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 for hula beans will be 100 cents per pound after the tariff. Domestic consumers will lose \$400 million while domestic producers will gain \$200 million. The government will generate revenue of \$2400 million from the tariff.

Step-by-step solution

Analyze the Supply Curve

The initial supply curve is \(P = 50 + Q\). Since the world hula bean market price is 60 cents per pound and the US does not influence this price, we need to find out the quantity supplied at this price. Setting \(P = 60\) in the supply equation we get \(Q = 60 - 50 = 10\) million pounds.

Analyze the Demand Curve

The demand curve is \(P = 200 - 2Q\). To find the quantity demanded at the world price of 60 cents per pound, we set \(P = 60\) in the demand equation, giving \(Q = (200 - 60)/2 = 70\) million pounds.

Determine the domestic price after the tariff

When a tariff of 40 cents per pound is imposed, the domestic price will rise by the amount of the tariff. The new domestic price \(P'\) is \(P + \text{tariff} = 60 + 40 = 100\) cents per pound. This shifts the supply curve to \(P' = 50 + Q + 40\), which can be simplified to \(P' = 90 + Q\). At this new price, the quantity supplied is \(Q = 100 - 90 = 10\) million pounds and the quantity demanded is \(Q = (200 - 100)/2 = 50\) million pounds.

Calculate Changes to Consumer and Producer Surplus

The gain or loss to domestic consumers can be represented by the decrease in consumer surplus, which is the area of the triangle formed by the demand curve, the horizontal line at the initial price, and the vertical line at the quantity after the tariff. With a base of \(70 - 50 = 20\) and a height of \(100 - 60 = 40\), the loss of consumer surplus is \(\frac{1}{2}.base.height = 0.5.20.40 = \$400\) million. The gain to domestic producers is the increase in producer surplus, which is the area of the triangle formed by the supply curve, the horizontal line at the new price, and the vertical line at the quantity after the tariff. This equals to \(\frac{1}{2}.base.height = 0.5.10.40 = \$200\) million.

Calculate Government Revenue

The government revenue from the tariff is \(price.quantity = 40. (70 - 10) = \$2400\) million.

Key concepts

Supply and Demand

In the world of economics, understanding the concepts of supply and demand is crucial. Here, the supply curve is given by the equation \(P = 50 + Q\), where \(P\) is the price in cents and \(Q\) is the quantity in millions of pounds. Think of this curve as a graphical representation showing how much of a good or service suppliers will make available at a given price. As we analyze this for hula beans at a global price of 60 cents, we find that the domestic supply amounts to 10 million pounds.
On the flip side, the demand curve \(P = 200 - 2Q\) depicts the relationship from the consumer's perspective. This curve helps us understand how much consumers are willing to purchase at various prices. When we place the world price of 60 cents into this equation, the demand for hula beans spikes at 70 million pounds.
These supply and demand calculations form the backbone of many economic discussions, offering a baseline for further analysis.

Consumer Surplus

Consumer surplus is a nifty concept that shows the difference between what consumers are willing to pay and what they actually pay. It’s like finding a good deal at a store when you were willing to pay more.
Before the tariff, consumers enjoyed buying hula beans at 60 cents, with a quantity demanded at 70 million pounds. However, with the introduction of a 40-cent tariff, the domestic price climbed to 100 cents. This price hike reduced the quantity demanded to 50 million pounds.
The painful consequence for consumers is a loss in their surplus—previously, they could buy more beans at a lower price. The loss in consumer surplus due to the tariff can be quantified as \[\text{Consumer Surplus Loss} = \frac{1}{2} \times (70 - 50) \times (100 - 60) = \$400 \text{ million}\] This simple calculation highlights the burden consumers bear following the tariff imposition.

Producer Surplus

When we talk about producer surplus, we are focusing on the benefits to sellers. Like consumer surplus, it represents the difference between the market price (after the tariff) and the least amount that producers would have been willing to accept.
Without the tariff, producers sell hula beans at the global price of 60 cents, leading to a certain satisfaction level. After applying a 40-cent tariff, the domestic price skyrockets to 100 cents, encouraging suppliers to provide up to 10 million pounds of beans.
This increase in price translates into an increase in producer surplus, calculated as\[\text{Producer Surplus Gain} = \frac{1}{2} \times (10 - 0) \times (100 - 60) = \$200 \text{ million}\]This measure helps us see how producers benefit from higher prices brought by the tariff, despite the overall market distortion.

Government Revenue

One of the primary motivations for imposing tariffs is to generate government revenue. In our scenario, the government rakes in income by charging a tariff of 40 cents per pound on hula bean imports.
Given that the domestic demand drops from 70 million pounds to 50 million after the tariff, this means that 20 million pounds are now imported under the new domestic pricing regime. Calculating the revenue becomes straightforward:\[\text{Government Revenue} = 40 \text{ cents} \times (70 - 10) \text{ million pounds} = \$2400 \text{ million}\]This revenue allows the government to utilize resources for public spending, but not without the trade-off of hurting consumer surplus. The balance between generating revenue and minimizing market inefficiencies is a delicate one, often the heart of economic policy debates.