Discussion
The total revenue (R) and total cost (C) functions of a firm are given by :
R = 30Q - Q2 C = 20 + 4Q
What would be the equilibrium output of the firm ?
Answer: B
The equilibrium output is 13.
The firm maximises profit where marginal revenue equals marginal cost:
\[ \begin{aligned} MR &= \frac{dR}{dQ} = 30 - 2Q \\ MC &= \frac{dC}{dQ} = 4 \\ 30 - 2Q &= 4 \Rightarrow Q = 13 \end{aligned} \]
The second-order condition holds, since MR falls with Q while MC is constant. At Q = 13 profit is 30(13) - 169 - 20 - 52 = 149. Q = 15, where marginal revenue is zero, would maximise revenue rather than profit; the options 9, 11 and 17 do not satisfy MR = MC.
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