A firm has total revenue equation TR = 5000Q – 5Q2 and total cost equation C = 500 + 3Q2 Calculate this firm’s profit maximizing price


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A firm has total revenue equation TR = 5000Q – 5Q2 and total cost equation C = 500 + 3Q2 Calculate this firm’s profit maximizing price, quantity, total revenue, total cost, and total profit. (This firm does not price discriminate.)

Answer:

To find Profit Maximizing Quantity:

First take the derivative of the TR equation:
dTR/dq=5000−10Q

Then take the derivative of the TC equation:
dTC/dq=6Q

Now set these two derivatives equal to each other:
5000−10Q=6Q

Now solving for Q you get Q = 312 is your profit maximizing quantity.

To get profit maximizing price you need to provide us with the demand equation. Please provide that to us.

Now that we know the Profit Maximizing Quantity (312) you can find the Total Cost and Total Revenue by plugging 312 into the TC and TR equations. Then to find total profit you do TR(312)−TC(312).

Total Cost:
TC(312)=500+3(312)2=292,532

Total Revenue:
TR(312)=5000(312)−5(312)2=1,073,280

Total Profit:
TR(312)−TC(312)=1073280−292532=780,748