2. Imagine that in the new Avengers movie there is a key scene in which the hero

Question

2. Imagine that in the new Avengers movie there is a key scene in which the heroes discuss their next move via cellphone. The producers approach first Apple and then Samsung to see if they are interested in paying for a product placement for $5 million. Apple estimates that if they agree to the deal, they will see an increase in prolits of S4 million (all changes in profit are not including the $5 million payment). They estimate that if they don't do it and Samsung does, they will lose $2 million in profits. If neither agrees to the deal, profits will not change. Samsung estimates that if they agree to the deal, profits will increase by $7 million. If Apple agrees to the deal, Samsung believes its profits will fall by $3 million. And if neither agree, profits will stay the same. Draw a tree diagram of this game with Apple moving first and Samsung moving second. a. b. What is the Nash Equilibrium? How might the NE change if Apple had some uncertainty about whether Samsung would accept or reject the deal? What is the advantage to Apple of being approached first? That is, how does the Nash Equilibrium change if Samsung gets to decide first? c. Chapter 8 1. What are the main diffcrences between the Cournot and Bertrand models of oligopoly? Specifically, what are the different assumptions? What do the resulting prices, quantities, and profits differ? Which leads to greater market efficiency? 2. Consider a market for a homogeneous product with demand given by Q 60- P/3. There are two firms, cach with constant marginal cost equal to 30. a. Determine output and price under a Bertrand equilibrium. b. Determine output and price under a Cournot equilibrium. c. Compute the efficiency loss in Cournot as a percentage of the efficiency loss under monopoly

Explanation / Answer

In Stackelberg model where Samsung is a first mover, it must take the reaction function of Apple in its computation of marginal revenue. Demand function is Q = 500 – 0.75P or P = 666.67 – 1.34Q

Derivation of Apple’s reaction function

Total revenue of Apple = P*(q2) = (666.67 – 1.34(q1 + q2))q2 = 666.67q2 – 1.34q22 – 1.34q1q2

Marginal revenue = 666.67 – 2.68q2 – 1.34q1

Marginal cost = 60

Solve for the reaction function

666.67 – 2.68q2 – 1.34q1 = 60

q2 = 303.335 – 0.5q1

b) Samsung is the leader and Apple is the follower. Compare the outcome with the demand P = A - Bq, Marginal cost = C, and number of firms = 2

q1 = A - c/2B = 666.67 - 60/2*1.34 = 226.37

q2 = A - c/4B = 666.67 - 60/4*3 = 113.18

Price = A - c/4 = 666.67 - 60/4 = 151.68

Profit of the leader = 226.37*151.68 = 34335.8

Profit of the follower = 113.18*151.68 = 17167.1

c) With a fine of $5, MC rises to $65.

Samsung is the leader and Apple is the follower. Compare the outcome with the demand P = A - Bq, Marginal cost = C, and number of firms = 2

q1 = A - c/2B = 666.67 - 65/2*1.34 = 224.57

q2 = A - c/4B = 666.67 - 65/4*3 = 112.25

Price = A - c/4 = 150.41

Profit of the leader = 224.37*150.41 = 33769.2

Profit of the follower = 112.25*150.41 = 16884.65

d) With equal quantities the market will become cournot duopoly.

quantity will same for both companies as

A - c1/2B = A - c2/4B

(666.67 - c1)/2 = (666.67 - 60)/4

666.67 - c1 = 303.34

c1 = 363.33

With the current marginal cost of 65, the fine should be increased by $298.33

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