Question

After 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 Q^D = 100 - 2P Total Costs are TC₁ = 20q₁ Which imply Marginal Costs of MC₁ = 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).

Consider the given problem here the demand for defense kits is, “Qd = 100 – 2*P”, => P = 50 – Q/2, with the marginal cost, “MC1=20”. A monopolist decides to produce the profit maximizing output by the following condition.

=> MR = MC1, => 50 – Q = 20, => Q = 30. So, the profit maximizing price is “P=50 – Q/2 = 50-30/2 = 35”.

=> the profit maximizing price and quantity are, “P*=35” and “Q*=30”.

At the socially efficient level of output the price should be equal to marginal cost, => P=MC.

=> 50 – Q/2 = 20, => Q/2 = 30, => Qc=60. So, the socially optimum price and quantity are “P=20” and “Qc=60”.

Consider the following fig.

Here “D” be the market demand schedule, MR be the corresponding marginal cost function and MC be the marginal cost function, => the equilibrium of the monopolist is Em, where MR is exactly equal to MC,=> the profit maximizing price and quantity are “Pm=35” and “Qm=30” respectively. The socially efficient equilibrium is given by “Ec”, where price is exactly equal to MC, => the socially efficient quantity is “Qc=60”.

b).

Here the profit of the monopolist is given by, => A = P*Q – MC1*Q = (P – MC1)*Q = (35-20)*30 = $450.

=> A = $450.

c).

Let’s assume “What about Barb” and “DemoGone” act as competing Duopolists, where “DemoGone” is producing “q1” and “What about Barb” is producing “q2”, the market price will be determined by the total output supplied by the two firms together.

So, the profit function of “DemoGone” is given by.

=> A1 = TR – TC = P*q1 – MC1*q1 = (50 – q1/2 – q2/2)*q1 – MC1*q1, where “P = 50 – q1/2 – q2/2”.

=> A1 = 50*q1 – q1^2/2 – q1*q2/2 – 20*q1, => A1 = 30*q1 – q1^2/2 – q1*q2/2. The profit maximizing condition is given by, dA1/dq1 = 0.

=> 30 – q1 –q2/2 = 0, => q1 = 30 – q2/2, be the best response function of “DemoGone”.

So, the profit function of “What about Barb” is given by.

=> A2 = TR2 – TC2 = P*q2 – MC2*q2 = (50 – q1/2 – q2/2)*q2 – MC2*q2, where “P = 50 – q1/2 – q2/2”.

=> A2 = 50*q2 – q2^2/2 – q1*q2/2 – 20*q2, => A2 = 30*q2 – q2^2/2 – q1*q2/2. The profit maximizing condition is given by, dA2/dq2 = 0.

=> 30 – q2 –q1/2 = 0, => q2 = 30 – q1/2, be the best response function of “What about Barb”.

Now, by solving these two functions we get the equilibrium production by both the firm. So, here “What about Barb” and “DemoGone” both produce “q1=q2=20 units” and the total output supplied by both the firms is “Q=q1+q2=40 units”, => the market price is “P = 50 - Q/2 = 50 – 20 = 30”, => P = 30.

So, the profit earn by both the firms is “A1=(P-MC1)*q1 = (30-20)*20 = $200 = A2”.

d).

If both the firms are forced to charge the MC that is “P=MC=20”, then the total output supplied by both the firms is “Qc=60”, => each firm produce “q1=q2=30”.

Here price is equal to marginal cost, => both the firms are getting normal profit that is zero economic profit.