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##### 1. in a market where inverse demand function comes from the equation: p = 6 2q, two rms are playing the standard version

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**Question**

1. in a market where inverse demand function comes from the equation: p = 6 2q;two rms are playing the standard version of the Bertrand game for 3 periods. They;have the same marginal cost which is equal to 2. Discount factor for the rst and second;rm is.8 and.6, respectively.;a. What would be the price in the market if one of them was the monopolist in the;market.;b. Using backward induction, nd the unique SPNE. of this game. Remember an;equilibrium of this games includes one action for each player at each period. So it;would look like: (p1, p1, p1), (p2, p2, p2), where superscripts represents the rm and;1 2 3;1 2 3;subscripts represents the period.;c. Find each rms present value of the prot they make in this equilibrium.;Now suppose they play this game for innitely many times.;d. (Tacit Collusion): If pm is the monopoly price you found in part a, can you nd a;strategy prole under which p1 = p2 = pm is a SPNE of this game. If yes give that;strategy and show that it is a SPNE. Find the present value of the prot for both;rms in this equilibrium.;Hint 1: Consider grim trigger strategies.;1;Hint 2: 1 = + 2 + 3... = 1 for both of discount factors.;2. Demand function in a market is q = 8 p.;a. What would be the price if the market structure was monopoly with the marginal;cost equal to 4?;b. What would be the price if market structure was competitive and full of identical;rms with marginal costs equal to 4?;Now consider the ex-ante production model in order to explain the eect of capacity;constraint on the outcome of a duopoly. There are two rms which have ex-ante;marginal cost of production c0 = 4.;c. What is the highest level of production (investment) that each rm would have in;this market? In particular, assume that one of the rms is the monopolist in the;market, so she maximizes;max p(8 p);p;Find the optimal level of prot () and then nd the highest level of production;q, beyond which prot (net of investment cost) is negative. That is nd q such that;for any q > q;c0 q < 0;d. Argue that for q1, q2 [0, 8/3] dumping the whole capacity is always a N.E. Note that;if they dump their capacities the price in the market will be equal to p = 8(q1 +q2).;e. Among the set of equilibria you found in part d does any of them coincide with;the pricing behavior in competitive equilibrium (part b)? How about pricing in;monopoly (part a)?;3. Demand function in a market is p = 6 2q. There are ve rms in the market;which are playing the Cornuot game. Each rms marginal cost is a constant and equal;to 2. Find the N.E. for this games.

Paper#18269 | Written in 18-Jul-2015

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