only typed solution Let's study the Cournot model more generally. Assume that there are n firms, wheren is exogenously given. The output of the i th firm is qi and the total output Q is thesum of the output of each firm: Q = q1 + q2 + ... + qn. The (inverse) marketdemand function is given by p(Q) = a - bQ and each Firm i's total cost is given by C(qi) = mqi, where a, b, and m are all positive constants. (a) We know that Firm 1 triesto maximize its profit through its choice of q1, i.e. Firm 1 chooses q1 to solve max q1 \pi 1(q1, q2, . .., qn) = q1·p(Q) - C(q1) Write down the profit maximizingcondition for Firm 1, and obtain the best - response function q* 1 (q2, q3, . .., qn)for Firm 1. (b) From part (a), we know that each Firm i 0 s best response function isgiven by q * i (q-i) = am 2b - Pj6 = iqj 2, where q-i denotes the quantitieschosen by all firms besides Firm i and Pj6 = iqj = q1 + q2 + ... qi-1 + qi+1 + . . . qn. Find the symmetric Nash equilibrium, i.e. find the Nash equilibrium inwhich all firms choose the same quantity: q* 1 = q*2 = ... = q*n = q*.What is the corresponding market price in this equilibrium? (c) For the symmetric Nashequilibrium found in part (b), if we set n = 1, we know that the equilibrium price andquantity correspond to the monopoly price and quantity. What then would happen tothe equilibrium price and quantity as n approaches infinity?

Market Demand : p (Q) = a - b QCost function of each firm = mqiWhere , P = Price , Q = Market…

. Let's study the Cournot model more generally. Assume that there are n firms, where n is exogenously given. The output of the i th firm is qi and the total output Q is the sum of the output of each firm: Q q1 + q2 +. . . + qn. The (inverse) market demand function is given by p(Q) = a - bQ and each Firm i's total cost is given by C( qi) = mqi, where a, b, and m are all positive constants. (a) We know that Firm 1 tries =

. Let's study the Cournot model more generally. Assume that there are n firms, where n is exogenously given. The output of the i th firm is qi and the total output Q is the sum of the output of each firm: Q q1 + q2 +. . . + qn. The (inverse) market demand function is given by p(Q) = a - bQ and each Firm i's total cost is given by C( qi) = mqi, where a, b, and m are all positive constants. (a) We know that Firm 1 tries =

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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only typed solution

Let's study the Cournot model more generally. Assume that there are n firms, where
n is exogenously given. The output of the i th firm is qi and the total output Q is the
sum of the output of each firm: Q = q1 + q2 + ... + qn. The (inverse) market
demand function is given by p(Q) = a - bQ and each Firm i's total cost is given by C(
qi) = mqi, where a, b, and m are all positive constants. (a) We know that Firm 1 tries
to maximize its profit through its choice of q1, i.e. Firm 1 chooses q1 to solve max q
1 \pi 1(q1, q2, . .., qn) = q1·p(Q) - C(q1) Write down the profit maximizing
condition for Firm 1, and obtain the best - response function q* 1 (q2, q3, . .., qn)
for Firm 1. (b) From part (a), we know that each Firm i 0 s best response function is
given by q * i (q-i) = am 2b - Pj6 = iqj 2, where q-i denotes the quantities
chosen by all firms besides Firm i and Pj6 = iqj = q1 + q2 + ... qi-1 + qi
+1 + . . . qn. Find the symmetric Nash equilibrium, i.e. find the Nash equilibrium in
which all firms choose the same quantity: q* 1 = q*2 = ... = q*n = q*.
What is the corresponding market price in this equilibrium? (c) For the symmetric Nash
equilibrium found in part (b), if we set n = 1, we know that the equilibrium price and
quantity correspond to the monopoly price and quantity. What then would happen to
the equilibrium price and quantity as n approaches infinity?

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