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Country H, which is small, exports good X
Country H, which is small, exports good X. Its excess supply curve is given by P=100+4X. The world price ratio Px/Py is P=200. It is suggested, but not required, that you use a graph to help answer the questions below. (Note that answers may be fractions of a unit.)
a. Find the free trade equilibrium quantity of exports.
b. What is the producer surplus in this equilibrium?
c. Country H elects to offer a 25% subsidy to exports of X. What is the equilibrium quantity of exports with this subsidy?
d. What is the producer surplus after the subsidy?
e. What is the government expenditure on the subsidy?
f. What is H's deadweight loss due to the subsidy?
Expert Solution
a.
Supply Curve P= 100+4x
Price ratio of world(Px/Py) P =200
Substitute the value of Price ratio in the supply curve equation.
P = 100 + 4X
200 = 100 + 4X
4X = 100
X= 25
Free trade quantity for exporting goods = 25 units
b)
The region between the price line and the supply curve for the export of goods is known as producer surplus.
The export supply curve minimum price = 100
Thus,
Producer Surplus= 1/2*(200-100)*25
=1/2*100*25
=1,125
C)
The subsidy was give at price of 200 is 25%
So, the supply curve price line will be 250 (200 of 25%=50, 200+50= 250)
substitute the supply curve value for finding the quantity of export is now
P = 100 + 4X
250 = 100 + 4X
4X = 150
X= 37.5
so, 37.5 is the value of equilibrium quantity of export after giving subsidy.
d)
Producer surplus =1/2*(250-100)*37.5 = $2,812.50
(The minimum price = 100 at export supply curve)
e) The government expenditure of the quantity is Price of 25%
Price is 200
So, Government Expenditure = 200*25%
= 50 Ans
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