Question

Calculation: suppose the demand and supply for cola is Q D = 15 – 10P and Q S = 40P – 50. The current equilibrium is $1.30 and 2 million bottles. a. Calculate the share of a tax that will be borne by consumers and the share borne by producers b. If a tax of $0.15 per bottle is created, what do buyers now pay for a bottle? What will sellers receive?

Answer 1

(a)

According to Tax Incidence:

Proportion of Tax bear by Consumer = (E_s/(-E_d + E_s))

Proportion of Tax bear by producer = (-E_d/(-E_d + E_s))

Here E_d = Elasticity Of demand and E_s = Elasticity of supply

Note we have use -ve sign before E_d because E_d is negative and we want absolute value of E_d

Elasticity of demand = E_d = (dQ_D/dP)(P/Q)

Here P = 1.3 and Q = 2 and dQ_D/dP = -10

Hence E_d = -10*1.3/2 = -6.5

Elasticity of Supply = E_s = (dQ_s/dP)(P/Q)

Here P = 1.3 and Q = 2 and dQ_s/dP = 40

Hence E_s = 40*1.3/2 = 26

Hence Using above formulas we have

Proportion(or share) of Tax bear by Consumer = (E_s/(-E_d + E_s)) = 26/(-(-6.5) + 26)

= 0.8 ~ 80%

Proportion(or share) of Tax bear by Producer = (-E_d/(-E_d + E_s)) = -(-6.5)/(-(-6.5) + 26)

= 0.2 ~ 20%

(b)

Tax = 0.15 , Amount of Tax bear by consumer = 0.8*0.15 = 0.12

Hence buyers will pay = 1.3 + 0.12 = $1.42

Amount of Tax bear by Consumer = 0.2*0.15 = 0.3

Hence Sellers will receive = 1.3 - 0.03 = $1.27