# Homework#4: Cournot

```Homework #4: Cournot competition (10pts)
Two firms (call them A and B) compete in Cournot fashion by choosing quantity. Both firms have
identical technologies with the following cost functions: C  Q   10  2Q . The market demand is given
by Q  P   26  P .
1. What is firm A’s residual demand if firm B produces 0 units? What price would firm A charge?
(calculate)
2. What is firm A’s residual demand if firm B produces 6 units? What price would firm A charge?
Hint: firm A is a monopoly after 6 units are subtracted from the demand
3. What is firm A’s residual demand if firm B produces QB units?
4. What is firm A’s marginal revenue if firm B produces QB units?
5. What is firm A’s quantity if firm B produces QB units?
6. How much should firm B produce so that firm A would not produce anything even if firm A did
not have a fixed cost?
7. Write firm A’s best response function?
8. Write firm B’s best response function?
9. Draw both firms response functions on the graph below. Label axis and points where best
response functions intersect axis. Label which reaction function belongs to which firm.
10. Solve for Cournot equilibrium quantity of each firm and the total market quantity.
11. Solve for Cournot equilibrium price.
12. Find profits of each firm. Do you expect entry or exit in the long run?
Imagine that the government wants to subsidize firm B by offering 1 dollar subsidy per unit. Firm B’s
cost becomes C  Q   10   2  1 Q  10  Q .
13.
14.
15.
16.
Write firm B’s best response function.
Add firm B’s best response function to the graph below
Find Cournot equilibrium output per firm, total market output, market price, and firms profits
Can the government tax firm B’s profit and recoup the cost of the subsidy?
a. Calculate the amount of subsidy as Subsidy=QBx1
b. Calculate the increase in profit by comparing profits of firm B with and without subsidy
c. Make a conclusion
Q__
Q__
```