14. A 2015 article published by the American Journal of Preventive Medicine studied the effects of an increase in alcohol prices on the incidence of new cases of sexually transmitted diseases. In particular, the researchers studied the effects that a Maryland policy increasing alcohol taxes had on the decline in gonorrhea cases. The report concluded that an increase in the alcohol tax rate by 3% resulted in 1,600 fewer cases of gonorrhea. Assume that prior to the tax increase, the number of gonorrhea cases was 7,450. Use the midpoint method to determine the percentage decrease in gonorrhea cases, and then calculate the cross-price elasticity of demand between alcohol and the incidence of gonorrhea. According to your estimate of this cross-price elasticity of demand, are alcohol and gonorrhea complements or substitutes?

a) Cross elasticity = -8.02

b) these are complementary items because the cross elasticity of gonorrhea and alcohol is less than 1.

Explanation:

Cross Price Elasticity is calculated using the following formula

[(Q2-Q1) / (Q2-Q1/2)]  /  [(P2-P1)/ (P2-P1/2)]

The meaning of the formula is the change in the quantity demanded of a good divided by the percentage change in the price of another good or product.

In this case we are comparing how the demand for alcohol affects the occurrence of gonorrhea.

1) We determine the change in the issues of gonorrhea.

The initial cases of Gonorrhea Q1 is 7,450 but it later reduced by 1600 due to an increase in alcohol price by 3%

Q2 = 7,450-1600= 5,850

Q1= 7,450

Plugging this into the formula we determine the percentage of decrease in gonorrhea.

= [(Q2-Q1) / (Q2-Q1/2)]

= (5850-7540)  / (5850-7450 /2)

= -1600/6,650 x 100

= -24.06%

2) We already know the change in the price of Alcohol to be 3% increase due to tax

Hence, the cross elasticity of the two as given in the formula above

= The percentage change in the cases of gonorrhea / the percentage change in the price of alcohol

= -24.06% / 3%

= -8.02

Also, these are complementary items because the cross elasticity of gonorrhea and alcohol is less than 1.

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