Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.
1. Find the marginal revenue MR1 of firm 1 as a function of q1 and q2.
2. Setting MR1=MC1, determine the reaction function of firm 1.
3. Find the marginal revenue MR2 of firm 2 as a function of q1 and q2.
4. Setting MR2=MC2, determine the reaction function of firm 2.
5. What quantity of output will each firm produce? That is, use the two reaction functions to find q1 and q2.
6. What is the market price P.
7. Determine the profits of each firm assuming there are no fixed costs.
Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.
1. Find the marginal revenue MR1 of firm 1 as a function of q1 and q2.
2. Setting MR1=MC1, determine the reaction function of firm 1.
3. Find the marginal revenue MR2 of firm 2 as a function of q1 and q2.
4. Setting MR2=MC2, determine the reaction function of firm 2.
5. What quantity of output will each firm produce? That is, use the two reaction functions to find q1 and q2.
6. What is the market price P.
7. Determine the profits of each firm assuming there are no fixed costs.
