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

Q = 40-3P

write it in other form ,we get :

P = 40/3 - Q/3

Total revenue , TR = P(Q)

= (40/3 - Q/3) Q

TR = (40/3)(Q) - (Q²/ 3)

Now to see the price that maximize revenue , take the derivative of TR w.r.t Q and equate it to 0 , we get :

dTR/dQ = 40/3 - 2Q/3 = 0

(40- 2Q)/ 3 = 0

40 - 2Q = 0

Q = 40/2

Q= 20 units

Q = 40-3P

20 = 40- 3P

3P= 20

P= 20/3 = $ 6.67

So, the current price is $10 per hamster is not the best price that maximize revenue . The best price that maximizes revenue is $6.67 per hamster.