Question

Today nutty bars cost $2.55/bar and 12.5 million bars are sold. Last week the price was $3.40/bar. Given the same nutty bar price elasticity of demand (-1.2) and a nutty bar supply elasticity of 0.4, what was the change in nutty bar sales (quantity demanded) from last week to today?

Answer 1

Let new quantity demanded (Millions) = Q. Using mid-point method,

Price elasticity = (Change in quantity demanded / Average quantity demanded) / (Change in price / Average price)

- 1.2 = [(Q - 12.5) / (Q + 12.5)] / [$(2.55 - 3.4) / $(2.55 + 3.4)]

- 1.2 = [(Q - 12.5) / (Q + 12.5)] / (- 0.85 / 5.95)

- 1.2 = [(Q - 12.5) / (Q + 12.5)] / (- 0.1429)

[(Q - 12.5) / (Q + 12.5)] = (- 1.2) x (- 0.1429)

[(Q - 12.5) / (Q + 12.5)] = 0.1714

Q - 12.5 = 0.1714 x (Q + 12.5)

Q - 12.5 = 0.1714 x Q + 2.14

0.8286 x Q = 14.64

Q = 17.67

Change in quantity demanded (Millions) = 17.67 - 12.5 = 5.17 (Increase)