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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 \((=\text { average })\) 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 the tariff, consumers pay \$10 for a pound and the quantity demanded are 150 million pounds. b. With the tariff, consumers pay \$12 per pound and the quantity demanded decrease to 130 million pounds. c. The lost consumer surplus is 220. d. The government collects 260 in tax revenue. e. There's a net gain of 40 for the society as a whole.

Step by step solution

01

Determine the price and quantity without tariff

Firstly, find the price & quantity demanded without the tariff. The cost of coffee to U.S. distributors is \$8 (harvest and shipping) + \$2 (distribution) = \$10. In a competitive market, the price equals the cost, so \(P = \$10\). Substitute \(P = \$10\) to the demand equation (\(Q=250-10 P\)): \(Q=250-10*10=150\). So, without the tariff, consumers pay \$10 per pound and the quantity demanded is 150 million pounds.
02

Determine the price and quantity with tariff

Then, determine the price & quantity demanded with the tariff. The total cost with the tariff becomes \$10 + \$2 = \$12. Replace \(P = \$12\) into the demand equation to get the new quantity: \(Q=250-10*12=130\). So, with the tariff, consumers pay \$12 per pound and the quantity demanded is 130 million pounds.
03

Calculate the lost consumer surplus

The consumer surplus is the area of the triangle between the price and the demand curve. The lost consumer surplus is the change in this area from the price increase due to the tariff. Without tariff, the consumer surplus is \(\frac{1}{2}(250-150)(10) = 500\). With tariff, the consumer surplus is \(\frac{1}{2}(250-130)(12) = 720\). The lost consumer surplus is \(500-720 = -220\).
04

Calculate the tax revenue collected by the government

The tax revenue is the tax per unit times the quantity sold, which is \$2 * 130 = 260.
05

Evaluate the net welfare effect

Lastly, evaluate the net effect on society. The tariff causes a loss to consumers (lost consumer surplus), but it also brings revenue to the government (tax revenue). The net effect is the sum of these two effects: \(-220 + 260 = 40\). The positive outcome means that there's a net gain for society as a whole.

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