Question

Consider a firm with the demand function P(Q)=(50-2Q), and the total cost function TC(Q)=10,000+10Q. Find the profit maximizing quantity. Calculate the profit maximizing price (or the market price). Hint: MR(Q)=(50-4Q),

Answer 1

Profit-maximizing stage would be the equality of MR and MC.

Given, P = 50 – 2Q

TR = P × Q = 50Q – 2Q^2

MR = Derivative of TR with respect to Q

      = 50 – 4Q

Given, TC = 10,000 + 10Q

MC = Derivative of TC with respect to Q

       = 0 + 10

       = 10

Now, MR = MC

50 – 4Q = 10

4Q = 50 – 10

Q = 40/4 = 10

By putting this value in the demand function we will get price

P = 50 – 2Q

   = 50 – 2 × 10

   = 50 – 20

   = 30

Answer: quantity = 10 units; Price = 30