Suppose a \(100 \%\) sales tax is placed on a good. Explain with the use of graphs what will determine the incidence of that sales tax.

Begin by drawing a supply-demand graph with price (P) on the vertical axis and quantity (Q) on the horizontal axis. Draw the initial demand curve (D1) with a negative slope, reflecting the inverse relationship between price and quantity demanded, and the initial supply curve (S1) with a positive slope, illustrating the direct relationship between price and quantity supplied. At the intersection of both curves, we find the initial market equilibrium price (P1) and equilibrium quantity (Q1).

Now, introduce the 100% sales tax, which means that for every unit of the good sold, there will be an equal amount of tax paid. Since the tax is ultimately borne by the buyer, we can translate this tax into an increase in the price of the good. To include the sales tax in our graph, the supply curve has to be shifted vertically upward by the amount of the sales tax (equal to the initial price P1). Draw the new supply curve (S2) parallel to S1, at the level equal to P1 above the initial supply curve.

Now that we have the new supply curve (S2) that considers the 100% sales tax, we can find the new market equilibrium price (P2) and equilibrium quantity (Q2). Locate the intersection of the demand curve (D1) and the new supply curve (S2). The price at this intersection point is the new equilibrium price (P2), and the corresponding quantity is the new equilibrium quantity (Q2).

To determine the incidence of the sales tax, we need to analyze the burden distribution of the tax between the buyers and the sellers. The incidence of the sales tax depends on the relative price elasticities of supply and demand: - If the demand (buyers) is more price elastic than the supply (sellers), the sales tax burden falls primarily on the sellers. In this case, the new equilibrium price, P2, would be relatively lower than P1, as the buyers are more sensitive to price changes and the sellers have to pay more of the tax. - If the supply (sellers) is more price elastic than the demand (buyers), the sales tax burden falls primarily on the buyers. In this case, the new equilibrium price, P2, would be relatively higher than P1, as sellers are more sensitive to price changes and can pass most of the tax to the buyers. In conclusion, the incidence of a 100% sales tax depends on the relative price elasticities of supply and demand. The graph helps in visualizing how the sales tax affects the market equilibrium and the tax burden distribution between the buyers and the sellers.