Answer to Question #313551 in Microeconomics for Souljaboy

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 increases to 6,000 pounds per year.

a) 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

Solution

Cross elasticity of demand (XED) measures the percentage change in quantity demand for a good after the change in price of another.



$E_{xy}=\dfrac{Q_{x2}-Q_{x1}}{P_{y2}-P_{y1}}\times\dfrac{P_{y2}+P_{y1}}{Q_{x2}-Q_{x1}}$

We are given;

$Q_{x2}=6,000$ $Q_{x1}=5,000$

$P_{y2}=\$12$ $P_{y1}=\$15$

$E_{xy}=\frac{6,000-5,000}{\$12-\$15}\times\frac{\$12+\$15}{6,000+5,000}$

$E_{xy}=-0.818$

$P_{y2}~for ~Q_{x2} ~of ~3000$ given that $E_{xy}$ does not change.

$-0.818=\frac{3,000-5,000}{P_{y2}-\$15}\times\frac{P_{y2}+\$15}{3,000+5,000}$

Solving for $P_{y2}$

$P_{y2}=\$28.204$