Question

Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is upward sloping. Let the price of red pencils and blue pencils be \(p_{r}\) and \(p_{b} .\) What would happen if the government put a tax only on red pencils?

Short answer

A tax on red pencils will lead consumers to switch entirely to buying blue pencils, decreasing demand for red pencils.

Step-by-step solution

Understanding the Problem

To solve this problem, we need to analyze how a tax on red pencils impacts their demand and what the implications are when red and blue pencils are perfect substitutes. Perfect substitutes mean that consumers are indifferent between choosing red or blue pencils.

Setting Up Initial Market Conditions

Assume initially that the market is in equilibrium, where the demand for red pencils is equal to their supply at some price \(p_r\). Similarly, the demand for blue pencils is equal to their supply at price \(p_b\). Since they are substitutes, generally \(p_r = p_b\).

Analyzing the Impact of the Tax

When a tax is imposed solely on red pencils, the cost to consumers for buying red pencils rises. The new effective price consumers see for red pencils is \(p_r + ext{tax}\).

Comparing Post-Tax Prices

With the introduction of the tax, the price of red pencils to consumers is \(p_r + ext{tax}\) while the price of blue pencils remains \(p_b\). Assuming \(p_r = p_b\) before the tax, now we have \(p_r + ext{tax} > p_b\).

Consumer Response to Price Change

Since consumers view red and blue pencils as perfect substitutes, they will shift their consumption entirely towards blue pencils, as they provide the same utility at a lower cost than red pencils after the tax.

Market Outcome

The demand for red pencils will decrease as all consumers switch their preference to blue pencils, resulting in a surplus of red pencils. The supply for blue pencils will need to increase to meet the new demand.

Key concepts

Impact of Taxation

When a government imposes a tax on a product, it affects both the price and the consumption behavior surrounding that product. In the context of red pencils, when a tax is applied, it effectively increases the price consumers have to pay. Here's how taxation impacts the market:

• The price of red pencils rises from \(p_r\) to \(p_r + \text{tax}\). This makes red pencils more expensive than the blue pencils, assuming blue pencils remain untaxed.
• The higher price discourages consumers from purchasing red pencils, as they will opt for cheaper alternatives.
• Manufacturers may also feel the strain if they end up with surplus stock that doesn't sell due to the tax increase.

Understanding these effects is crucial, as taxation is a tool often used by governments to influence consumer behavior and market outcomes.

Market Equilibrium

Market equilibrium occurs when the quantity of a good supplied equals the quantity demanded at a given price. Before the red pencil tax, the market was likely in equilibrium with \(p_r = p_b\) for both red and blue pencils. However, after the tax:

• The equilibrium price for red pencils shifts upward, unsettling the balance between supply and demand.
• With a higher price (\(p_r + \text{tax}\)), demand for red pencils falls below supply, creating a surplus.
• The blue pencil market adjusts, with demand increasing as consumers shift their preference due to the price change.

Market equilibrium is sensitive to changes like taxation. Observing these shifts helps us understand how taxes can disturb initially balanced markets.

Consumer Behavior

Consumer behavior revolves around the choices individuals make which influence market demand. When presented with perfect substitutes like red and blue pencils, consumers base their purchasing decision predominantly on price and personal preference. Given a tax on one option:

• Consumers will typically choose the cheaper alternative. Here, all demand shifts to blue pencils as they provide the same utility at a lower cost.
• Perfect substitutes mean switching is seamless, as no utility loss occurs from choosing one product over the other.
• This behavior emphasizes the sensitivity of consumer choices to changes in price—crucial for companies updating product strategies or anticipating tax impacts.

Grasping consumer behavior helps businesses and policymakers forecast how markets react to fiscal policies and price changes.

Supply and Demand Analysis

Supply and demand are foundational economic concepts depicting how prices and quantities of goods are determined in markets. In the scenario of taxed red pencils:

• The supply curve for red pencils, being upward-sloping, shows an increase in price leading to increased quantities producers wish to sell. However, with falling demand due to the tax, a surplus develops.
• The demand curve for blue pencils shifts rightward as consumers migrate from red pencils, leading to increased consumption and the need for augmented supply.
• This analysis portrays how a tax-induced change can ripple through related markets, creating shortages, surpluses, and altered equilibrium prices.

Through supply and demand analysis, we can visualize these market changes and predict the outcomes of economic policies.