Question

Duopoly Continuing with our latinum market example from last week, imagine that the government has noted the extreme restriction in latinum supplied and wishes to remedy the situation. While regulators are not willing to completely reopen the market, they are considering allowing the possibility of a second mining firm to enter the market. As we've seen, the price and quantity that result from duopoly depend greatly on assumptions about how the firms interact. For the following situations (1-4), give the • Quantity produced by each firm • Total Quantity supplied in the market • Price of latinum in the market • Profit earned by each firm Recall that the market demand is given by P = 225 - Q, and the production technology is TC = 5q. 1. The firms collude as a single monopolist 2. Bertrand Competition 3. Cournot Competition 4. Stackelberg Competition Mixed Strategies 5. Find the MSNE for the following game: LR U (8,10) (1,15) D (12,0) (-9,-5)

P = 225 - q
TC = 5q
MC = MR
MC = 5
MR = 225 - 2q

5 = 225 - 2q
2q = 225 - 5
q = 220/2
= 110

P = 225 - 110
= 115

Answer 1

1)

Monopoly Pricing.

P = 225 - q
TC = 5q

TR = (225-Q)*Q

MR = 225 -2Q
MC = MR
MC = 5
MR = 225 - 2q

5 = 225 - 2q
2q = 225 - 5
q = 220/2
= 110

P = 225 - 110
= 115

Profit = TR - TC

= 110*115 - 5*110

= 12100

2)

Under the bertrand competition, firms compete and price fall until it becomes equal to MC.

Condition for bertrand competition: P = MC

calculate the competitive output:

P = MC

225 - q = 5

Q = 220

Each firm produces the 110 units

Profit shall be zero as the price is equal to the MC or AC of production.

3)

Cournot output:

First calculate the competitive output:

P = MC

225 - q = 5

Q = 220

Cournot output = (N/N+1)*Competitive output

= (2/3)*220

= 146.66

Cournot output = 146.66

Cournot Price = 225 -146.66

= 78.34

Each firm output = 146.66/2

= 73.33

Each firm profit = 78.34*73.33 - 5*73.33

= 5378.02

4)

Stackelberg Competition:

Leader output = ( a-c)/2b

= (225-5)/2

= 110

Follower output = (a-c)/4b

= (220/4)

= 55

total output = 165

P = 225 - 165

= 60

Leader Profit = TR - TC

= 110*60 - 5*110

= 6050

Follower profit = TR - TC

= 55*60-5*55

= 3025