Question

1. The government is thinking about a tax on potash of $00 per kg. The government knows that the elasticity of demand for potash is ε= -0.50, while the elasticity of supply is η=5. The current market equilibrium quantity is 10,000,000 kg, while the current equilibrium price that consumers pay is $5.00 per kg. Suppose that the tax is assessed on producers who collect the tax for the government.
   1. What is the statutory incidence of the tax? (You must show your work)
2. 2. What will be the economic incidence of the tax? (You must show your work)
3. 3. What will be the after-tax price that consumers pay? (You must show your work)
4. 4. What will be the after-tax quantity that consumers buy? (You must show your work
5. 5. What will be the after-tax price that producers receive? (You must show your work)
6. 6. How much revenue will be generated by the tax? (You must show your work)
7. 7. What will be the dead-weight loss from the tax? (You must show your work)
8. 8. What will be the efficiency-loss ratio? (You must show your work)

Answer 1

Given:

tax = $1.00 per kg

elasticity of demand ε= -0.50, elasticity of supply η=1.5

market equilibrium quantity = 10,000,000 kg,  equilibrium price = $5.00

Some calculations are needed first:

(i) Incidence of tax:

Economic incidence of tax is the share of the tax amount paid by consumers and by producers. It is the actual amount of tax paid by each of them. It is calculated by the formula:  η/ (η- ε) = 1.5/2 = 75%

75% of the tax amount ($0.75 per kg) is paid by consumers. 25% of the tax amount ($0.25 per kg) is paid by the producers.

(ii) Price paid by consumers:

Equilibrium price = $5. Tax burden = $0.75 (from (i) )

Therefore, pricepaid by consumers = 5 + 0.75 = $5.75

(iii) Price paid by producers:

Equilibrium price = $5 Tax burden on producers = $0.25

Therefore, price recceived by producers = 5 - 0.25 = $4.75

(iv) New quantity:

When tax is imposed, the price goes up. Demand falls. There is a new equilibrium point now. Quantity produced also falls according to the elasitcity of demand. Tax is charged on the reduced quantity of the new equilibrium. It is calculated as follows:

ε = (∆Q/ ∆P) * P/Q

0.5 = (∆Q/ 0.75) * 5/ 10,000,000 0.375 = ∆Q. 0.0000005 ∆Q = 750,000

So, the new quanity is 10,000,000 - 750,000 = 9,250,000

a) What is the statutory incidence of the tax?

Ans: $ 9,250,000

reason: When tax is imposed, the price goes up. Demand falls. There is a new equilibrium point now. Quantity produced also falls according to the elasitcity of demand. Tax is charged on the reduced quantity of the new equilibrium. The new quanity is 10,000,000 - 750,000 = 9,250,000 (from (iv) above)

Tax @ $1 pe kg = $9,250,000

b) What will be the economic incidence of the tax?

Ans : 75% borne by consumers; 25% borne by producers (from (ii) above )

c) What will be the after tax price that consumers pay?

The after tax price paid by consumers = $5.75 (5+ 0.75) (from (ii) above)

d) What will be the after-tax quantity that consumers buy？

After tax quantity = 9,250,000 kg (10,000,000 - 750,000) (from (iv) above)

e) What will be the after-tax price that producers receive?

Producers receive $4.75 (from (iii) above)

reason: Tax incidence borne by producers is $0.25 per kg. So, they will receive 5 - 0.25 = $4.75

f) How much revenue will be generated by the tax?

Tax revenue will be quantity after tax * tax amount

= 9,250,000 * 1 = $9,250,000

g) What will be the dead-weight loss from the tax?

Deadweight loss will be ½ * 1 * 750,000 = $375,000

h) What will be the efficiency-loss ratio?

Efficiency loss ratio = deadweight loss / tax revenue

= 375,000 / 9,250,000 = 0.04