Question

1. Assume that the demand curve is given by Q = 1000 – 0.25P. What is the inverse demand curve?

B) Using the inverse demand curve you solved for in 1, solve for the total revenue for this

Monopolist.

C) Using the total revenue curve you solved for in 2, solve for the marginal revenue curve.

D) Assume that Marginal costs are given by 100 + 2Q. What is the profit-maximizing quantity and

price for the monopolist?

E) Now, turn your attention to the Excel Spreadsheet. What is the Profit Maximizing quantity and

price for the monopolist?

Answer 1

Assume that the demand curve is given by Q = 1000 – 0.25P.

A) Inverse demand curve is given by

Q = 1000 - 0.25P

0.25P = 1000 - Q

P = 1000/0.25 - Q/0.25

P = 4000 - 4Q

B) Total revenue for this Monopolist is R = PQ

R = (4000 - 4Q)Q

R = 4000Q - 4Q^2

C) Marginal revenue curve is derivative of R

MR = dR/dQ

MR = 4000 - 8Q

D) Assume that Marginal costs are given by 100 + 2Q.

At profit maximizing quantity we have MR = MC

4000 - 8Q = 100 + 2Q

3900 = 10Q

Q = 390 units

P = 880 per unit

E) It is same as D)

Q = 390 units

P = 880 per unit

Both MR = MC = $880

Q	MR	MC
0	4000	100
100	3200	300
200	2400	500
300	1600	700
350	1200	800
390	880	880
400	800	900