What is consumer surplus when there is no tariff?
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. (40 points) Suppose a “large country” H has an excess demand curve for good X given by P=70-2X. The worldwide excess supply curve for good X is P=10+X.
a. Graph the curves.
b. What is the free trade equilibrium quantity and price when there is no tariff? Mark the equilibrium on your graph as point A.
c. What is consumer surplus when there is no tariff?
d. A tariff of 20% is imposed on imports of good X. Mark the new equilibrium on the graph as point B. Calculate the equilibrium quantity, consumer price and producer price after the tariff. (Hint: We can analyze this by “shifting” the supply curve to P=1.20*(10+X). It is OK to get fractions of units.
e. What is the consumer surplus with the 20% tariff? What is the tariff revenue? [Hint: Start with the producer price you got in c. Multiply by .05 to get the tax per unit. Multiply by the number of units to get the revenue.] Add these together to get total welfare for the home country. Has welfare gone up for H due to the tariff?
f. Now suppose the tariff is 100%. As in part d, mark the new equilibrium on the graph as point C. Calculate the equilibrium quantity, consumer price and producer price after the tariff.
g. What is the consumer surplus with the 100% tariff? What is the tariff revenue? Add these together to get total welfare for the home country. Has welfare gone up for H due to the tariff?
h. At point A, what is the price elasticity of supply?
i. Given your answer for h, what is the “optimal” tax rate? That is, apply the inverse elasticity rule from the end of lesson 9 to the original equilibrium. [Technical note. Applying the inverse elasticity rule as I want you to do here with the original equilibrium will get us close to the “optimal.” But it is not exact. The inverse elasticity technically is the optimal rate to charge at the optimal post-tax equilibrium!! But actually solving for what that is non-trivial (remember, the elasticity of supply is changing along the supply curve). In this problem, it is .60, but that should not be your solution to this question
j. Calculate the consumer surplus, tariff revenue and total surplus to H at the tax rate you calculated in i.
2. (20 points) Refer to the following graph for the Home country before and after a tariff. The home producer of the good is a monopolist prior to trade.
a. Under free trade (prior to the tariff), the home country produces 75 units and imports (185 – 75) = 110 units.
b. The consumer surplus prior to the tariff is
c. According to the graph, the home country imposed a tariff of _____ dollars per unit, and the new quantity of imports is _____.
d. After the tariff, what is the decrease in consumer surplus?
e. After the imposition of the tariff, the home monopolist saw an increase in production of ______ and the producer surplus increased by ________.
f. The home government collects __in tariff revenue.
g. The deadweight loss due to the tariff is:
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