Question

The domestic supply and demand curves for hula beans are as follows: \\[ \begin{aligned} \text {Supply:} & P=50+Q \\ \text {Demand:} & P=200-2 Q \end{aligned} \\] where \(P\) is the price in cents per pound and \(Q\) is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff.

Short answer

The domestic price of hula beans with the tariff imposed will be 100 cents per pound. The imposition of the tariff results in a loss of $8 million to consumers, a gain of $44 million to producers, and $20 million in government revenue.

Step-by-step solution

Establish the World Price

The current world price (without tariff) for hula beans is given as 60 cents per pound.

Calculate the Domestic Price with Tariff

The proposed tariff is 40 cents per pound. So, the domestic price will be the sum of the world price and the tariff, which gives \(60 + 40 = 100\) cents per pound.

Determine the Quantity Supplied and Demanded at the New Price

At this new price, the quantity supplied can be determined by substituting the price into the supply equation, which gives \(Q = 100 - 50 = 50\) million pounds. The quantity demanded can be found by substituting the price into the demand equation: \(Q = (200 - 100) / 2 = 50\) million pounds.

Calculate the Gain or Loss to Consumers

The loss to consumers is defined as the change in price times the quantity demanded. Before the tariff, consumers paid 60 cents per pound for 70 million pounds (from substituting \(P = 60\) into demand equation), which totals to $42 million. After the tariff, they pay 100 cents per pound for 50 million pounds, which totals $50 million. The change is therefore $50 million - $42 million = $8 million loss for consumers.

Calculate the Gain or Loss to Producers

The gain to producers is defined as the change in price times the quantity supplied. Before the tariff, producers sold at 60 cents per pound for 10 million pounds (from substitifying \(P = 60\) into supply equation), which totals to $6 million. After the tariff, they sell at 100 cents per pound for 50 million pounds, which equates to $50 million. The change is therefore $50 million - $6 million = $44 million gain for producers.

Determine the Government's Revenue from the Tariff

The government's revenue from the tariff is the tariff rate times the quantity demanded after the tariff is imposed. This gives 40 cents per pound times 50 million pounds, which equals $20 million in government revenue.

Key concepts

Domestic Price Calculation

Understanding the domestic price calculation in the context of international trade and tariffs is essential for comprehending how a country's market can be affected by policy changes. When a government imposes a tariff on imports, it artificially raises the price of those goods within the domestic market. In our example with hula beans, the initial world price is 60 cents per pound. By imposing a tariff of 40 cents per pound, the domestic price becomes 100 cents per pound, as tariffs are effectively a tax added on top of the original price. It's important to note this new price serves as the baseline for all further calculations regarding consumer and producer surpluses, as well as government revenue.

With this adjustment, the domestic market has to adapt, and the interaction between domestic supply and demand will now occur at this new, higher price level. Calculating the domestic price with the tariff included is a straightforward addition of the world price and the tariff rate. However, the implications of this new price are far-reaching, affecting both the behavior of consumers and producers and subsequently influencing the overall economy.

Consumer Surplus

Consumer surplus represents the difference between what consumers are willing to pay for a good and what they actually pay. It reflects the economic benefit to consumers from engaging in transactions in the market. When tariffs drive up prices, consumer surplus decreases because the price consumers pay moves closer to or exceeds their maximum willingness to pay. In the case of hula beans, consumers initially enjoyed a lower price, corresponding to a higher consumer surplus. After the tariff, they face a higher domestic price of 100 cents per pound, which reduces the consumer surplus.

The loss to consumers can be quantified by the increase in price multiplied by the quantity purchased. Prior to the tariff, consumers were enjoying lower prices, but after the tariff, they have to spend more for the same amount, leading to a significant reduction in surplus. This loss is a direct result of the tariff's impact on the market price and demonstrates the immediate economic impact tariffs can have on the well-being of domestic consumers.

Producer Surplus

Producer surplus is the benefit producers receive when they sell a good or service at a price greater than their minimum acceptable price, which is often represented by the supply curve. Imposing a tariff can increase producer surplus in the domestic market because the higher price allows domestic producers to either sell more of their product at the higher price or to sell the same amount of product at an increased price.

In our exercise with the hula beans, the domestic producers' surplus increased due to the tariff raising prices from 60 cents to 100 cents per pound. The higher price results from the tariff's artificial inflation of costs for imported goods, making domestically produced hula beans more competitively priced. By comparing the producer revenue before and after the tariff, we can measure the gain in surplus. This gain is significant because it not only reflects higher prices but also potentially an expanded market share as the domestic product becomes more attractive relative to the now more expensive imports.

Government Revenue

Government revenue generated from tariffs is calculated by multiplying the tariff rate by the quantity of imported goods post-tariff. This revenue is a form of taxation on imports and becomes an important fiscal tool for governments. In the hula beans example, the imposed tariff of 40 cents per pound on imported hula beans led to $20 million in government revenue.

This revenue arises because consumers still need to purchase hula beans, despite the increased price, and the government collects 40 cents for every pound sold domestically. It presents a direct financial gain for the government, but it's important to consider that this revenue comes at the cost of consumer surplus and can also lead to international trade tensions. When assessing the economic impact of tariffs, one must balance this source of government income against the potential losses in consumer welfare and any retaliatory measures from trade partners.

Supply and Demand Analysis

Supply and demand analysis is foundational in understanding the effects of tariffs on domestic prices, consumer and producer surplus, and government revenue. This analysis relies on the supply and demand curves, which graphically represent the relationship between price and quantity for goods. When a tariff is imposed, the supply and demand equilibrium is disrupted, leading to a new domestic price.

For our exercise, before any tariff imposition, the market equilibrium can be found where the supply and demand curves intersect. However, the imposition of a tariff changes the conditions of the market, as the added cost shifts the equilibrium. After the tariff's application, as demonstrated in our example, both the quantity supplied and demanded at the new price level will align with the tariff-inclusive price. The ability to precisely calculate these new quantities, along with the post-tariff price, allows us to measure the direct economic impacts of the tariff on different market stakeholders, formalizing the abstract concepts of surpluses and government revenue into tangible figures.