Question

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?

Short answer

The derived linear demand and supply curves for the cigarette market are \(Q_d = -0.4 * (P-5.00) + 15.75\) and \(Q_s = 0.5 * (P - 5.00) + 15.75\) respectively. The price elasticity of demand for the change in consumption given the data from 1998 and 2010 is calculated using the elasticity formula and the provided figures. It indicates the responsiveness of the quantity demanded to a change in price, and the extent to which the quantity demanded falls as price increases depends on the elasticity value.

Step-by-step solution

Derive the Linear Demand and Supply Curves

Firstly, use the formula for price elasticity of demand, which is \(E_d = \frac{%ΔQ}{%ΔP}\). Given that this is -0.4, or \(-0.4 = \frac{%ΔQ}{%ΔP}\) and that the initial price (P1) was \$5.00 and quantity demanded (Q1) was 15.75 billion packs, we don't have the values for new quantity demanded (Q2) or new price (P2). But we can express them in terms of %ΔQ and %ΔP using the elasticity formula again, and create a equation such as -0.4 = \(\frac{Q2 - 15.75}{P2 - 5.00}\) * \(\frac{5.00}{15.75}\). Solving this equation for Q2 yields the demand curve formula: \(Q_d = -0.4 * (P-5.00) + 15.75\). Similarly for supply, with elasticity 0.5, the supply curve is: \(Q_s = 0.5 * (P - 5.00) + 15.75\).

Derive the Price Elasticity of Demand for the Change in Consumption

Assuming that the entire decline in cigarette consumption was due to the increase in price, calculate the price elasticity of demand: \(E_d = \frac{%ΔQ}{%ΔP}\). Using the provided figures, 23.5 billion packs were smoked in 1998 at a price of \$2.00, and 15.75 billion packs were smoked in 2010 at a price of \$5.00. So, %ΔQ = \(\frac{15.75 - 23.5}{23.5}\) and %ΔP = \(\frac{5.00 - 2.00}{2.00}\). Substituting these values into the elasticity formula gives the new price elasticity of demand.

Interpret the Results

The new price elasticity of demand determined in step 2, will help to understand the sensitivity of demand with respect to the changes in price. If the elasticity is less than 1 in absolute value, demand is inelastic: consumers do not significantly reduce their consumption when the price increases. If the elasticity is greater than 1 in absolute value, demand is elastic: consumers significantly reduce their consumption in response to price increases. The numerical value will also provide insights on this.

Key concepts

Demand Curve

The demand curve is a fundamental concept in microeconomics, representing the relationship between the price of a good and the quantity demanded by consumers. It typically slopes downward because, as the price decreases, consumers are willing to purchase more of the good. This reflects the law of demand.
In the context of cigarette consumption, drawing a demand curve involves understanding the price elasticity of demand. The price elasticity indicates how sensitive the quantity demanded is to a price change. Here, we have a price elasticity of demand of \[-0.4,\] meaning a 1% increase in price results in a 0.4% decrease in quantity demanded. Implementing this elasticity into the demand equation creates a linear demand curve, \[Q_d = -0.4 imes (P - 5.00) + 15.75,\] where \(Q_d\) represents quantity demanded, and \(P\) is the price. This equation makes the demand curve a straight line, giving us a clear visual representation of price and quantity relationships.

Supply Curve

The supply curve expresses the relationship between the price of a good and the amount suppliers are willing to produce and sell. Typically upward-sloping, it indicates that as the price increases, suppliers are more incentivized to produce more, reflecting the law of supply.
The price elasticity of supply helps us determine how the quantity supplied responds to price changes. In this example, the elasticity is 0.5, implying that a 1% increase in price leads to a 0.5% increase in quantity supplied. By integrating this into the supply function, we derive a linear supply curve: \[Q_s = 0.5 imes (P - 5.00) + 15.75,\] where \(Q_s\) stands for quantity supplied, and \(P\) represents the price.
Linear supply curves such as this allow easy analysis of the interactions with the demand curve and help us understand market dynamics and potential equilibrium outcomes.

Cigarette Consumption

Cigarette consumption presents a significant variable in the demand and supply equilibrium, particularly due to its inelastic characteristics. Inelastic goods have demand that doesn't respond strongly to changes in price; however, changes still have an effect, as seen with cigarettes.
Consumption decreased from 23.5 billion packs in 1998 to 15.75 billion packs in 2010 largely due to increases in price from \(2.00 to \)5.00 per pack. Even though demand elasticity is only \[-0.4,\] this shift demonstrates that price changes, coupled with greater awareness of health risks, significantly affect consumption.

• Continued price increases may lead to further consumption declines.
• Non-price factors, such as public health campaigns, can also shift consumption.

This illustrates the complexities involved when assessing how consumption adjusts over time.

Microeconomics

Microeconomics is the study of individual markets and the behaviors of consumers and firms. It examines how these entities make decisions about resource allocation and product pricing. Key concepts like demand, supply, and elasticity underpin microeconomic analysis by helping us understand how prices are determined and how they affect consumption and production.
The cigarette market exemplifies these principles well, where microeconomic concepts elucidate how prices influence behaviors and equilibrium.

• Elasticity provides insights into how sensitive consumers and producers are to price changes.
• The demand curve and supply curve offer frameworks for predicting market responses.

These elements together allow for a comprehensive analysis of how small changes can have substantial effects within particular markets.