Question

After the recent Demogorgon invasion in Hawkins, Indiana, Will, Dustin, Lucas, Mike and Eleven start a firm, named DemoGone, which sells Demogorgon defense kits door-to-door. These kits include, among other things,Christmas lights, a baseball bat, and upon Eleven’s request, Eggo Waffles. Since nobody else knows how to defeat Demogorgons, DemoGone is a Monopoly.

Demand for these defense kits is

??=100−2?

Total costs are: ??1=20?1

Which imply Marginal Costs of: ??1=20

A) Assume that DemoGone is making profits, graph the firms profit maximization problem. Be sure to label all axes and relevant lines and curves. Also point out DemoGone’s profit maximizing price and quantity as well as the socially efficient output level.

B) Calculate DemoGone’s solution (i.e. the monopoly equilibrium). How much profit is generated by that choice?After observing the killer profit her brother’s firm is making, Nancy and her rebel boyfriend Steve enter the Demogorgon Defense market selling their own, identical kit. Their firm, “What about Barb” faces the same production costs as DemoGone.

C) If “What about Barb” and DemoGone act as competing Duopolists, what is the duopoly outcome of quantities and price? What about profits?

D) If both firms were forced to price at marginal costs, what are quantities, price and profits here?

E) If both firms perfectly colluded, what is the optimal quantity and price? Profits?

F) Is this cartel sustainable?

Answer 1

A)

B) Q=100-2p

P=50-0.5q

MR=50-q

MC=20

Monopolist equilibrium at MR=MC

50-q=20

Q=30

P=50-0.5*30=35

Profit=(35-20)*20=600

C)P=50-0.5q1-0.5q2

MR1=50-q1-0.5q2

MC1=20

50-q1-0.5q2=20

Q1=30-0.5q2{ best response function of firm 1( gemo)

By symmetry

Q2=30-0.5q1{ best response function of firm 2 barb)

Q2=30-0.5(30-0.5q2)

Q2=15/0.75=20

Q1=30-0.5*20=20

Q=40

P=50-0.5*40=30

Profit of each firm=(30-20)*20=200

D)If P=MC

Then Q=100-2*20=60

Q1=Q/2=60/2=30

Q2=30

Profit=0