given by Q$iP) = 200P and QP(P) = 400 (a) Suppose this is a closed economy. Find the equi What are the consumer surplus, producer surpl For the remainder of the question, assume that the e (b) The world supply is perfectly elastic at price Pa price, quantity traded, and total import. What producer surplus, aggregate surplus, and gains
answers for part b,c,d and e
The domestic (ss) supply is,
Qs = 200P
The domestic (dd) demand is,
Qd = 4000- 200P
At free market equilibrium, dd = ss
⟹ 4000- 200P = 200P
⟹ 400P = 4000
⟹ P = $10
Qs = 200P
= 200*10
= 2000 units
The equilibrium price (P*) and quanity (Q*) are : $10 and 2000 units.
(b) The world price is Pw = 5.
The free market equilibrium price is P* = $ 10 (as calculated above).
The domestic dd at Pw = $5 is,
Qd’ = 4000- 200*5
= 3000 units
The domestic ss at Pw = $5 is
Qs’ = 200*5
= 1000 units
The quantity traded in the domestic market is 1000 units.
At the Pw = $5 there is a shortage of commodity as quantity (ss) supplied is less than quantity (dd) demanded. This excess dd will be met by imports from foreign markets.
The import dd function is,
Md = Qd – Qs
= 4000- 200P – 200
Md = 4000 – 400P
Therefore, Md at Pw = $5 is,
= 4000 – 400*5
= 2000 units.
Therefore, total import is 2000 units.
CS at P* = $10
= 1/2 * (20 - 10) * 2000
= 10000 units
PS at P*= $10
= 1/2 * 10 * 2000
= 10000 units
TS at P*= $10
= PS + CS
= 10000 + 10000
= 20000 units
CS at Pw = $5
CSw = 1/2 * (20 - 5) * 3000
= 22500 units.
PS at Pw = $5
PSw = 1/2 * 5 * 1000
= 2500 units.
TS at Pw = $5
= PSw + CSw
= 2500 + 22500
= 25000 units
Gains from trade = rise in TS
= TSw – TS
= 25000 – 20000
= 5000 units.
Therefore, at Pw = $5 the consumer surplus is CSw = 22500 units, producer surplus is PSw = 2500 units and TSw = 25000 units. The gains from trade is: 5000 units.
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