Question

The following table shows the demand curve facing a monopolist who produces at a constant marginal cost of $6.00 Price Quantity 0 18 16 2 14 12 6 10 8 10 12 8 6 4 14 2 16 0 18 Calculate the firm's marginal revenue curve. The firm's marginal revenue (MR) curve is A. MR 18-1.00Q B. MR 10 1.00Q C. MR 10-0.50Q O D. MR 18-0.25Q O E. MR 18-2.000 What are the firm's profit-maximizing output and price? The firm's profit-maximizing output is units. (Enter your response rounded to two decimal places.)

Answer 1

Derivation of MR

Q1=2 P1=16

Q2=4 P2=14

Equation of the demand line

P-P1=(14-16)/(Q2-Q1)(Q-Q1)

P-16=(14-16)/(4-2)(Q-2)

P-16=(-2/2)(Q-2)

P-16=-Q+2

P=2+16-Q

P=18-Q

TR=PQ

=(18-Q)Q

=18Q-Q²

Derivative of TR with respect to Q

dTR/dQ=18*1-2Q

MR=18-2Q

Hence option E is the correct answer.

2.

TR MR MC 18 0 0... 16 2 32 16 6 14 4 56 12 6 12 6 72 8 6 10 8 80 6 61 8 10 80 0 72 6 12 -4 6 14 4 56 -8 6 2 16 32 -12 6 0 18 0 -16 6

Profit-maximizing condition is

MR=MC or MR should be greater than MC

Corresponding to this condition quantity is 6 units.

Hence corresponding to this quantity price is $12.

Profit=(P-MC)Q

=(12-6)6

=$36