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# H2S4 - What is the Nash equilibrium in prices(Bertrand...

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Econ 467 Maria Muniagurria Homework 2 (Make sure to show your work) . (I) Consider two identical firms (Firm 1 and Firm 2) that produce an homogenous product . The demand for their product is : P= 200 -Q, where Q= q 1 + q 2 . Each firm has a cost function: C(q i ) = 20 q i ( i.e. the Mc i is 20 and there are no fixed costs) (1) Calculate the Stakelberg equilibrium assuming that Firm 1 is the Leader and Firm 2 the Follower (i.e. calculate the SPNE assuming that Firm 1 moves first). (2) Assume firms choose quantities simultaneously, play the game for an infinite number of periods and use trigger strategies. (a)Write down the condition that needs to be satisfied for cooperation to be observed (i.e for the trigger strategy equilibrium to be a SPNE). (b) For which values of the discount factor will cooperation be observed (will the trigger strategy equilibrium be a SPNE)? (3) Suppose now that firms play a static game where they choose prices simultaneously
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Unformatted text preview: What is the Nash equilibrium in prices (Bertrand equilibrium)? What are the profits for each firm? (II) Suppose now that the cost function for a firm is: C(q i ) = 20 q i + 400 ( i.e. the MC i is 20 and the fixed cost is 400) but the market demand is the same as in (I): P= 200 - Q. What is the free entry number of firms if they behave in a Cournot fashion? Justify. (III) Differentiated Products Two firms compete by choosing price. Their demand functions are: q 1 = 20 - p 1 + p 2 q 2 = 20 - p 2 + p 1, where p 1 and p 2 are the prices charged by each firm, and q 1 and q 2 the resulting quantities demanded. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash Equilibrium in prices. Calculate prices, quantities and profits for each firm....
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