Question

The marginal cost of producing a paperback is half the marginal cost of producing a hardback version sold to consumers at four times the paperback price. If the price elasticity of demand for paperbacks is –4, then the price elasticity of demand for hardcover books is:

a. –1.6

b. –0.6
	c. –4.6
	d. –2.6
	e. –3.6

Answer 1

Price elasticity of demand for paperbacks is –4

Ppaperbacks = MCpaperbacks(-4/-4 + 1)

Ppaperbacks/MCpaperbacks = 4/3

Similarly, Price elasticity of demand for hardbacks is e

Phardbacks = MChardbacks(e/e + 1)

Phardbacks/MChardbacks = (e/e + 1).....................1)

Given that MCpaperbacks/MChardbacks = 0.5 and Ppaperbacks/Phardback = 0.25

This implies MCpaperbacks/MChardbacks = 2*Ppaperbacks/Phardback

Phardbacks/MChardbacks = 2*Ppaperbacks/MCpaperbacks

= 2*4/3

= 8/3

Use this in equation 1

8/3 = (e/e + 1)

8e + 8 = 3e

5e = -8

e = -8/5 = -1.6

Option A is correct.