Question

A country imports 3 billion barrels of crude oil per year and domestically produces another 3 billion barrels of crude oil per year. The world price of crude oil is $18 per barrel. Assuming linear schedules, economists estimate the price elasticity of domestic supply to be 0.25 and the price elasticity of domestic demand to be − 0.10 in the neighbourhood of the current equilibrium. a. Assuming that the world price of crude oil does not change when the country imposes a $6 per barrel import duty on crude oil, determine the domestic price, and the three quantities: domestic consumption, domestic production, and import volume after the imposition of the import duty. b. Calculate the impact on producer surplus, consumer surplus, and government revenues. Also calculate the net social benefits associated with the imposition of the import duty. c. Redo the calculations for (a) and (b) on the assumption that the reduction in the country’s demand for crude oil reduces the world price by $2 per barrel. d. By how much does the “terms of trade effect” of the import duty (i.e. the import price reduction impact) offset the efficiency losses. In other words, what are the net social benefits to the importing country? If foreign exporters were also given standing in the cost-benefit calculation, would overall welfare be increased?

Answer 1

a)

The imposition of the import fee would have the following effect on the domestic market:

The domestic price increases by $6 due to import fee. New Domestic price = 24
Change in quantity consumed: -.1 = (Δq/Δp)(p/q)
Δq = (-.1)Δp(q/p)
Δq = (-.1)($6)(6 billion)/($18)
Δq = -.2 billion
Change in domestic supply: .25 = (Δq/Δp)(p/q)
Δq = (.25)Δp(q/p)
Δq = (.25)($6)(3 billion)/($18)
Δq = .25 billion

Thus, after imposition of the fee

• Domestic consumption will fall to 5.8 billion barrels per year
• Domestic production will rise to 3.25 billion barrels per year
• Imports will fall to 2.55 billion barrels per year (5.8 billion - 3.25 billion)

B)

Change in domestic producer surplus

Surplus from additional .25 billion barrels produced Revenue = (.25 billion)($24) = $6 billion/year
Production costs (area under supply schedule) = (.5)($24-$18)(.25 billion) + ($18)(.25 billion) = $5.25 billion/year
Net change in surplus from new production = $6 billion/year-$5.25 billion/year = $0.75 billion/year
Surplus from higher prices on original production = ($6)(3 billion) = $18 billion/year
Total change in producer surplus = $0.75 billion + $18 billion = $18.75 billion/year

Change in consumer surplus:
"Deadweight loss" from reduced consumption = (.5)($24-$18)(.2 billion) = $0.6 billion/year
Additional payments on quantity still consumed = ($6)(5.8 billion) = $34.8 billion/year
Total change in consumer surplus =(-$0.6 billion) + (-$34.8 billion) = -$35.4 billion/year

Change in tax revenues:
Import fee applied to new import level: ($6)(2.55 billion) = $15.3 billion/year

CBA from country's perspective:
Costs: Change in consumer surplus -$35.4 billion/yr
Benefits: Change in domestic producer surplus $18.75 billion/yr
Net gain to tax-payers $15.3 billion/yr
Net benefits:   -$1.35 billion/yr

The import fee would have negative net benefits of -$1.35 billion/year and therefore does not pass the CBA test.

C)

The world price reduces by $2 , So Domestic decreases by 2 from 6 : New Domestic Price : 22 , New World Price : 16

Change in quantity consumed: -.1 = (Δq/Δp)(p/q)
Δq = (-.1)Δp(q/p)
Δq = (-.1)($4)(6 billion)/($18)
Δq = -.133 billion
Change in domestic supply: .25 = (Δq/Δp)(p/q)
Δq = (.25)Δp(q/p)
Δq = (.25)($4)(3 billion)/($18)
Δq = .167 billion

Thus, after the tax,

• 5.867 billion barrels are consumed,
• 3.167 billion barrels are domestically produced
• 2.7 billion barrels are imported.

Consumer surplus loss = (.5)(.134 billion)($22-$18) + (5.867 billion)($22-$18) = $23.736billion/year
Producer surplus gain  = (.5)(.167 billion)($4) + (3 billion)($4)
= $12.334 billion/year

Net taxpayer gain = ($6)(2.7 billion) = $16.2 billion/yr.

net benefits are $4.798 billion per year.