Reference no: EM13293504
1. [10 marks] Suppose a monopolist has a total cost function of TC=100Q+1000, where Q is the total number of units he produces. He is able to separate his market into two distinct segments with no possibility of arbitrage, where in market one P1=500-10Q1 and in market two P2=300-20Q2. This implies that Q=(Q1+Q2). In each market he aims to maximise profit by selling Q1 andQ2 but he produces all Q in his one firm.
What price and quantity does the monopolist sell in market one?
What price and quantity does the monopolist sell in market two?
What is his total profit?
Calculate price, quantity, and profit if he were unable to separate the
two markets.
2. Suppose each of the towns A, B, C, D, E, F, and G has a weekly market day, but different towns have a different market day. Example, if A has market day on Tuesday, then deciding to go to market at A and deciding to go to market on Tuesday are the same thing. Assume everyone knows which town has a market day on which day (unique). Suppose one buyer and one seller are simultaneously deciding, right now as you solve this problem, to visit a town on a day next week for buying and selling. Not going to a market is not an option. They can only trade if they are both at the same market. If they meet they can trade and each person’s net payoff is 3. If they fail to meet then each person’s payoff is -1 which represents the travel cost. Represent this game in normal (matrix/table) form indicating the players, their respective strategies and their payoffs [5 marks] and determine the pure strategy Nash Equilibrium(s) [3 marks]. Explain why Nash equilibrium happens and why the other strategies do not generate Nash equilibriums.
3. One famous game is a variant of the Prisoner’s Dilemma called the “Tragedy of the Commons.” Assume there are two cattle herders who share a common plot of grazing land. The market price for a cow is given by P=300-10C, where C is the total number of cows grazed (this is because as more cows are grazed on the same plot of land, they become skinnier and less tasty). There is no cost associated with this activity, so Profit is simply P*C. Finally, let C1 be the number of cows grazed by the first cattle herder and C2 be the number of cows grazed by the second cattle herder, so C1+C2=C.
Calculate the number of cows grazed by each cattle herder in the Nash equilibrium to this game.
How much profit does each cattle herder earn?
Is this arrangement Pareto Optimal (i.e., what would arise if the two
firms collude)? Show (mathematically) why/why not. (Pareto optimal means that you cannot make one player better off without making the other player worse off)
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