Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 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 q_1 and q_2.
2. Setting MR1=MC1, determine the reaction function of firm 1.
3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.
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 reactions functions to find q_1 and q_2.
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=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 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 q_1 and q_2.
2. Setting MR1=MC1, determine the reaction function of firm 1.
3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.
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 reactions functions to find q_1 and q_2.
6. What is the market price P.
7. Determine the profits of each firm assuming there are no fixed costs.
