An increase in the price of hot dogs from $1.60 to $2.00 per pound increased the average number of hamburgers demanded per capita per week from 1 to 1.4. Assuming that all other economic variables were held constant, the arc cross-price elasticity of demand between hot dogs and hamburgers is
A) -1.5, which indicates that the two goods are substitutes.
B) -1.5, which indicates that the two goods are complements.
C) 1.5, which indicates that the two goods are substitutes.
D) 1.5, which indicates that the two goods are complements.

Question

Quizplus · Accepted Answer

The arc cross-price elasticity of demand is calculated as [(Q2 - Q1) / ((Q2 + Q1)/2)] / [(P2 - P1) / ((P2 + P1)/2)], where Q1 and Q2 are the initial and final quantities demanded of hamburgers, and P1 and P2 are the initial and final prices of hot dogs. Substituting the given values, we get [(1.4 - 1) / (1.4 + 1)/2] / [(2 - 1.6) / (2 + 1.6)/2] = 0.4 / 0.4 = 1. The positive value indicates that the goods are substitutes, as the increase in the price of hot dogs leads to an increase in the demand for hamburgers.

An Increase in the Price of Hot Dogs from $1