Question 1:
Consider the following market:
There are two firms,
Firm 1 with a cost function of c(q1) = 16q1
and Firm 2 with a cost function ofc(q2) = 4q2.
Market demand is given by Q = 64 − p.
1. Solve for the Nash equilibrium of the Cournot duopoly model for this
market. Additionally, find the market price, individual firm profits,
consumer surplus, and total welfare.
2. Solve for the subgame perfect Nash equilibrium of the Stackelberg
model for this market. Assume that Firm 1 chooses its output first,
then Firm 2 observes Firm 1‘s output and selects its own output. Additionally,
give the quantities that will be produced, price, individual
firm profits, consumer surplus, and total welfare at the SPNE.
3. Compare output, price, individual firm profits, consumer surplus, and
total welfare in your answers to parts A and B. Are the differences
in any of those market outcomes in a different direction from what
we normally expect with Cournot and Stackelberg? If there are any,
identify which market outcome is different from your expectation, and
explain what drives the difference in this case. If there