Question

(Related to Solved Problem 5.3 on page 160 ) Solved Problem 5.3 contains the statement "Of course, the government actually collects the tax from sellers rather than from consumers, but we get the same result whether the government imposes a tax on the buyers of a good or on the sellers." Demonstrate that this statement is correct by solving the problem, assuming that the increase in the tax on gasoline shifts the supply curve rather than the demand curve.

Short answer

An increase in tax flips the supply curve upwards, leading to a new market equilibrium with a higher price and decreased quantity of goods supplied. The same result would be obtained if the demand curve was shifted downwards to represent a tax increase imposed on the buyer. Hence, the tax imposition on either the buyer or the seller leads to an equivalent outcome.

Step-by-step solution

Establishing the Initial Supply and Demand Curves

Start with the original supply and demand curves. Let's denote the supply curve as \( S1 \) and the demand curve as \( D1 \). With no tax, these curves intersect at equilibrium point \( E1 \), defining equilibrium price \( P1 \) and quantity \( Q1 \).

Shifting the Supply Curve

An increase in tax will increase the cost of production for the sellers, causing the supply curve to shift upwards. For every unit of the good sold, the sellers now have to pay the tax to the government. This adds to their cost, and thus, for the same price, they are willing to supply less. The new supply curve, \( S2 \), reflecting the state with the tax, will lie above \( S1 \) by the amount of the tax per unit.

Establishing the New Equilibrium

The market achieves a new equilibrium where the shifted supply curve \( S2 \) intersects with the demand curve \( D1 \). Let's call this point \( E2 \). Here, we have a new equilibrium price (let's call it \( P2 \)) and quantity (let's call it \( Q2 \)). Note that \( P2 > P1 \) (price has increased) and \( Q2 < Q1 \) (quantity supplied has decreased), as expected.

Showing the Equivalence of Tax on Buyers or Sellers

Now imagine the tax was directly added to the price the buyers have to pay. This would have the effect of shifting the demand curve downwards instead of shifting the supply curve upwards. This happens because the buyers are now willing to buy less of the good for the same price. The result would still be the same - a higher equilibrium price and a smaller equilibrium quantity. Thus, implying that it doesn’t matter whether a tax is levied on the buyer or the seller, the effect is the same.

Key concepts

Supply and Demand

Supply and demand are the fundamental building blocks of economic theory. They define how the market operates and influence the price and quantity of goods. In a marketplace without taxes, the supply curve (noted as \( S1 \)) shows the relationship between the price of a good and the quantity that producers are willing to supply. Similarly, the demand curve (noted as \( D1 \)) represents the relationship between the price and the quantity that consumers are ready to buy.

When both curves intersect, they create a point known as the equilibrium. This is where the supply perfectly matches demand, determining both the equilibrium price \( P1 \) and quantity \( Q1 \). This concept is crucial in understanding how markets reduce from chaos to order.

• The supply curve slopes upwards. This is because higher prices motivate producers to supply more.
• The demand curve slopes downwards. Higher prices usually mean consumers buy less.

Understanding supply and demand can help predict how different factors, like taxes, might shift these curves, and consequently how they affect equilibrium.

Equilibrium Analysis

Equilibrium analysis helps us understand how prices and quantities change in response to shifts in supply or demand. In the exercise, we looked at how a new tax impacts these curves, particularly focusing on the supply curve.

When a tax is imposed, it generally causes a shift in the relevant curve, which is either the supply or demand. In our case of imposed tax, the supply curve shifts upward from \( S1 \) to \( S2 \). This shift represents an increase in costs for sellers due to the tax. Hence, the new equilibrium, where the supply \( S2 \) meets the demand \( D1 \), is marked by an increased price \( P2 \) and decreased quantity \( Q2 \).

• Equilibrium price increases from \( P1 \) to \( P2 \).
• Equilibrium quantity decreases from \( Q1 \) to \( Q2 \).

By analyzing these new equilibrium conditions, we can effectively see the impact of the tax on the marketplace.

Tax Impact

The impact of taxes on the economy can be significant. Taxes not only increase the cost burden on producers and consumers but also affect market equilibrium. By shifting the supply or demand curve, taxes influence prices and quantities.

The key takeaway is that whether the tax is imposed on producers or consumers, the ultimate effect on market equilibrium remains unchanged. This principle, known as tax incidence, means that the market adjustments result in the same conditions regardless of who "officially" pays the tax. For instance, if the tax had been imposed directly on buyers, it would've shifted the demand curve downward. But the new equilibrium would still show a higher price and lower quantity as before.

• Tax incidence is neutral in terms of who pays it; the outcome is the same.
• Price increases while quantity decreases are typical responses to taxes.

Understanding tax impact helps policymakers and stakeholders anticipate market reactions and plan accordingly.