Question

Shaughnessy Consulting, LLC currently enjoys a patent on software that estimates economic damages for clients involved in personal injury lawsuits. Demand for my software is

Q_D = 60.3 – 0.1P. Creating the software cost me about $2,000 in development and coding. I can produce a copy of the software for $3.00 per unit (constant cost).

a.   How many copies of the software should I attempt to sell? At what price should I sell it? How much profit would I make?

b.   My patent expires in a year, and I know other economic consultants will produce competing software. What quantity and price will result once competing software emerges? How much consumer surplus will my clients (lawyers) gain once the competitors enter? (For measuring consumer surplus, recall that area of a triangle = ½ * base * height.)

c.   How much deadweight loss is created by my patent and monopoly in this software?

Answer 1

QD=60.3-0.1P

P=603-10QD

a) Total cost for producing 'Q' copies,TC = 2000+3Q

marginal cost, MC = d(TC)/dQ = 3

Total revenue from selling 'Q' copies,TR = P*Q = (603-10Q)Q = 603Q-10Q^2

Marginal revenue, MR= 603-20Q

For profit maximiztion

MR=MC

603-20Q=3

Q=30

P=603-10*30 = 303

Profit= TR-TRC = 303*30-2000-3*30 = 7000

copies sold = 30

Price=$303

Profit = $7000

b)In competitive market

Marginal revenue, MR=Price,P= 603-10Q

MC=MR

3=603-10Q

Q=60

P=30

consumer surplus gained by clients = CS in competition-CS in monolpoly = 0.5*(603-30)*60-0.5*(603-300)*30 = $12690

c) deadweight losss due to monopoly = 0.5*(P2-P1)*(Q2-Q1) = 0.5*(303-30)*(60-30) = $ 4095