Question

The arc elasticity is 1.5 as advertising expenditure increases from $10 to $12 million. If demand is 50 at an advertising expenditure of $12 million, what will demand be at an advertising expenditure of $10 million?

Answer 1

Solution:Let p1=12. p2=10. Q1=50. we must to find Q2.The arc elasticity found by the formula

$$E= \frac{Q2-Q1}{p2-p1} \times \frac{p2+p1}{Q2+Q1}$$

$$1.5= \frac{50-Q1}{12-10}\times \frac{12+10}{50+Q1}$$

$$1.5\times(50+Q1)=11\times(50-Q1)$$

$$75+1.5Q1=550-11Q1$$

$$12.5Q1=475$$

$$Q1=38$$

Answer: 38