Question

Use the following information to answer questions #1 – 3: A monopolist has the following demand curve: P = 100 – Q and total cost curve: TC = 16 + Q2 and marginal cost curve: MC = 2Q.

1. Find the profit maximizing quantity. a. Q = 20 b. Q = 33.33 c. Q = 25 d. Q = 4 e. Q = 30

2. Find the profit maximizing price. a. $96 b. $80 c. $75 d. $66.67 e. $70

3. Find the profit. a. Profit = $1875 b. Profit = $1234 c. Profit = $1184 d. Profit = $1825 e. Profit = $1250

Answer 1

Profit maximization condition of Monopoly Is MR=MC.

P= 100-Q

TR= P(Q)

= (100-Q)(Q) = 100Q-Q²

MR= 100-2Q

MC = 2Q

1. Under monopoly : MR=MC

100-2Q = 2Q

4Q =100

Q = 25 units

So, profit maximization quantity under monopoly is 25 units .

Hence,option(C) is correct.

2. P=100-Q

= 100-25 = $75.   

So, profit maxmization price is $75.

Henec, option(C) is correct.

3. At Q=25 ,TC = 16+(25)² = $641

TR = (25)(75) = $1875

Profit =TR -TC

=$(1875-641) = $1234

Hence, option(B) is correct.