The Total Revenue (R) and the total cost (C) function of a company are

1.	The Total Revenue (R) and the total cost (C) function of a company are given by R(Q) = 300Q – Q2 and C(Q) = 20 + 4Q (Q = output). Find the equilibrium output. (Hint: equilibriums MR = MC).
Answer» Given T.R = R(Q) = 300Q – Q² M.R = \(\frac{d}{dq}\)(T.R) = 300 – 2Q T.C = 20 + 4Q M.C = \(\frac{d}{dq}\)(T.C) = 4 M.R = M.C ⇒ 300 – 2Q = 4 ⇒ 296 = 2Q ⇒ Q = 148.

The Total Revenue (R) and the total cost (C) function of a company are given by R(Q) = 300Q – Q2 and C(Q) = 20 + 4Q (Q = output). Find the equilibrium output. (Hint: equilibriums MR = MC).

Answer»

Given T.R = R(Q) = 300Q – Q²

M.R = \(\frac{d}{dq}\)(T.R) = 300 – 2Q

T.C = 20 + 4Q

M.C = \(\frac{d}{dq}\)(T.C) = 4

M.R = M.C

⇒ 300 – 2Q = 4

⇒ 296 = 2Q

⇒ Q = 148.