Question

Please show work.

Monopoly

The demand is Q_D= 9,000 – .3 P and TC = 6,000 Q.

1. What price should we charge? How much profit can we make?

2. What quantity of output should we make?

3. How much surplus will result from this (consumer and producer)? How much deadweight loss it there? Explain and add graph is necessary.

Answer 1

Q = 9000-0.3P

Or,

0.3P = 9000-Q

P = 30,000 - 3.3Q

MR = dPQ/dQ = 30,000-6.6Q

TC = 6000Q

MC = dTC/dQ = 6000

A)

A monopoly sets prices at the point MR = MC

30,000-6.6Q = 6,000

Q = 3600 approx

P = $18000

Profit = (P-MC)Q = (18000-6000)3600 = $43,200,000

B)

Q = 3600 units approximately

C)

Consumer surplus = (1/2)(P where Qd is 0 - P)(Q)

Consumer surplus = (1/2)(30000-18000)(3600)

Consumer surplus = $21,600,000

Producer surplus = (P-MC)Q

Producer surplus = (18000-6000)3600

Producer surplus = 43,200,000

Dead weight loss = (1/2)(P-MC)(Q when P equals MC - Q of monopoly)

Dead weight loss = (1/2)(18000-6000)(7200-3600)

Dead weight loss = 21,600,000