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Chapter 5: Problem 10

(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

Expert verified
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

01

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 \( Q1 \).
02

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.
03

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.
04

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.

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