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.
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
A demand equation is Q = 270 - P. MR is described by the function 270...
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