d) When P = $4,

QD = 15 - (2 * 4)

=> QD = 7

QS = P

=> QS = 4

As QS = 4 which is less than QD, hence market Q = 4.

Therefore, the price is, P = $4 and quantity is, Q = 4.

Deadweight loss = 0.5 * $\Delta$P * $\Delta$Q

=> Deadweight loss = 0.5 * (5 - 4) * (5 - 4)

=> Deadweight loss = 0.5

Therefore, the deadweight loss is $0.5.

e) When Q = 3,

From demand function,

P = 7.5 - (0.5 * 3)

=> P = 7.5 - 1.5

=> P = 6

As market demand price is P = $6, hence the market price is, P = $6.

Therefore, the price level is, P = $6 and quantity is, Q = 3 units.

Deadweight loss = 0.5 * $\Delta$P * $\Delta$Q

=> Deadweight loss = 0.5 * (6 - 5) * (5 - 3)

=> Deadweight loss = 1

Therefore, the deadweight loss is $1.