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Consider a firm facing market demand qa p with a > 0; its cost of production c0 (a)(2pt] Find the optimal price p for this fi
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(a) Market demand function: cost of production (c) 0 Firm maximize its profit Profit = p*q-c Derivate profit w.r.t to p ES Th

where qq1+q2 given firm 1 choice q1, firm 2 demand is q2= 1-q1-p firm 2 maximization problem is profit 2 p q2-c firm 2 maximi

(c) firm 1 maximize its profit Therefore its maximization problem is profit1 p qi-c -(1-q1-q2 1- substituting value of q2

to calculate optimal quantity of firm 2 profit (1- 3q1 /2 91- aprofit/oqi-1-3q1-0 p 1- 3 (1/3)/2 therefore optimal quantity f

firm 1 produce 1/3 quantity at price 1/2 and firm 2 produce 1/6 at price 1/2

(f) when the firms play simultaneously The profit (objective) function of firm 1 is: Profit 1-p qi- as c 0 Profit1 1- q1 -q2)

The profit (objective) function of firm 2 is: Profit 1-p 42- (1-q1-92)92-c as c= 0 To solve firm 1 maximization problem, der

0) The pure nash equilibrium is substituting value of q2 in q1 q1(1-q2)/2 q1(1-(1-q1)/2)/2 (1+q14 3q1/4 1/4 Therefore q1 1/3

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