Consulting, LLC currently enjoys a patent on software that estimates economic da

Question

Consulting, LLC currently enjoys a patent on software that estimates economic damages for clients involved in personal injury lawsuits. Demand for my software is QD=60.3–0.1PQD=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).

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

a. Q=150Q=150; P=$7.50P=$7.50; profit = $1,250

b. Q=35Q=35; P=$253P=$253; profit = $8500

c. Q=30Q=30; P=$303P=$303; profit = $9,000

d. Q=9Q=9; P=$125P=$125; profit = $466.66

2. 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.)

a. Q=8Q=8; P=$2.50P=$2.50; CSCS increases by $74,600 (from $11,000 to $85,600)

b. Q=40Q=40; P=$6P=$6; CSCS increases by $2000 (from $2600 to $4600)

c. Q=140Q=140; P=$185.50P=$185.50; CSCS increases by $3,050 (from $10,050 to $13,100)

d. Q=60Q=60; P=$3P=$3; CSCS increases by $13,500 (from $4,500 to $18,000)

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

a. $9,800

b. $4,500

c. $40.50

d. $6,250

Explanation / Answer

QD = 60.3 - 0.1P

0.1P = 60.3 - QD

P = 603 - 10QD

(1) (c)

Profit is maximized by equating MR with MC.

Total revenue (TR) = P x QD = 603QD - 10QD2

MR = dTR / dQD = 603 - 20QD

Equating with MC,

603 - 20QD = 3

20QD = 600

QD = 30

P = 603 - (10 x 30) = 603 - 300 = 303

Profit = QD x (P - MC)= 30 x (303 - 3) = 30 x 3009,000 - 2,000

(Development & Coding cost is a sunk cost and is not included in cost computation).

(2) (d)

In competitive equilibrium, P = MC

603 - 10QD = 3

10QD = 600

QD = 60

P = MC = 3

From demand function, when QD = 0, P = 603 (Reservation price)

Consumer surplus (CS) = Area between demand curve & Price

In question (1), CS = (1/2) x (603 - 303) x 30 = 15 x 300 = 4,500

In competitive equilibrium, CS = (1/2) x (603 - 3) x 60 = 30 x 600 = 18,000

Increase in CS = 18,000 - 4,500 = 13,500

(3) (b)

Deadweight loss = (1/2) x Change in price x Change in quantity = (1/2) x (303 - 3) x (60 - 30) = (1/2) x 300 x 30

= 4,500

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