Question

PLEASE EXPLAIN IN DETAIL

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 1

We know that Revenue, R = price*quantity = P*Q = P*(80-2P) = 80P - 2P²

We maximise revenue to find the price at which revenue is maximized. For this, we find first order derivative of revenue function (R) with respect to P and equate it to zero.

So, 4P = 80
So, P = 80/4 = 20

So, as second order derivative of R is less than zero then it means that R is maximized at P = 20.

The best price to charge in order to maximize revenues is not $30. It is $20 per toaster.

When the price = $30, Q = 80-2P = 80 - 2(30) = 80 - 60 = 20. So, R = P*Q = 30*20 = $600
When the price = $20, Q = 80-2P = 80 - 2(20) = 80 - 40 = 40. So, R = P*Q = 20*40 = $800
Thus, revenue has increased when the price is reduced from $30 to $20