ECON 401 Lecture Notes - Lecture 20: Subgame Perfect Equilibrium, Subgame, Bertrand Competition

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D(p) = 12 - p; c1(q1) = 2q1; c2(q2) = 2q2; The only bertrand (nash) equilibrium: p1 = p2 = 2: (profit = 0 each. ) P = p1 = p2 = 7: (profit = 12. 5 each. ) But: each firm wants to undercut price 7. Thus, it is not a bertrand (nash) equilibrium. (tacit) collusion: finding ways to implement the cartel outcome. Cournot duopoly: p(q) = 12 q; c1(q1) = 2q1; c2(q2) = 2q2; Q1 = q2 = 10=3: (profit = (10/3)2 ~ 11. 11 each. ) Q = 5 (q1 = q2 = 2. 5) (profit = 12. 5 each. ) But: each firm i "s best response to qj = 2:5: The only cournot (nash) equilibrium: (confess, confess). (payoffs: -2 each. ) Better for both: (don"t confess, don"t confess). (payoffs: -1 each. ) But: each prisoner"s best response to (don"t confess): confess. ) The main idea of (tacit) collusion: if you deviate from the cartel outcome, you will be punished in the future.

Related Questions

1. Suppose that two identical firms produce widgets and they are the only firms in the market. The cost functions of the two firms are given by C1(Q1) = 60Q1 and C2(Q2) = 60Q2. The demand function of the market is given by the function P = 300 - Q where Q=Q1+Q2.

a. Find the Cournot equilibrium output levels and profit for each firm.

b. Suppose the two firms form a Cartel and to maximize joint profit. Calculate how many widgets each firm will produce and their output levels.

c. Suppose firm 1 is the only firm in the market. Determine the output and price that firm 1 will produce and charge. Also, determine the profit level.

d. Suppose firm 2 takes its output decision after firm1 has announced its output decision. Calculate the output levels and profit levels of the two firms. Comparing the output and profit of part (a), which firm is better off and which firm is worse off ? Explain your answer.

raspberrymoose322

The market for authentic poutine in Vancouver is controlled by two shops, PierrePoutine (i = P) and MeanPoutine (i = M). The market demand is given by p = 12âq, where p is the price, and q is aggregate output. Both shops produce at constant marginal cost of $ 2 per dish of poutine.

a) Suppose first that each firm i = 1, 2 chooses its output qi , taking the output of the other firm as given [Cournot Competition]. Aggregate output is thus q = qP + qM. Determine the best-response functions q br 1 (q2) and q br 2 (q1). Calculate the Nash equilibrium quantities, the market price, and profits (Note that everything is symmetric here).

b) Now suppose firm i = 1,2 chooses its price pi , taking the price of the other firm as given [Bertrand Competition]. Give the Nash equilibrium prices and quantities. Explain carefully why i) this is a Nash equilibrium and why ii) there is no other equilibrium. Note: most of the credit will be for your explanation.

c) What if Pierre Poutine finds a cheaper cheese curd supplier, which reduces its marginal cost to $1 instead (MeanPoutine continues to have $ 2 production cost). Assuming that prices are quoted in dollars and cents (the smallest unit of measurement is a cent), determine new Nash equilibrium prices and quantities for the Bertrand Competition situation. Explain!

Assume that two firms, say firm 1 and firm 2, sell differentiated goods and face the following demand functions:

q1 = 4/3 - 2/3a - 4/3 p1 + 2/3 p2 and q2 = 4/3a - 2/3 + 2/3 p1 - 4/3 p2

where a > 1. In addition assume that the firms target own profit maximization, compete (simultaneously) in quantities and have marginal costs equal to c1 = c2 = c. Assume that 1 > c > or equal to 0. Describing the necessary mathematical steps, and providing the related mathematical intuition,

1. Find the inverse demands faced by the two firms (Hint: Solve the two demands simultaneously with respect to prices.

2. Derive each firm's best response function. Are quantities strategic substitutes or complements.

3. Derive the equilibrium in quantities.

4. Explain the economic meaning of parameter a. What happens to the equilibrium quantities and profits if a increases?

The instruction for this question is that I have to make sure to use proper mathematical notation used.

violeteel399

ECON 401 Lecture Notes - Lecture 20: Subgame Perfect Equilibrium, Subgame, Bertrand Competition

ECON 401 Full Course Notes

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