Problem (2 pages)
Part 1
Suppose the inverse market demand function for a two-firm Cournot model is given by where is the total output produced in the market, P is the market price, is the quantity of output produced by firm 1, is the quantity of output produced by firm 2.
The marginal costs of the two firms are and .
For a linear inverse demand function , the marginal revenue is given by .
1. Find the marginal revenue of firm 1 as a function of and .
2. Setting , determine the reaction function of firm 1.
3. Find the marginal revenue of firm 2 as a function of and .
4. Setting , 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 and .
6. What is the market price P.
7. Determine the profits of each firm assuming there are no fixed costs.
Part 2
Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by where is the total output produced in the market, P is the market price, is the quantity of output produced by firm 1, is the quantity of output produced by firm 2. Firm is leader and firm 2 is follower.
The marginal costs of the two firms are and .
1. What is the follower’s reaction function?
2. Determine the equilibrium output level for both the leader and the follower.
3. Determine the equilibrium market price.
4. Determine the profits of the leader and the follower assuming there are no fixed costs.
Part 3
Use information from parts 1 & 2 to compare the output levels and profits in settings characterized by Cournot and Stackelberg.
|
Models |
Output |
Profits |
|
Cournot Duopoly |
q1=? and q2=? |
Profit1=?; Profits2=? |
|
Stackelberg Duopoly |
q1=?and q2=? |
Profit1=?; Profits2=? |
0 comments