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Part B: Consider a two firm oligopoly facing a market demand $P = 100 - 2Q$, where $Q = q_1 + q_2$; $q_1$ is Firm 1s output and $q_2$ is firm 2s output. Let Firm 1s marginal cost is $12 while Firm 2s marginal cost is $20. In a cournot equilibrium: 1. How much output does each firm produce? 2. What will the market price be? 3. Draw the best response curves and label clearly.

          Part B: Consider a two firm oligopoly facing a market demand $P = 100 - 2Q$, where $Q = q_1 + q_2$;
$q_1$ is Firm 1s output and $q_2$ is firm 2s output. Let Firm 1s marginal cost is $12 while Firm 2s marginal
cost is $20. In a cournot equilibrium:
1. How much output does each firm produce?
2. What will the market price be?
3. Draw the best response curves and label clearly.

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part b consider a two firm oligopoly facing a market demand p 100 2q where q q1 q2 q1 is firm 1s output and q2 is firm 2s output let firm 1s marginal cost is 12 while firm 2s marginal co 45741

Added by Olivia C.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Aarya B

12/14/2023

Step 1

How much output does each firm produce? First, we need to find the reaction functions for each firm. The demand function is $P = 100 - 2Q = 100 - 2(q_1 + q_2)$. Firm 1's revenue is $R_1 = Pq_1 = (100 - 2q_1 - 2q_2)q_1 = 100q_1 - 2q_1^2 - 2q_1q_2$. Firm 1's Show more…

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Part B: Consider a two firm oligopoly facing a market demand $P = 100 - 2Q$, where $Q = q_1 + q_2$; $q_1$ is Firm 1s output and $q_2$ is firm 2s output. Let Firm 1s marginal cost is $12 while Firm 2s marginal cost is $20. In a cournot equilibrium: 1. How much output does each firm produce? 2. What will the market price be? 3. Draw the best response curves and label clearly.

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Transcript

00:01 Here we are given p equal to 100 minus 0 .5 times q1 plus q2 and c1 equal to 5q1, c2 equal to 0 .5 q2 square.

00:14 Now, first one we have to think of the cournot model.

00:20 So, first one here we have to find the reaction functions.

00:28 Now, profit function of firm 1 is pi 1 equal to tr1 minus tc1.

00:41 So, it is pq1 minus 5q1 because c1 is given as 5q1.

00:47 So, which is equal to p minus 5 times q1, mark it as equation 1.

00:52 Now, from this we may have pi 1 equal to p is 100 minus 0 .5 q1 minus 0 .5 q2 minus 5 multiplied by q1.

01:05 Hence, d5 for optimal condition d51 by dq1 is equal to so differentiate this with respect to q.

01:14 So, it is 95 minus 0 .5 q1 minus 0 .5 q2 minus 0 .5 q1 which is equal to 95 minus q1 minus 0 .5 q2 which is 0.

01:43 Hence, 95 minus 0 .5 q2 equal to q1.

01:48 Hence, the reaction function for firm 1 we are denoting it as rf1.

01:55 Next one, profit function of firm 2.

02:03 So, it is pi 2 equal to tr2 minus tc2.

02:08 So, it is pq2 minus 0 .5 q2 square mark it as equation 2.

02:14 So, for the optimal condition we may have d52 divided by dq2 equal to 100 minus 0 .5 q1 minus q2 minus q2 which is 0.

02:28 So, 100 minus 0 .5 q1 minus 2 q2 equal to 0.

02:33 Hence, 100 minus 0 .5 q1 divided by 2 equal to q2.

02:39 So, this one is the profit function that is rf1 and br2...

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