Question

2.-Airtight and Longlife are competitors in the commercial container industry. The demand curves for an important product of both companies are:

Airtight PA = 1000 - 5QA QA = 200- .2Pa
Longlife PL = 1600 - 4QL

The companies currently sell 100 and 250 units of their product, respectively:
a) What are the price point elasticities currently facing the two firms?
b) Suppose Longlife lowers its prices and increases its sales to 300 units, and that this action results in Airtight's sales decrease to 75 units. What is the indicated cross price elasticity between Airtight and Longlife containers?
c) Does Longlife's supposed price reduction make sense from an economic point of view, assuming that the managers of that company operate under the slogan of maximizing profits?

Answer 1

2. Demand curve for Airtight is given as, P_A = 1000 - 5Q_A
We can also write, 5Q_A = 1000 - P_A
or, Q_A = 1000/5 - P_A/5
or, Q_A = 200 - 0.2P_A

Demand curve for Longlife is given as, P_L = 1600 - 4Q_L
We can also write, 4Q_L = 1600 - P_L
or, Q_L = 1600/4 - P_L /4
or, Q_L = 400 - 0.25P_L

Given that currently, Q_A = 100units and Q_L = 250 units
At this quantities, prices are as follows:
P_A = 1000 - 5Q_A
or, P_A= 1000 - 5*100 = 1000 - 500 = 500
P_L = 1600 - 4Q_L
or, P_L = 1600 - 5*250 = 1600 - 1000 = 600

Hence we have the following:

• Demand for Airtight : P_A = 1000 - 5Q_A or, Q_A = 200 - 0.2P_A
• Demand for Longlife : P_L = 1600 - 4Q_{L or,} Q_L = 400 - 0.25P_L
• Q_A = 100units &   P_A = 500
• Q_L = 250 units &   P_L = 600

a) Point price elasticities:

Formula for point price elasticity is (P/Q)*(dQ/dP)

For Airtight:
Formula is (P_A /Q_A )* (dQ_A /dP_A)

dQ_A /dP_A = -0.2
Hence elasticity = (500/100)*-0.2 = -1 (Unitaty elastic)

For Longlife:
Formula is (P_L /Q_L )*(dQ_L /dP_L)

dQ_L /dP_L = -0.25
Hence elasticity = (600/250)*-0.25 = -0.6 (inelastic)

b) Given that, longlife decreased price and as a result its sells increases to 300 units and airtight's sells has decreased to 75 units. Hence the price fall of longlife causes a demand increase for longlife and a demand fall of airtight. Thus cross elastictiy between the two firms is positive. Because they change in the same direction. That means the two products are substitute of each other.

c) Since Airtight have a unitary elastic demand, thus the decrease in price of longlife will cause a equal demand decrease in airtight and demand for longlife will increase. As a result, profit will increase for longlife and that of will fall for airtight.