Answer to Question #312201 in Microeconomics for Pat

Question

Acme Tobacco is currently selling 5,000 pounds of pipe tobacco per year. Due to competitive pressures, the average price of a pipe declines from $15 to $12. As a result, the demand for Acme pipe tobacco increase to 6,000 pounds per year.

a. What is the cross elasticity of demand for pipes and pipe tobacco?

b. Assuming that the cross elasticity does not change, at what price of pipes would the demand for pipe tobacco be 3,000 pounds per year? Use $15 as the initial price of a pipe.

Answer 1

A) The cross elasticity is given of tobacco and pipe is given as:

$\epsilon_c=\frac{Q_2-Q_1}{Q_2+Q_1}/\frac{P_2-P_1}{P_2+P_1}$

$\epsilon_c=\frac{6000-5000}{6000+5000}/\frac{12-15}{12+15}$

$\epsilon_c=-0.82$

B) If cross elasticity foes not change, then

$-0.82=\frac{3000-5000}{3000+5000}/\frac{x-15}{x+15}$

$-0.82=-0.25×\frac{x+15}{x-15}$

$-0.25x-3.75=-0.82x+12.3$

$0.57x=16.05$

$x=\$28$