Question

In: Economics

In working the following problem, I solved for P to derive: P=60.65-.5Q. From there I calculated...

In working the following problem, I solved for P to derive: P=60.65-.5Q. From there I calculated TR and MR. I set up excel with Q ranging up to 60 and used P as a function of Q with the P equation. TR=60.65Q-.5Q^2 MR=60.65-1Q I set MC = to the .65 (constant cost but I am not sure that this was correct.) I was able to solve for Q=60 and plug in to Price equation to get profit but I am not sure that this is correct. Please help!

Games to Get, LLC currently enjoys a patent on gaming software that predicts usage for clients involved in civil lawsuits. Demand for this software is

QD = 121.3 – 2P. Software creation and development was $2,350. G2G can generate each copy for a (constant cost) of $0.65).

a. How many copies of the software should G2G attempt to sell? At what price? How much profit would be generated?

b. G2G’s patent expires in 12 months, and soon other gaming companies will produce competing software. What quantity and price will result once competing software emerges? How much consumer surplus will my clients gain once the competitors enter? (For measuring consumer surplus, recall that area of a triangle = ½ * base * height.) My calculation suggests that while in monopoly status, a price of 30.65 can be charged, whereas in competition, P rises. :(

c. How much deadweight loss is created by G2G’s patent and monopoly on this software?

Expert Solution

QD = 121.3 - 2P

2P = 121.3 - QD

P = 60.65 - 0.5QD

(a) The firm will maximize profit by equating MR and MC.

TR = P x QD = 60.65QD - 0.5QD²

MR = dTR/dQD = 60.65 - QD

60.65 - QD = 0.65

QD = 60 (Your answer is correct).

P = 60.65 - (0.5 x 60) = 60.65 - 30 = $30.65

Profit = QD x (P - MC)** = 60 x $(30.65 - 0.65) = 60 x $30 = $1,800

**Since software development cost is a sunk cost, it is not included for computing profit.

(b) In competitive equilibrium, price equals MC. So

60.65 - 0.5QD = 0.65

0.5QD = 60

QD = 120

P = MC = $0.65

From demand function, when QD = 0, P = $60.65 (Vertical intercept of demand curve)

Consumer surplus = Area between demand curve & price

With monopoly, CS = (1/2) x $(60.65 - 30.65) x 60 = 30 x $30 = $900

With competition, CS = (1/2) x $(60.65 - 0.65) x 120 = 60 x $60 = $3,600

Gain in CS = $3,600 - $900 = $2,700

(c) Deadweight loss = (1/2) x Change in P x Change in Q = (1/2) x $(30.65 - 0.65) x (120 - 60) = (1/2) x $30 x 60 = $900

Rahul Sunny answered 2 years ago

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