3. The (market) inverse demand function for a good is as follows: Pp(q) = {12-2q if g € (0,6], if q> 6. There are two firms: N = {1,2}. Each firm's cost function is such that producing r units of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is, they simultaneously choose their quantities. The firms are profit-maximizers. (1) Find a Nash equilibrium. (2) What is the size of the deadweight loss incurred by the Duopoly, compared to the competitive equilibrium allocation?
3. The (market) inverse demand function for a good is as follows: Pp(q) = {12-2q if g € (0,6], if q> 6. There are two firms: N = {1,2}. Each firm's cost function is such that producing r units of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is, they simultaneously choose their quantities. The firms are profit-maximizers. (1) Find a Nash equilibrium. (2) What is the size of the deadweight loss incurred by the Duopoly, compared to the competitive equilibrium allocation?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![3. The (market) inverse demand function for a good is as follows:
12- 2q
if q = [0,6],
if q> 6.
Pp(q) = { 12
There are two firms: N = {1,2}. Each firm's cost function is such that producing a units
of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is,
they simultaneously choose their quantities. The firms are profit-maximizers.
(1) Find a Nash equilibrium.
(2) What is the size of the deadweight loss incurred by the Duopoly, compared to the
competitive equilibrium allocation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F751f61a1-9f95-48ad-8fd0-33faa44bd79d%2F19504d3e-2380-44d2-ad58-0f0dfbc2c8b7%2F98slexb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. The (market) inverse demand function for a good is as follows:
12- 2q
if q = [0,6],
if q> 6.
Pp(q) = { 12
There are two firms: N = {1,2}. Each firm's cost function is such that producing a units
of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is,
they simultaneously choose their quantities. The firms are profit-maximizers.
(1) Find a Nash equilibrium.
(2) What is the size of the deadweight loss incurred by the Duopoly, compared to the
competitive equilibrium allocation?
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