Question

1. A shoes manufacturing company finds from the sales data of the other manufactures of similar product that the demand functions for the shoes can be expressed as
Q=10,000-20 P
Find:-
a. Number of shoes sold when P=$300
b. Price for selling 5400 pair of shoes
c. Price of zero sales
d. Point elasticity of demand at price $500

Answer 1

Solution:

a.). Number of shoes sold when P = $300

Substitute for P in the demand function:

$Q =10,000 -(20\times 300)$

$Q=10,000-6,000$

$Q=4000$

Number of shoes sold = 4000 shoes

b.). Price for selling 5400 pair of shoes:

Substitute for Q in the demand function:

$5400 =10,000-20P$

$20P =10,000-5400$

$20P = 4,600$

$P= \frac{4,600}{20} = 230$

The price for selling 5400 pair of shoes is $230

c.). Price of zero sales:

Substitute for Q in the demand function:

$0=10,000-20P$

$20P=10,000$

$P=\frac{10,000}{20} = 500$

The price of zero sales is $500

d.). Point elasticity of demand at price $500:

From the demand function: Q=10,000 - 20P, the

$PED=\frac{∆Q}{∆P} \times \frac{P}{Q}$

$\frac{∆Q}{∆P}= -20$

$PED=(-20) \times (\frac{50}{0} ) = 0$

Point Elasticity of Demand = 0