Answer to Question #158486 in Microeconomics for nfraser

Question

1.      Massy super store, wishes to increase its total revenue. It offers 30% discount on every item it sells.

Group A Group B

Volume of sales before the 30% discount 1.79 million 1.76 million

Volume of sales after the 30% discount 1.84 million 1.86 million

(a)   Using the midpoint method, calculate the price elasticities of demand for group A and group B.

(b)  If Massy wants to increase its total revenue, which group should it offer the discount to? 

Answer 1

Answer

Step 1

The elasticity of demand depicts %change in quantity demanded to %change in price. The price elasticity of demand can be measured by:

• Percentage method
• Mid-point method
• Arc method
• Total expenditure method

Step 2

The Mid-point elasticity of demand is given by:

e_p= $∆q \over {q_1 +q_2 \over 2}$ x ${p_1 +p_2 \over 2} \over ∆p$

a. The elastic d of group A is:

q₁= 1.79

q₂₌ 1.84

∆q= q₁- q₂

=1.84−1.79

=0.05

e_p= $0.05 \over {1.79 +1.84 \over 2}$x $1 \over 0.3$

e_p= $0.05 \over 1.815$ x $1 \over 0.3$

= $0.05 \over 0.5445$

=0.0918

∆q= q₂ - q₁

     =1.86−1.76

     =0.1

e_p= $0.1 \over {1.76 +1.86 \over 2}$x $1 \over 0.3$ 

e_p= $0.1 \over 1.81$ x $1 \over 0.3$

= $0.1 \over 0.543$

=0.1841

The elasticities of both the groups are less than one. 

b. As the elasticities of both the groups are less than one, if price falls then total expenditure falls. So, Store M does not have benefit to offer discount because after that its total expenditure will also decline.