Question

The following scenarios describe the price elasticity of supply and demand for a particular good. All else equal (equilibrium price, equilibrium quantity, and size of the \(\operatorname{tax}\) ), in which scenario will government revenues be the highest? Choose only one. [LO 6.5] a. Elastic demand, inelastic supply. b. Inelastic demand, inelastic supply. c. Elastic demand, elastic supply. d. Inelastic demand, elastic supply.

Short answer

Scenario (b) will result in the highest government revenue.

Step-by-step solution

Understanding Elasticity Terms

Elasticity refers to how much the quantity demanded or supplied reacts to a change in price. 'Elastic' means a large reaction, while 'inelastic' means a small reaction. If demand is elastic, consumers buy much less of a good if the price rises, and if supply is elastic, producers make much more if the price rises.

Analyzing Scenarios

We need to determine which combination of elasticities will maximize government revenue from taxes. Government revenue from a tax is calculated as the tax rate times the quantity sold. Thus, revenue is maximized if the quantity sold doesn't decrease significantly when a tax is applied.

Evaluating Elastic Demand, Inelastic Supply (a)

With elastic demand and inelastic supply, consumers will reduce their quantity demanded significantly due to a tax increase, leading to a large decrease in quantity sold, reducing government revenue.

Evaluating Inelastic Demand, Inelastic Supply (b)

With inelastic demand and inelastic supply, both consumers and producers do not significantly change their behavior with a price increase. Thus, the quantity sold stays more stable, potentially leading to higher government revenue.

Evaluating Elastic Demand, Elastic Supply (c)

With elastic demand and elastic supply, both consumers and producers react strongly to price changes, reducing the quantity sold dramatically when a tax is applied, thus hurting government revenue.

Evaluating Inelastic Demand, Elastic Supply (d)

With inelastic demand, consumers are not very responsive to price increases, keeping the quantity sold high. However, since supply is elastic, producers can easily reduce production, potentially leading to significant changes in quantity sold.

Conclusion on Highest Government Revenue

The scenario with inelastic demand and inelastic supply (b) is the most likely to result in the highest government revenue from a tax. This is because neither consumers nor producers change their purchasing or selling quantities significantly, maintaining a stable quantity of goods sold.

Key concepts

Supply and demand

Supply and demand are fundamental concepts in economics that explain how markets function. The interaction between Supply, which is the total amount of a product or service available to consumers, and Demand, which is the consumers' desire and willingness to buy a product or service, determines the price and quantity of goods sold in the market.

When supply and demand are balanced, the market reaches an equilibrium price and quantity. This is where the amount consumers want to buy equals the amount producers want to sell. Any changes in market conditions, such as taxes, can shift the supply or demand curve, affecting the equilibrium. In the context of elasticity, supply and demand can react differently. Elastic supply or demand means a small change in price leads to a large change in quantity supplied or demanded. Conversely, inelastic supply or demand means those changes are small.

Government revenue

Government revenue from taxes is a crucial element for funding public services like education, healthcare, and infrastructure. The revenue generated depends significantly on how much of the good is sold after a tax is applied.

To understand this, think of government revenue as the product of the tax rate and the quantity of goods sold. If the demand and supply for a good are inelastic, it means that the quantity sold does not drastically drop after a tax is implemented. Therefore, the government can collect more revenue because sales remain stable despite the tax. Understanding the elasticity of goods is essential for governments when considering which goods to tax. High government revenue is usually achieved when both supply and demand are inelastic because both consumers and producers continue to engage in the market despite higher prices.

Taxation impact

Taxes can impact a market's equilibrium and the overall economic efficiency. When a tax is imposed, it essentially drives a wedge between the price buyers pay and the price sellers receive. This can lead to a drop in the quantity sold, altering the supply and demand balance.

The impact of taxation is closely connected to the elasticity of both supply and demand. If either of these is elastic, a small tax can lead to a significant decrease in the quantity sold, which can reduce government revenue. On the other hand, if both supply and demand are inelastic, the market can absorb the tax better, resulting in smaller changes to the equilibrium quantity. This is why inelastic markets tend to yield higher government revenues post-taxation, as both buyers and sellers are less responsive to price changes.

Equilibrium analysis

Equilibrium analysis involves examining the state of a market where supply equals demand. In this state, there is no tendency for change because the quantity of the goods supplied matches the quantity demanded.

When analyzing taxes and their effects, understanding equilibrium helps assess where the market stands after a new tax is implemented. If the market is inelastic, the equilibrium quantity remains relatively stable even after taxation, thereby maintaining higher government revenue.

• Elastic demand: Significant change in quantity demanded with price change.
• Inelastic demand: Little to no change in quantity demanded with price change.
• Elastic supply: Significant change in quantity supplied with price change.
• Inelastic supply: Little to no change in quantity supplied with price change.

A stable equilibrium in the context of taxes ensures minimal negative impacts on sales volumes, allowing better revenue optimization for governments.