Question

A firm has the following revenue and cost functions.

TR = 120 Q – Q2

TC = 1/2 Q2 +30 Q + 10

Determine the quantity level at which the firm maximizes its total profit. (Hint: use marginal revenue = marginal cost rule)

Answer 1

Solution:

Derive Marginal Revenue = Marginal Cost

MR = $\frac{\partial TR} {\partial Q} = 120 - 2Q$

MC = $\frac{\partial TC} {\partial Q} = Q + 30$

Set MR = MC

120 – 2Q = Q + 30

120 – 30 = Q + 2Q

90 = 3Q

Q = 30

The quantity level at which the firm maximizes its total profit = 30 units