Given the following demand curve: p = 24 - 8q
express this demand curve in terms of q.
use either the original equation or the one in part (a) and find p if q=2.
use either the original equation or the one in part (a) and find q if p = 8.
write out the equation for total revenue in terms of q.
write out the equation for marginal revenue in terms of q. hint: marginal revenue is the first derivative of total revenu
find the values of p and q that will maximize total revenue.
calculate this maximum value of total revenue.

Maximum value of total revenue = 18

Step-by-step explanation:

P = 24 - 8Q (it is the same equation)

P= 24-8(2)

P=24-16

P=8

P = 24 - 8Q

8= 24 - 8Q

8Q= 24-8

8Q=16

Q=16/8

Q=2

Total revenue is P times Q, that is

P*Q=TR=(24-8Q)*Q

TR=24Q-8Q^2

It is the first derivative of TR

TR'(Q)= 24-16Q

To find them first TR'(Q)=0, that is

0=24-16Q

16Q=24

Q=24/16

Q=3/2

Q=1.5

and we plug in 1.5 in P=24-8Q, which is,

P=24-8Q

P=24-8(1,5)

P=24-12

P=12

P=12 Q=1.5

P*Q=Total Revenue

12*1.5=Total Revenue

18=Total Revenue

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