A country imports 5 billion tonnes of coal per year and domestically produces an
ID: 1190039 • Letter: A
Question
A country imports 5 billion tonnes of coal per year and domestically produces another 4.5 billion tonnes of coal per year. The world price of coal is $50 per tonne. Assuming linear schedules, economists estimate the price elasticity of domestic supply to be 0.3 and the price elasticity of domestic demand to be 0.2 at the current equilibrium. Consider the changes in social surplus that, would result from imposition of a $20 per tonne import fee on coal that would involve annual administrative costs of $125 million. Assume that the world price will not change us a result of the country imposing the import fee, but that the domestic price will increase by $20 per tonne. Assume national standing. Calculate the following: Quantity consumed after the imposition of the benefits import fee. Quantity produced after the imposition of the import fee. Quantity imported after the benefits inquisition of the import foe. Estimate the annual social net benefits of the import fee.Explanation / Answer
a) When the price change from $50 to $70 then the domestic demand will change from 9.5 billion metric tonne to [{-0.2*($70-$50)/$50*9.5}+9.5] = 8.74 billion tonnes.
b) Now domestic supply will change from 4.5 billion tonnes to [{0.3*($70-$50)/$50*4.5}+4.5] = 5.04 billion tonnes
c) New import quantity will be 8.74-5.04 = 3.7 billion tonnes.
d)
1)Change in domestics producer surplus
Revenue = (5.04-4.5)*70 = $37.8 billion
Cost = 0.5*($20)*0.54+50*0.54 = $32.4
Net change = $5.4 billion
Surplus of higher prices on previous production = 20*4.5 = $90 billion/year
so total domestic producer surplus = 90+5.4 = $95.4 billion/year
2) Change in consumer surplus
Deadwieght loss from reduced demand = 0.5*$20*0.76 = $7.6 billion/year
Additional payment on quantity still consumed = $20*8.74 = $174.8/year
total change in consumer surplus = (-$7.6 billion) + (-$174.8 villion) = -$182.4 billion/year
3) change in tax revenues
import fee on new import = $20*3.7 = $74 billion/year
administrative cost = -$0.125 billion/year
=$74 - $0.125 = $73.875 billion/year
So Annual social net benefit =1) + 2) + 3) = 95.4-182.4+73.875 = -$13.125 billion . That is there is annual net social loss of $13.125 billion/year
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