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Chapter 9: Problem 7

The United States currently imports all of its coffee. The annual demand for coffee by U.S. consumers is given by the demand curve \(Q=250-10 P,\) where \(Q\) is quantity (in millions of pounds) and \(P\) is the market price per pound of coffee. World producers can harvest and ship coffee to U.S. distributors at a constant marginal (= average) cost of \$8 per pound. U.S. distributors can in turn distribute coffee for a constant \(\$ 2\) per pound. The U.S. coffee market is competitive. Congress is considering a tariff on coffee imports of \(\$ 2\) per pound. a. If there is no tariff, how much do consumers pay for a pound of coffee? What is the quantity demanded? b. If the tariff is imposed, how much will consumers pay for a pound of coffee? What is the quantity demanded? c. Calculate the lost consumer surplus. d. Calculate the tax revenue collected by the government. e. Does the tariff result in a net gain or a net loss to society as a whole?

Short Answer

Expert verified
a. Without a tariff, consumers pay $10 per pound of coffee and the quantity demanded is 150 million pounds. b. With a tariff, consumers pay $12 per pound of coffee and the quantity demanded reduces to 130 million pounds. c. The lost consumer surplus is $20 million. d. The tax revenue collected by the government is $260 million. e. The tariff results in a net gain of $240 million to society.

Step by step solution

01

No Tariff Scenario

To start, it is necessary to determine the equilibrium price and quantity in the no tariff scenario. The supply is the cost of production, which is $8 for harvesting and shipping, and $2 for distribution. Thus, the price that distributors will sell at, will be $10 per pound. Substituting this into the demand curve \(Q=250-10 P, \) you get the quantity demanded as: \(Q=250-10*10=150\) million pounds.
02

Tariff Scenario

When a $2 tariff is imposed, this effectively increases the distributors' price to $12. Substituting this into the demand curve again results in a new quantity demanded. This is: \(Q=250-10*12=130\) million pounds.
03

Lost Consumer Surplus

Consumer surplus is the area between the demand curve and the price level. When the price increases from $10 to $12, the triangle formed between these prices and the demand curve represents the lost consumer surplus. This can be calculated as \(\frac{1}{2} * dP * dQ = \frac{1}{2} * 2 * (150-130) = 20\) million.
04

Calculate Tax Revenue

The tax revenue for government can be calculated as the tariff times the new quantity, hence, the tax revenue is $2 * 130 = $260 million.
05

Net Effect on Society

Considering the tax revenue gained by the government and the consumer surplus lost by the consumers, the net change to society is tax revenue minus lost surplus, which is $260 million - $20 million = $240 million. Since this is a positive number, the tariff results in a net gain to society.

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