Suppose there are two firms competing in a market. They are selling identical goods, but since there is only two competitors, they strategically compete (rather than act as a price taker). Let the quantity produced by firm A be denoted q and the quantity produced by firm B be qs. While the firms choose their quantity levels,the "market"determines the market-clearing price. Suppose,then,that consumer preferences are described by the linear,inverse demand function P(Q)=a-bQwhere b>O and Q is the aggregate quantity produced,Q=q+qs.Furthermore,suppose each firm has the cost function of C(q)=f+cqwhere a>c>0andf0. (a) If the two firms compete in a one-shot,simultaneous-move game,what is the Nash Equilibrium levels of production and profit? (b) What is the impact of an increase in the fixed cost,f.have on the Nash Equilibrium quantity produced and profit of each firm? Suppose,instead,that firm A is the market leader.Specifically,firm A gets to set its quantity level first. Firm B observes firm A's output level before deciding its value of qs.The market demand curve and the cost functions are unchanged(only the timing of decisions changes) (c) With this leader-follower setup,what is the Subgame Perfect Nash Equilibrium quantity produced and profit of each firm?
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