After economics class one day, your friend suggests that taxing food would be a good way to raise revenue because the demand for food is quite inelastic. In what sense is taxing food a "good" way to raise revenue? In what sense is it not a "good" way to raise revenue?

When we say that the demand for a good is inelastic, we're describing a situation where the quantity demanded does not change significantly even when there is a substantial change in the product's price. Essentials such as food, medication, and utilities tend to have inelastic demand because consumers need these products for their daily survival, regardless of price fluctuations.

Consider this practical example: even if the price of bread doubles, people will still purchase roughly the same amount because it's a staple of many diets. A formula to represent elasticity is the price elasticity of demand (PED), which is calculated as the percentage change in quantity demanded divided by the percentage change in price. This is represented as \( PED = \frac{\% \Delta Qd}{\% \Delta P} \), where \( \Delta Qd \) is change in quantity demanded and \( \Delta P \) is change in price.

For inelastic goods, this ratio is less than one in absolute value, reflecting the relatively unresponsive nature of quantity demanded to price changes.

The impact of taxation on different goods can vary greatly depending on the elasticity of demand. When the government imposes a tax on a good with inelastic demand, it can expect to collect revenue without causing a significant drop in sales. This is because consumers are likely to continue purchasing the item even at higher prices.

For instance, let’s say a government decides to impose a tax on gasoline. Although the price per gallon may increase, people will generally still need to fill their cars to go about their daily lives. However, it's crucial to analyze who bears the brunt of the tax. Usually, the supplier and the consumer share the tax burden, but the exact split depends on the relative elasticities of supply and demand for the good in question.

Regressive taxation refers to a tax system where the tax rate decreases as the taxable amount increases, meaning it takes a larger percentage from low-income earners than from high-income earners. Taxes on necessities like food and clothing are often considered regressive because these items make up a larger fraction of the budget of low-income families compared to wealthier ones.

Let's imagine a scenario where both a wealthy individual and a person living paycheck to paycheck spend the same amount on food each month. If a tax is introduced on food, both pay the same amount of tax in absolute terms, but for the low-income individual, this tax represents a heftier slice of their total income. This creates a disproportionate financial strain on lower-income households, leading to debates about the fairness of such taxation policies.

Public revenue is the income that governments collect from various sources, such as taxes, fees, fines, and from the sale of goods and services. The purpose of public revenue is to fund essential services and projects that benefit society, such as infrastructure, education, healthcare, and public safety.

In the context of taxing inelastic goods, like food, the government can secure a steady stream of revenue due to the predictability of consumer purchasing behavior. While this might seem advantageous from a fiscal standpoint, it is essential to consider the broader economic and social implications, particularly the impact on low-income groups.

Ultimately, when strategizing about raising public revenue, governments must weigh the benefits of increased funds against the potential downsides, such as economic inequality and potential public dissatisfaction.