Answer to Question #274168 in Microeconomics for Edet

Question

A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q

equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces

no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is

not required to be presented), either way, please provide a brief description of how you arrived at your

results.

Answer 1

Solution:

A monopoly maximizes profit where MR = MC

Derive MR:

TR = P $\times$ Q = (500 – 10Q) $\times$ Q = 500Q – Q²

MR = $\frac{\partial TR} {\partial Q}$ = 500 – 2Q

 

Set MR = MC:

500 – 2Q = 100

500 – 100 = 2Q

400 = 2Q

Q = 200

Profit maximizing quantity = 200

Substitute in the demand function to derive price:

P = 500 – Q = 500 – 200 = 300

Profit maximizing price = 300