Find the subgame perfect nash equilibrium (SPNE) of the problem: 2 firms are competing (Stackelberg): 1st...
Find the subgame perfect nash equilibrium (SPNE) of the problem:
2 firms are competing (Stackelberg): 1st firm 1 picks q1, then firm 2 observes q1 and picks q2. Price is determined by P(Q) = 40 - q1 - q2.
Firms 1 and 2 both have a fixed or marginal cost of 8.
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Find the subgame perfect nash equilibrium (SPNE) of the
problem:
2 firms are competing (Stackelberg): 1st...
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Two firms sequentially choose quantities q1, q2 to produce an identical good. First, firm 1 chooses q1, then firm 2 chooses q2. The price per unit in the market is p(q1, q2) = 1 − (q1 + q2). Assume that both firms have a constant marginal cost of zero. Both firms seek to maximize their profit. a. Formulate this story as an extensive form game b. Find all Nash equilibria of this game. c. Find the Subgame Perfect Nash equilibria...
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2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
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Suppose that the inverse market demand for a commodity is given by P = 240 Q...
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Suppose there are two firms, 1 and 2, competing in quantity. The market demand is p = 15-(q1 +q2), where q1 and q2 are the quantities produced by rms 1 and 2. Both rms have constant marginal cost c1 = c2 = 3. (a) [10] Find the Cournot equilibrium of this market. Compute the consumer surplus in equilibrium. b) Now suppose firms 1 and 2 merge, so that they become a monopolist with demand function p = 15 ? q,...
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4. Consider 2 firms selling fertilizer competing as Cournot duopolists. The inverse demand function facing the fertilizer market is P = 1 - where Q = 94 +98. For simplicity, assume that the long-run marginal cost for each firm is equal to X, i.e. C(q)=Xq for each firm. a) Find the Cournot Nash equilibrium where the firms choose output simultaneously b) Find the Stackelberg Nash Equilibrium where firm A as the Stackelberg leader. How much does the leader gain by...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
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