Question

If demand function is given as the following: 

Qz = 230 -2.75 Pz + 0.5 I + 1.2 Pm + 0.6A 

Where Qz is quantity of Good z sold, Pz is price of Good z per unit, I is per capita income, Pm is price of competitor and A is the amount of advertising spent. 

Current values:  Pz= RM 55 I= RM 9000    Pm= RM 50    A =RM 12,000

a) Should the firm consider giving a price discount in order to increase total revenue?

Answer 1

A price discount (lower price) will increase revenue if demand is inelastic, such that

$\mid d\mid <1, where$

Ed: Elasticity of demand $=\frac{\delta Q_z}{\delta P_z}\times\frac{P_z}{Q_z}=-2.75\times\frac{P_z}{Q_z}$

Using given values,

$Q_z=230-(2.75\times 55)+(0.5\times 9000)+(1.2\times50)+(0.6\times 12000)$

$Q_z=11838.75$

s0,

$Ed=-2.75\times \frac{55}{11838.75}$

$=-0.013$

since $\mid Ed\mid <1,$ demand is inelastic so the firm should offer a discount to increase revenue.