Question

In each of the following examples, determine whether the price effect or the quantity effect dominates when the tax is applied. [LO 20.3] a. The government raises taxes on the 10 million iPods sold each year from \(\$ 10\) per iPod to \(\$ 20\) per iPod. The new equilibrium quantity is 9 million iPods. b. In response to concerns about chewing gum in schools, the government raises the tax on packs of gum from 20 cents per pack to 30 cents per pack. Before the tax increase, 50 million packs were sold each year. After the tax increase, 40 million packs are sold each year. c. Worried that Americans are addicted to coffee, the government raises the 5 -cent tax on a cup of coffee to 10 cents. Before the tax increase, 10 billion cups were sold each year. Afterward, 5 billion cups are sold each year.

Short answer

a: Price effect dominates; b: Price effect dominates; c: Neither effect dominates, both are equal.

Step-by-step solution

Calculate Price Effect for iPods

The price effect is calculated by multiplying the increase in tax per unit by the new quantity sold. Here, the tax increase is \(20 - 10 = 10\) dollars per iPod, and the new quantity sold is 9 million iPods. Thus, the price effect is \(10 \times 9,000,000 = 90,000,000\) dollars.

Calculate Quantity Effect for iPods

The quantity effect is determined by multiplying the original tax by the reduction in quantity sold. The original tax is \10\ dollars per iPod, and the quantity reduced from 10 million to 9 million, a reduction of 1 million. Thus, the quantity effect is \(10 \times 1,000,000 = 10,000,000\) dollars.

Determine Dominant Effect for iPods

Compare the price and quantity effects for iPods. The price effect of 90 million dollars is greater than the quantity effect of 10 million dollars. Therefore, the price effect dominates.

Calculate Price Effect for Gum

Here, the tax increased by 10 cents (from 20 cents to 30 cents). The new quantity sold is 40 million packs. Thus, the price effect is calculated by \(0.10 \times 40,000,000 = 4,000,000\) dollars.

Calculate Quantity Effect for Gum

The original tax was 20 cents per pack. The quantity decreased from 50 million to 40 million, a reduction of 10 million. Thus, the quantity effect is \(0.20 \times 10,000,000 = 2,000,000\) dollars.

Determine Dominant Effect for Gum

Compare the price and quantity effects for gum. The price effect of 4 million dollars is greater than the quantity effect of 2 million dollars. Therefore, the price effect dominates.

Calculate Price Effect for Coffee

The tax increase is 5 cents (from 5 cents to 10 cents) with the new quantity being 5 billion cups. Hence, the price effect is \(0.05 \times 5,000,000,000 = 250,000,000\) dollars.

Calculate Quantity Effect for Coffee

The original tax was 5 cents per cup. The quantity decreased from 10 billion to 5 billion, a reduction of 5 billion. Thus, the quantity effect is \(0.05 \times 5,000,000,000 = 250,000,000\) dollars.

Determine Dominant Effect for Coffee

For coffee, the price effect and quantity effect are equal at 250 million dollars each. Thus, neither effect dominates; they are balanced.

Key concepts

Price Effect

The price effect is a pivotal concept when analyzing the impact of taxes on goods. When a tax is imposed or increased, the price effect measures how much additional revenue is generated from each unit sold after the tax increase. It’s calculated by multiplying the increase in tax per unit by the new quantity sold.

Understanding the price effect can help us determine whether the tax adjustment significantly generates more revenue based on the quantity that continues to be sold. If the price effect dominates, it indicates that the extra revenue from each unit outweighs the loss in selling fewer units.

For instance, in the iPod example, with a tax increase from $10 to $20 per unit, but sales dropping to 9 million units, the price effect was found by calculating:

• Increase in tax per unit = $10
• New quantity sold = 9 million
• Price effect = $10 x 9,000,000 = $90,000,000

Here, the increased revenue from the tax hike per unit significantly bolstered the overall tax revenue despite a slight drop in sales.

Quantity Effect

The quantity effect occurs when changes to tax influence the volume of goods sold. When the tax on a product is increased, it can lead to a decrease in quantity sold, as fewer consumers are willing to purchase the product at a higher effective price.

The quantity effect is calculated by multiplying the original tax rate by the reduction in the quantity sold. This effect shows the loss in revenue due to the decreased number of sales.

Take the example of the coffee tax where the tax increased from 5 cents to 10 cents per cup. Sales dropped drastically from 10 billion to 5 billion cups:

• Original tax rate = 5 cents per cup
• Reduction in quantity = 5 billion cups
• Quantity effect = $0.05 x 5,000,000,000 = $250,000,000

The dramatic decrease in sales due to the higher tax shows a strong quantity effect, indicating the higher effective price caused a significant reduction in purchased quantity.

Equilibrium Quantity

The equilibrium quantity is a core concept in economics, representing the quantity at which the supply and demand in the market are balanced. After a tax is imposed, this equilibrium can shift, leading to a new equilibrium quantity.

Taxes alter the equilibrium by increasing the cost of goods, thereby affecting consumer demand and production supply. The new equilibrium quantity is the quantity sold after the market settles post-tax, reflecting the adjustments made by consumers and producers in response to the tax.

Let's consider the gum tax example. The tax per pack increased by 10 cents, and the number of packs sold dropped from 50 million to 40 million annually. This reflects a new equilibrium quantity post-tax, showing the market adjustment:

• Original equilibrium = 50 million packs
• New equilibrium quantity = 40 million packs

This shift illustrates how taxes can influence the overall market behavior, leading to a new balance between what consumers are willing to purchase and what producers supply.