A demand equation is given by P20005Q What are the equations

A demand equation is given by P=200-0.5Q. What are the equations for TR and MR based on this demand equation. At what level of P and Q would we find maximum TR?

Solution

Total revenue = price earned * quanity sold

= P*Q

= (200-0.5Q) * Q

TR = 200Q-0.5Q^2

take first derivative of the TR equation to get MR or marginal revenue

so MR = 200-Q

TR maximize when MR=0

So MR=0

200-Q=0

Q=200

So put this in P=200-0.5Q

P= 200-0.5*200

P= 100

q=200 , P=100 would maximize TR