The inverse market demand is P=160 4Q. The firms have cost functions TC 1 = 8+12q 1 +2q 1 TC 2 = 8+12q

1. The inverse market demand is P=160 – 4Q. The firms have cost functions

TC₁ = 8+12q₁+2q₁²

TC₂ = 8+12q₂+2q₂²

a.      Determine monopoly profit-maximizing output for each firm.

1. 2. Determine the industry profit-maximizing output under collusion.
2. 3. Calculate the equilibrium price under collusion.   
3. 4. Determine if the firms should collude. Assume your initial game is Cournot.

Joint profits

Profits Collusion = $1079.2

Profits Cournot = 1010.75

Profits Stackelberg = 971.17

Profit monopoly 1 = 904.67

Profits monopoly 2 = 904.67

Collude since profits are strictly higher for each firm.

5. Assume firm 1 offers to buy firm 2. What is the maximum price firm 1 will pay? Assume your initial game is Stackelberg.

Make an offer that keeps firm 1 indifferent between operating as a Stackelberg or multi-plant monopoly. Firm one must be reimbursed $513.52 so the maximum is the difference between multi-plant monopoly and firm 1 as a Stackelberg.

Offer 1079.2 - 513.52 = 565.68