1. Consider a duopoly with a homogeneous good. Two firms simultaneously decide how much to produce. After they bring the goods to the market, they see what price emerges as a result. Specifically, if firm 1 chooses q₁and firm 2 chooses q₂, then the quantity brought to the market is Q= q₁+ q₂, and the price that emerges is p= 8 0.25Q. The variable cost of production is 2 per unit. Due to some technological constraints, each firm can select only quantities {0,6,8,12}. The information provided above makes it possible to calculate the operating profit. For example, the operating profit of firm 1, if they choose q₁and their competitor chooses q₂, is depicted in the following table. The situation is entirely symmetric from the point of view of firm 2.

Competitor's choice q₂

q₂= 0 q₂= 6 q₂= 8 q₂= 12

0	0	0	0
27	18	15	9
32	20	16	8
36	18	12	0

q₁= 0

Own choice q_{1 1}= 6 q

q₁= 8

q₁= 12

Table 1: Operating profit of firm 1 in

Additionally, in order to operate, each firm has to maintain a plant. The cost of maintaining the plant is F= 8, but this cost can be avoided if the firm shuts down the plant, leading to q_i= 0. The actual profit is equal to the operating profit in the table above minus the cost of maintaining the plant.

1. What is the equilibrium outcome? What is the associated equilibrium price? What is the total surplus achieved in this equilibrium? Explain using appropriate terminology.