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Problem 1. There are two suppliers of distilled water, labeled firm A and firm B. Distilled...

Problem 1. There are two suppliers of distilled water, labeled firm A and firm B. Distilled water is considered to be a homogenous good. Let p denote the price per gallon, qA quantity sold by firm A, and qB the quantity sold by firm B. Firm A and firm B bear a production cost of cA = cB = 2 per one gallon of water. The inverse demand function for distilled water is given by p = 12 − 1Q, 3 where Q = qA + qB denotes the aggregate industry supply of distilled water. Solve the following problems:

(a) Suppose the firms compete in quantities (production levels). Compute each firm’s quantity best response function, and conclude how much each firm produces in a Cournot-Nash equilibrium.

(b) Compute the price and the profit of each firm in a Cournot-Nash equilibrium.

(c) Compute the quantity produced by each firm in a sequential (Stackelberg) game in which firm A sets its output level before firm B.

(d) Compute the price and the profit of each firm in a Stackelberg equilibrium.

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