Question

Answer the following question with a clear explanation. Show any steps or processes used to reach the answer.

Currently, the demand equation for pet hamsters is Q = 40 – 3P. The current price is $10 per pet hamster. Is this the best price to charge in order to maximize revenues? If not, what is?

PLS DO NOT PASTE PICTURES.

Answer 1

the demand equation for pet hamsters is Q = 40 – 3P.

3P=40-Q

P=40/3-Q/3

TR=P*Q

=(40/3-Q/3)Q

=(40/3)Q-Q2/3

taking dervatives of TR with respect to Q

dTR/dQ

=40/3 -2Q/3

Total revenue maximisation

dTR/dQ=0

40/3 -2Q/3=0

2Q/3= 40/3

Q=40/3 *3/2

=20 units

Substituting Q into price equation

P=40/3-Q/3

=40/3 - 20/3

=20/3

=$6.66

TR=P*Q

=6.66*20

=$133.33

When P =10

Q=40-3P

=40-3(10)

=40-30

=10 units

TR=P*Q

=10*10

=100

It means price $10 is not the best price to charge in order to maximize revenues because TR is =100

While maximum revenue will be when price is $6.66 and Q=20 units.