Cost function.

Show your work and calculations in each part. You will not get points even if you have

the correct answer but don’t show the steps on how you reach your answer or if you don’t

explain your reasoning. All submitted work must be independent work. Late submissions

will not be accepted. GOOD LUCK!

1. Answer the following questions assuming that inverse demand function is given by

P = 100 – q1 – q2 and that the cost function is given by Ci(qi) = q

2

i

for a market with

two firms.

a. (5 points) Suppose that the firms are in a Cournot duopoly. Find the Nash

Equilibrium quantities of each firm.

b. (4 points) What is the profit of each firm in the Cournot duopoly setup?

c. (8 points) Suppose that the firms are in a Stackelberg’s duopoly. Find the Subgame Perfect Nash Equilibrium quantities of each firm.

d. (4 points) What is the profit of each firm in the Stackelberg’s duopoly setup?

e. (4 points) Compare quantities you found in a vs c, then compare profits you

found in b vs d. Write down an intuitive explanation to why you think the profits

changed this way.