In Example 8, the demand and supply curves are given by...

In Example $8,$ the demand and supply curves are given by $q=100-2 p$ and $q=3 p-50,$ respectively; the equilibrium price is $$ 30$ and the equilibrium quantity is 40 units. A sales tax of $5 \%$ is imposed on the consumer. (a) Find the equation of the new demand and supply curves. (b) Find the new equilibrium price and quantity. (c) How much is paid in taxes on each unit? How much of this is paid by the consumer and how much by the producer? (d) How much tax does the government collect?

In Example $8,$ the demand and supply curves are given by $q=100-2 p$ and $q=3 p-50,$ respectively; the equilibrium price is $$ 30$ and the equilibrium quantity is 40 units. A sales tax of $5 \%$ is imposed on the consumer.
(a) Find the equation of the new demand and supply curves.
(b) Find the new equilibrium price and quantity.
(c) How much is paid in taxes on each unit? How much of this is paid by the consumer and how much by the producer?
(d) How much tax does the government collect?

Key Concepts

Demand Curve

The demand curve shows the relationship between the price of a good and the quantity that consumers are willing to purchase. It typically slopes downward, reflecting that lower prices trigger higher demand. Taxes affecting consumers shift the effective price they face, thereby altering the demand curve and the resulting market outcomes.

Government Tax Revenue

Government tax revenue is the total amount collected from a tax, computed by multiplying the per-unit tax by the number of units sold in the post-tax equilibrium. This concept is fundamental in evaluating the fiscal impact of taxation and its role in transferring resources within the economy.

Tax Incidence

Tax incidence examines how the burden of a tax is distributed between consumers and producers. Even when a tax is legally imposed on one party (such as consumers), market dynamics often lead to the burden being shared. The relative shifts in demand and supply, along with the elasticities of each, determine how the tax is economically divided.

Market Equilibrium

Market equilibrium is the point at which the quantity demanded by consumers equals the quantity supplied by producers, resulting in a stable market price and quantity. When taxes are introduced, the equilibrium shifts as the effective prices and quantities change, and analyzing this new equilibrium is critical for understanding market responses to policy changes.

Supply Curve

The supply curve displays the relationship between the price of a good and the quantity that producers are willing to sell, usually with an upward slope, indicating that higher prices incentivize greater production. Understanding how taxes influence the interaction between demand and supply helps determine the new equilibrium in the market.

Sales Tax (Consumption Tax)

A sales tax, or consumption tax, is levied on goods at the point of sale and directly increases the price paid by consumers. This tax alters the purchasing power of buyers, hence shifting the demand curve. Analyzing the impact of a sales tax is essential for understanding its effect on market equilibrium and the overall welfare of buyers and sellers.

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