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Chapter 6: Problem 14

A recent report by the U.S. Centers for Disease Control and Prevention (CDC), published in the CDC's Morbidity and Mortality Weekly Report, studied the effect of an increase in the price of beer on the incidence of new cases of sexually transmitted disease in young adults. In particular, the researchers analyzed the responsiveness of gonorrhea cases to a tax-induced increase in the price of beer. The report concluded that "the.... analysis suggested that a beer tax increase of \(\$ 0.20\) per six-pack could reduce overall gonorrhea rates by \(8.9 \% . "\) Assume that a sixpack costs \(\$ 5.90\) before the price increase. Use the midpoint method to determine the percent increase in the price of a six-pack, and then calculate the cross-price elasticity of demand between beer and incidence of gonorrhea. According to your estimate of this cross-price elasticity of demand, are beer and gonorrhea complements or substitutes?

Short Answer

Expert verified
Answer: The cross-price elasticity of demand between beer and the incidence of gonorrhea is -2.67, and they are complements since the calculated value is negative.

Step by step solution

01

Determine the New Price of a Six-Pack with the Tax Increase

To determine the new price of a six-pack after the tax increase of \(0.20\), we need to add the tax increase to the original price. The original price is \(5.90\), so the new price is \(5.90 + 0.20 = \$ 6.10\).
02

Calculate the Percent Increase in the Price of a Six-Pack using the Midpoint Method

The midpoint method is given by the formula: `Percent Increase = (New Price - Old Price) / Midpoint × 100` Here, the midpoint is `((Old Price + New Price) / 2)`. So we have: Midpoint = (5.90 + 6.10) / 2 = \(6.00\) Percent Increase = (6.10 - 5.90) / 6.00 × 100 ≈ 3.33 %
03

Calculate the Cross-Price Elasticity of Demand Between Beer and Incidence of Gonorrhea

The cross-price elasticity of demand is given by the formula: `Cross-Price Elasticity = (Percentage Change in Quantity Demanded of Good 2) / (Percentage Change in Price of Good 1)` In this case, the percentage change in the price of beer is 3.33%, and the percentage change in the incidence of gonorrhea is -8.9%. So we have: Cross-Price Elasticity = (-8.9) / 3.33 ≈ -2.67
04

Determine if Beer and Gonorrhea are Complements or Substitutes

The cross-price elasticity of demand tells us the relationship between two goods. If the cross-price elasticity is positive, the two goods are considered substitutes. If it's negative, the goods are considered complements. Since the cross-price elasticity we calculated in Step 3 is -2.67, which is negative, we can conclude that beer and gonorrhea are complements. This means that an increase in the price of beer leads to a reduction in the incidence of gonorrhea.

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Most popular questions from this chapter

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