Question

IN THIS PROBLEM, I ALREADY HAVE SOLUTION TO THE QUESTION. PLEASE REVIEW THE SOLUTION AND HIGHLIGHT ANY ISSUES WITH IT.

iF THE ANSWER IS WRONG PLEASE PROVIDE THE ANSWER.

Question: Answer the following question with a clear explanation, showing any steps or processes used to reach the answer. Explain your process as though you are teaching the concept to

a student who isn't familiar with economics.

Currently, the demand equation for toasters is Q = 80 – 2P. The current price is $30 per toaster. Is this the best price to charge in order to maximize revenues? If not, what is?

Answer: No, $30 is not the best price per toaster.
When the demand and supply is in equilibrium, the value of the demand function is zero. At zero demand function mathematically, the value of Q will be zero. Thus to get the maximum revenue of the toaster, substituting Q=0 in the demand function and solving it further will the value of P which is the price per toaster.
Q= 80 - 2P
=> 0= 80 - 2P
=> 2P = 80
=> P = 80/2
=> P = 40
Thus the best price per toaster is $40.*

Answer 1

Answer : No, $30 is not the best price to maximize the revenue level.

Given,

Demand : Q = 80 - 2P

=> 2P = 80 - Q

=> P = (80 - Q) / 2

=> P = 40 - 0.5Q

TR (Total Revenue) = P * Q = (40 - 0.5Q) * Q

=> TR = 40Q - 0.5Q^2

Now, to get the maximum revenue price level first of all we have to derivative the TR function with respect to Q and then we have to set the derivative result equal to 0.

dTR / dQ = 40 - Q = 0

=> Q = 40
Now, P = 40 - (0.5 * 40)

=> P = 20

Therefore, in order to maximize revenue the best price is $20.