Question

Melissa has a company that produces T-shirts for charities. Her market consists of two groups, Ceria Orphanage (C), and Jaya Orphanage (J). Their individual demand equations are as follows:

C: P = 40 – 2.00Q_c

J: P = 55 – 1.25Q_J

Where Q = represents quantity demanded (in hundreds), and

P = price per T-shirt

1. If Melissa charges $30 per T-shirt, what is the quantity demanded by each group and by the market as a whole?

2. At the price of $30, calculate and interpret the price elasticity of demand.

Answer 1

For Ceria: P = 40 - 2Qc, or 2Qc = 40 - P, or Qc = 20 - 0.5P

For Jaya: P = 55 - 1.25Qj, or 1.25Qj = 55 - P, or Qj = 44 - 0.8P

(1) When P = $30,

Qc = 20 - (0.5 x 30) = 20 - 15 = 5 (hundred)

Qj = 44 - (0.8 x 30) = 44 - 24 = 20 (hundred)

Market quantity = Qc + Qj = 5 + 20 = 25

(2) Elasticity of demand: (dQ/dP) x (P/Q)

For Ceria, Elasticity = (dQc/dP) x (P/Qc) = - 0.5 x (30 / 5) = - 3

Since absolute value of elasticity is higher than 1, demand for Ceria is elastic.

For Jaya, Elasticity = (dQj/dP) x (P/Qj) = - 0.8 x (30 / 20) = - 1.2

Since absolute value of elasticity is higher than 1, demand for Jaya is elastic. But since it is less than elasticity for Ceria, demand for Ceria is more elastic than demand for Jaya.