Question

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

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

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.

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.

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 \(500-720 = -220\).

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.

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.

Key concepts

Consumer surplus

The concept of consumer surplus revolves around the difference between what consumers are willing to pay for a good and what they actually pay. This difference is represented visually by the area between the demand curve and the market price on a graph. In simpler terms, it's like a bonus for consumers because they get the good for less than the maximum price they are willing to pay.

In a coffee market without a tariff, the consumer surplus can be calculated using the formula for the area of a triangle: \(\frac{1}{2}\times \text{base} \times \text{height}\). Initially, the base is the difference in quantity demanded, and the height is the price. Without a tariff, the base is 250 - 150 = 100 million pounds and the height is \$10, giving a consumer surplus of \(\frac{1}{2} \times 100 \times 10 = 500\) million dollars.

After the tariff, the consumer surplus decreases due to the increased price and reduced quantity demanded. Consumers end up paying more, which decreases their surplus from what it was before the tariff.

Competitive market

A competitive market is characterized by many buyers and sellers, all of whom sell a standardized product and are price takers. This means that no single buyer or seller can influence the market price. Instead, the price is determined by the aggregate supply and demand.

In the case of the U.S. coffee market, being competitive means that the price consumers pay directly reflects the total costs faced by distributors. Before any tariff imposition, the price of coffee was perfectly aligned to the costs: \\(8 for harvest and shipping added to \\)2 for distribution, totaling \$10 per pound.

This efficient market mechanism ensures that, in a competitive market, prices are set at a level where supply matches demand, resulting in optimal levels of production and consumption.

Import tariffs

Import tariffs are taxes imposed on goods brought into a country, and they directly affect the price of imported goods. Tariffs are often used to protect domestic industries from foreign competition by making imported goods more expensive.

In our coffee exercise, the U.S. considered adding a \\(2 tariff per pound of coffee, which directly increased the cost from \\)10 to \$12. As a result, the quantity demanded decreased from 150 million pounds to 130 million pounds, because higher prices tend to reduce the quantity that consumers are willing to purchase.

The imposition of tariffs is a double-edged sword: while they can provide benefits like increased government revenue, they often lead to reduced consumer surplus and can distort market outcomes.

Tax revenue

Tax revenue from tariffs is the income that a government earns from the taxes on imported goods. It's calculated by multiplying the tariff amount by the quantity of imports.

In this scenario, with the coffee tariff, the collected tax revenue is \\(2 times the 130 million pounds of coffee, equaling \\)260 million. This revenue is a gain for the government and can be used for public expenditures and services.

However, while tax revenue from tariffs supports government budgets, it can also have broader economic implications. Consumers, paying more due to the tariff, may reduce their overall consumption. Thus, while the government benefits from increased revenue, it often comes at the cost of reduced consumer welfare and potential efficiency losses in the market.