In 2010, Americans smoked 315 billion cigarettes, or 15.75...

In $2010,$ Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The average retail price (including taxes) was about $\$ 5.00$ per pack. Statistical studies have shown that the price elasticity of demand is $-0.4,$ and the price elasticity of supply is 0.5. a. Using this information, derive linear demand and supply curves for the cigarette market. b. In $1998,$ Americans smoked 23.5 billion packs of cigarettes, and the retail price was about $\$ 2.00$ per pack. The decline in cigarette consumption from 1998 to 2010 was due in part to greater public awareness of the health hazards from smoking, but was also due in part to the increase in price. Suppose that the entire decline was due to the increase in price. What could you deduce from that about the price elasticity of demand?

In $2010,$ Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The average retail price (including taxes) was about $\$ 5.00$ per pack. Statistical studies have shown that the price elasticity of demand is $-0.4,$ and the price elasticity of supply is 0.5.
a. Using this information, derive linear demand and supply curves for the cigarette market.
b. In $1998,$ Americans smoked 23.5 billion packs of cigarettes, and the retail price was about $\$ 2.00$ per pack. The decline in cigarette consumption from 1998 to 2010 was due in part to greater public awareness of the health hazards from smoking, but was also due in part to the increase in price. Suppose that the entire decline was due to the increase in price. What could you deduce from that about the price elasticity of demand?

Key Concepts

Price Elasticity of Demand

This concept measures the responsiveness of the quantity demanded to changes in the price of a good. It is defined as the percentage change in the quantity demanded divided by the percentage change in price. A negative value indicates that the quantity demanded moves in the opposite direction to price changes, reflecting the law of demand. Understanding this elasticity is crucial for predicting how changes in price can affect overall consumption and revenue in the market.

Price Elasticity of Supply

This concept measures how sensitive the quantity supplied is to a change in the market price. It is calculated as the percentage change in the quantity supplied divided by the percentage change in price. A positive elasticity implies that an increase in price will encourage producers to supply more of the good. This measure is key for analyzing how quickly and effectively producers can adjust their output in response to market price changes.

Linear Demand Curve

A linear demand curve is a straight-line relationship between price and quantity demanded, usually expressed in the form P = a - bQ. The slope and intercept of this line can be determined by using known elasticity at a given point and information about market equilibrium. Deriving this curve involves linking changes in quantity demanded with corresponding changes in price, thus incorporating the concept of price elasticity of demand.

Linear Supply Curve

Similarly, a linear supply curve represents the relationship between price and quantity supplied with a constant slope, typically written as P = c + dQ. By applying information about the price elasticity of supply at a known equilibrium, one can derive the constants that define this curve. This linear form simplifies the analysis of how production levels respond to price changes in the market.

Market Equilibrium

Market equilibrium occurs when the quantity demanded equals the quantity supplied, resulting in a stable price and quantity exchanged in the market. This concept is essential when deriving demand and supply curves because equilibrium data provides a reference point from which the slopes and intercepts of the linear equations can be calculated. It links the theoretical measures of elasticity to observable market outcomes.

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