Solution:
Given Oil's inverse demand function in France: P = 364 - 48*Q and inverse supply function as: P = 12 + 40*Q
1) Finding equilibrium price and quantity (in autarky):
Equating the two equations above (since at equilibrium same amount will be supplied as demanded) and the price charged will also be equal. So,
364 - 48*Q = 12 + 40*Q
364 - 12 = 40*Q + 48*Q
352 = 88*Q
Q = 352/88 = 4.
And equilibrium price, P = 364 - 48*4 = $172
So, equilibrium quantity is 4 billions of barrels per year and equilibrium price is $172 per barrel.
2) Given that the international price of a barrel of oil = $100
a) Since, the price per barrel of oil is lower for rest of the world as compared to France, we can claim that the rest of the world have comparative advantage.
b) Given inverse demand function: P = 364 - 48*Q, so demand function becomes: Qd = (364/48) - (1/48)*P
And with inverse supply function: P = 12 + 40*Q, supply function becomes: Qs = (1/40)*P - (12/40)
As the world price is lower than that which prevails in France, under free trade, consumers will wish to import the barrels of oil. In such case, producers in France will not be able to sell out anything, suffering a huge loss. Thus, in order to compete with the world in oil market, producers in France will reduce the price of oil to world price, that is, $100 per barrel.
So, at price of $100 per barrel of oil, Quantity demanded domestically, Qd = (364/48) - (1/48)*100 = 5.5
While the quantity supplied domestically, Qs = (1/40)*100 - (12/40) = 2.2
c) Since, the domestic quantity demanded (consumption) of barrels of oil is higher than the domestic quantity supplied, this clearly means that France is an importer of oil (as the excess demand is fulfilled by imports).
Imports = Domestic consumption - domestic production
Imports = 5.5 - 2.2 = 3.3 billions of barrels of oil
Thus, France will produce 2.2 billions of barrels of oil domestically, and import 3.3 billions of barrels of oil, to meet the domestic demand of 5.5 billions of barrels of oil.
3) Keep referring the graph below:
Under autarky:
Consumer surplus (area of triangle AEC) = (1/2)*(equilibrium qty)*(maximum willingness to pay - equilibrium price)
CSa = (1/2)*4*(364 - 172) = $384 (grey triangle in graph)
Producer surplus (area of triangle CEB) = (1/2)*(equilibrium qty)*(equilibrium price - minimum willingness to receive)
PSa = (1/2)*4*(172 - 12) = $320 ((yellow+blue) triangle in graph)
So, national surplus (i.e. total welfare) = CSa + PSa = 384 + 320 = $704
Under free trade:
Consumer surplus (area of triangle AGD) = (1/2)*(quantity demanded)*(maximum willingness to pay - price paid)
CSt = (1/2)*5.5*(364 - 100) = $726 ((grey+yellow+green) triangle in graph)
Producer surplus (area of triangle BDF) = (1/2)*(quantity supplied)*(price received - minimum willingness to receive)
PSt = (1/2)*2.2*(100 - 12) = $96.8 (blue triangle in graph)
So, national surplus (i.e. total welfare) = CSt + PSt = 726 + 96.8 = $822.8
We can see that by moving from autarky to free trade, consumers have gained (their surplus increased from 384 to 726, as now they have to pay lower price for each barrel of oil; more oil is consumed at a lower price), producers have lost (their surplus has decreased from 320 to 96.8, as now with global openness due to high domestic price, demand for their oil has decreased as consumers can buy same barrel at lower price globally, so even domestic sellers are forced to decrease their price; lower oil is supplied at lower price). Overall the nation has gained (as gain in consumer surplus is higher than loss in producer surplus).
So, well being of consumers has increased by (726 - 384=) $342, well being of sellers has decreased by (320 - 96.8=) $223.2, and nation's well being has increased by (822.8-704= or 342-223.2=) $118.8 (green triangle).
I know that the eq. price is 172 and quantity is 172 for France. I know...
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