Revnol, a manufacturer of cosmetics, prices its popular pink lipstick at $8. On the basis of test-marketing, Revnol believes that women between the ages of 18 and 20 have an own-price elasticity of −1.5 and that 60 percent of them are likely to purchase the product. In the age group from 21 to 25 years, the own-price elasticity is −0.8 and 50 percent of them are likely to buy.
(i) In a market with 25,000 women aged 18 to 20, and 15,000 aged 21 to 25, how many lipsticks can the firm expect to sell at a price of $8 per unit lipsticks
(ii) If Revnol were to cut prices by 14 percent, approximately how many more pink lipsticks would it expect to sell?
(c) On a certain product market, 500 units are demanded at a price of $15. The own-price elasticity is −1.5. What is the equation of a linear inverse demand that passes through the point (500, 15)? p(Q) =___________
(d) What is the equation of a constant-elasticity demand function that has an own-price elasticity of −2 and passes through the point (400, 10)? Q(p)=____________