jabraeshaw
09.12.2019 •
Business
The firms in a duopoly produce differentiated products. the inverse demand for firm 1 is:
p1 = 52 - q1 - 0.5q2.
the inverse demand for firm 2 is:
p2 = 70 - q2 - 0.5q1.
each firm has a marginal cost of m = $1 per unit. solve for the nash-cournot equilibrium quantities.
the cournot equilibrium quantities are:
q1 = and q2 = units. (enter your responses rounded to two decimal places.)
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Ответ:
we get q1= 18 and q2 = 30
Explanation:
There is a standard way of solving for Q1 and Q2.
The profit function for firm 1 equals π1 = P1Q1-C1
The profit function for firm 2 π2 = P2Q2-C2
we know that
Determine the profit functions.
Determine the best response function for the firms.
Substitute Q1 or Q2 in the other profit function and solve.
we know that Marginal cost: MC = dC/dq
where C= total cost.
we have MC = 1
so dC=dq
integrate on both sides
we get C = q + a(constant)
marginal cost for both firms are same so we get two cost equations as
C1=q1+a
C2=q2+b
where a and b are integral constants.
π1 = P1Q1-C1
π2 = P2Q2-C2
substitute inverse demand function and cost function for both firms
we get
π1 = P1Q1-C1 = (52-q1-0.5q2)q1-(q1+a)
π2 = P2Q2-C2= (70-q2-0.5q1)q2-(q2+b)
The best response function can be determined by deriving the profit function of firm 1 w.r.t. Q1 and for firm 2 w.r.t. Q2 and set them equal to zero
so first derivative π1 = 52-2q1-0.5q2-1=0
sendond derivative π2 = 70-2q2-0.5q1-1=0
2q1+0.5q2=51
2q2+0.5q1=69
solving these both we get q1= 18 and q2 = 30
Ответ:
answer: sorry
explanation: ds