Country H, which is large, exports good X. Its excess supply curve is given by P
ID: 1116639 • Letter: C
Question
Country H, which is large, exports good X. Its excess supply curve is given by P=100+4X. The world’s excess demand curve for X is 600-2X. 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.)
Find the free trade equilibrium quantity and price of exports.
What is the producer surplus in this equilibrium?
Country H elects to offer a 25% subsidy to exports of X. What is the equilibrium quantity of exports with this subsidy?
What is the producer surplus after the subsidy?
What is the government expenditure on the subsidy?
What is the deadweight loss due to the subsidy?
Calculate the “Terms of Trade” loss for H due to the subsidy.
Explanation / Answer
Free trade equilibrium exists where Supply = Demand
Hence equilibrium is = 100 + 4 X = 600 - 2X
4X +2X = 600-100
6 X. = 500
X. =. 500/6 =83.3 units
Putting the value of x in Supply curve Price = 100+ 4*83.3 = 433.2
B. Producer surplus = 1/2 (* Equilibrium price. - Supply price) * Equilibrium quantity where Supply price is obtained by putting X= 0 units in the eq. P = 100 +4X .
Producer surplus =(433.2-100)*83.3 = 27755.56
c.country H gives a subsidy of 25 percent so the producer can sell the product at 25% less price original price =100+4X
After a subsidy of 25% the P = 0.75 (100+4X) =75+3X ,
Equilibrium = supply = demand , 75+3X =600-2X solving we get X = 105
d.New equilibrium price =75+3*105 =390
Producer surplus = 1/2 (equilibrium subsidised price - supply price )* equilibrium quantity. supply price = value of P = 75 +3*0 =75 when quantity 0, hence producer surplus =1/2(390-75)*105 = 16537.5