Question

A demand equation is Q = 270 - P. MR is described by the function 270 - 2Q. Total Cost is described by the function TC = 30 + 9Q. MC is constant at $9.

Calculate the profit (or loss) at the profit maximizing quantity. Please ensure that you show detailed calculations.

Answer 1

As per the information provided in the question demand equation Q=270 –P

Then Average Revenue(AR) or P = 270 –Q

Total Revenue (TR) = PxQ = (270 –Q)xQ = 270Q –Q²

Marginal Revenue or MR = 270 – 2Q

Total Cost (TC) = 30 + 9Q

Marginal cost (MC) = $9

At the profit maximising level of output the marginal cost should equal with marginal revenue

So MC = MR

9 = 270 -2Q

2Q = 270 – 9

Q =261/2 = 130.5 units

So the profit maximising level of output is = 130.5 units

Profit = Total Revenue (TR) - Total Cost (TC)

Profit = 270Q –Q² –( 30 + 9Q)

Profit = 270Q –Q² – 30 - 9Q

Profit = 261Q –Q² – 30

Profit = 261(130.5) –(130.5)² – 30              replacing the value of Q=130.5

Profit = 34060.5 –17030.25 – 30

Profit = $17000.25

The total profit at the profit maximising quantity is = $17000.25