Question

S&S Manufacturing Co. supplies automotive parts in three outlets in Selangor. The inverse demand equations faced by each outlet are as follows:
Outlet 1: P = 150 – 2.50 Q1
Outlet 2: P = 200 – 8.40 Q2
Outlet 3: P = 450 – 0.75 Q3
a. If the firm charges RM100 per unit, determine the quantity demanded by each outlet.
b. Given the price, compute the own price elasticity for each outlet and identify which outlet is the most responsive to price change. Why?
c. If S&S Manufacturing Co. plans to increase the price by 10 percent, do you think the Company is making a right decision? Explain your answer.

Answer 1

a.

If P=100:

Outlet 1: P = 150 – 2.50 Q1

100= 150-2.50Q1

2.50Q1 = 150-100

Q1= 50/2.5= 20 Quantity demand by outlet 1

Outlet 2: P = 200 – 8.40 Q2

100= 200-8.40Q2

8.40Q2= 200-100

Q2 = 100/8.40= 11.9 Quantity demand by outlet 2

Outlet 3: P = 450 – 0.75 Q3

100= 450-0.75Q3

0.75Q3= 450-100

Q3= 350/0.75= 466.67 Quantity demand by outlet 3

b.

Price elasticity of demand= (dQ/dP) x (P/Q)

Outlet 1: P = 150 – 2.50 Q1

Q1 = (150-P)/2.5

dQ1/dP= Differentiation wrt P= -(1/2.5)

Q1= 20 and P=100 (Given)

Price elasticity of demand= -(1/2.5) x (100/20)= -(2)

Outlet 2: P = 200 – 8.40 Q2

Q2= (200-P)/8.40

dQ2/dP= Differentiation wrt P= -(1/8.40)

Q2= 11.9 and P=100 (Given)

Price elasticity of demand= -(1/8.40) x (100/11.9)= -(1)

Outlet 3: P = 450 – 0.75 Q3

Q3= (450-P)/0.75

dQ3/dP= Differentiation wrt P= -(1/0.75)

Q2= 466.67 and P=100 (Given)

Price elasticity of demand= -(1/0.75) x (100/466.67)= -(0.28)

Price elasticity of demand measures the responsiveness of demand with respect to a unit change in price. If elasticity is greater than 1, it implies that demand is highly elastic that is highly responsive to a price change. If elasticity is less than 1, it implies that demand is less elastic that is less responsive to a price change. If elasticity is equals to 1, it implies that demand is unitary elastic that is equally responsive to a price change.

Here Price elasticity of demand is absolute term(without negative sign) is highest in outlet 1 so this outlet is most responsive to the price change.

c.

If price increases by 10%:

In outlet 1:

Price elasticity of demand= % change in quantity demand / % change in price

-2 = % change in quantity demand / 10

% change in quantity demand = -20%

New price= 100+100(10%)= 110

New quantity= 20-20(20%)= 16

Intial revenue= old price x old quantity= 20 x 100= 2000

New revenue= new price x new quantity= 110 x 16= 1760

Revenue in outlet 1 decreases by 240

In outlet 2:

Price elasticity of demand= % change in quantity demand / % change in price

-1 = % change in quantity demand / 10

% change in quantity demand = -10%

New price= 100+100(10%)= 110

New quantity= 11.9-11.9(10%)= 10.7

Intial revenue= old price x old quantity= 11.9 x 100= 1190

New revenue= new price x new quantity= 110 x 10.7= 1177

Revenue in outlet 2 decreases by 13

In outlet 3:

Price elasticity of demand= % change in quantity demand / % change in price

-0.28 = % change in quantity demand / 10

% change in quantity demand = -2.8%

New price= 100+100(10%)= 110

New quantity= 466.67-466.67(2.8%)= 453.6

Intial revenue= old price x old quantity= 466.67 x 100= 46667

New revenue= new price x new quantity= 110 x 453.6= 49896

Revenue in outlet 2 increases by 3229

Total change in revenue after price increase= 3229-13-240= 2976

Yes company is making a right decision because increase in price by 10% cause an increase in revenue earned by the company by an amount of 2976.