Question

Two firms operate in an industry with inverse demand given by p = 16 - q. Each firm operates with constant marginal and average cost equal to 0. Firms compete by setting the quantity to sell in the market. 1) Determine the best reply function of each firm. 2) Determine what are in equilibrium the quantities offered by each firm, the market price and the profits obtained by each firm. 3) Assume firms cooperate and choose joint output to maximize their joint profit, sharing the resulting demand. Calculate market price and production and profits of firms A and B. 4) Using a normal-form representation, illustrate a one-shot simultaneous game in which firms can only choose between the cooperative and Cournot quantities (hint: you may need some additional work to derive some of the firms' profits). Find the equilibrium of this game and discuss. 

          Two firms operate in an industry with inverse demand given by p = 16 - q. Each firm operates with constant marginal
and average cost equal to 0. Firms compete by setting the quantity to sell in the market.
1) Determine the best reply function of each firm.
2) Determine what are in equilibrium the quantities offered by each firm, the market price and the profits obtained
by each firm.
3) Assume firms cooperate and choose joint output to maximize their joint profit, sharing the resulting demand.
Calculate market price and production and profits of firms A and B.
4) Using a normal-form representation, illustrate a one-shot simultaneous game in which firms can only choose
between the cooperative and Cournot quantities (hint: you may need some additional work to derive some of
the firms' profits). Find the equilibrium of this game and discuss.
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Two firms operate in an industry with inverse demand given by p = 16 - q. Each firm operates with constant marginal and average cost equal to 0. Firms compete by setting the quantity to sell in the market. 1) Determine the best reply function of each firm. 2) Determine what are in equilibrium the quantities offered by each firm, the market price and the profits obtained by each firm. 3) Assume firms cooperate and choose joint output to maximize their joint profit, sharing the resulting demand. Calculate market price and production and profits of firms A and B. 4) Using a normal-form representation, illustrate a one-shot simultaneous game in which firms can only choose between the cooperative and Cournot quantities (hint: you may need some additional work to derive some of the firms' profits). Find the equilibrium of this game and discuss.

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Principles of Economics
Principles of Economics
Gregory Mankiw 8th Edition
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Two firms operate in an industry with inverse demand given by p=16-q. Each firm operates with constant marginal and average cost equal to 0 . Firms compete by setting the quantity to self in the market. Determine the best reply function of each firm. Determine what are in equilibrium the quantities offered by each firm, the market price and the profits obtained by each firm. Assume firms cooperate and choose joint output to maximize their joint profit, sharing the resulting demand. Using a normal-form representation, illustrate a one-shot simultaneous game in which firms can only choose between the cooperative and Cournot quantities (hint: you may need some additional work to derive some of the firms' profits). Find the equilibrium of this game and discuss. & Two firms operate in an industry with inverse demand given by p=16-q.Each firm operates with constant marginal and average cost equal to 0.Firms compete by setting the quantity to self in the market. 1)Determine the best reply function of each firm. 2 Determine what are in equilibrium the quantities offered by each firm, the market price and the profits obtained by each firm. 3Assume firms cooperate and choose joint output to maximize their joint profit,sharing the resulting demand. Calculate market price and production and profits of firms A and B.-xn 4) Using a normal-form representation,illustrate a one-shot simultaneous game in which firms can only choose between the cooperative and Cournot quantities (hint: you may need some additional work to derive some of the firms'profits.Find the equilibrium of this game and discuss.
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Transcript

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00:02 So, farc will analyze both parts as forward parts of the game.
00:09 First is 8 parts, simultaneous capacity, efficiency, construction.
00:49 Construction here.
00:53 First point is capacity, efficiency, construction.
01:02 Both farms simultaneously decide whether to build a small or a large facility.
01:08 So, there are four possible outcomes.
01:11 Small -small, which is small -small, small -large, large -small, and large -large.
01:23 Then is output decision.
01:30 After observing the capacity chosen by both farms, they simultaneously decide on their output level.
01:36 So, given capacity and output, the market price is determined by the demand function, which is p equals 900 minus q1 minus q, and that is profit maximization.
02:00 So, farms aim to maximize their profit by considering the cost of building that facility, producing the output, and selling it at the determined market price.
02:09 So, game perfectness equilibrium, or nest equilibrium, large -large and q1 -q2, or large -large and q1 -q2 here, such that it maximizes both farm profits, given the observed capacity and output decision.
02:42 And for the b part of the equilibrium, this n, not q, nest.
02:58 You can see the sequential capacity, construction.
03:10 For farm one decision, farmers decide to build a small or a large facility...
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