$1.[5$ marks total; make sure to show your work$]$

Suppose the inverse demand function for two Cournot duopolists is given by:

$$

P $=150($q$1+$ q$2).$

$$

Each firm has a marginal cost of $$90$ per unit.

$$

a$.$ What is Firm One$$s marginal revenue?

$$

$$

$$

$$

$$

$$

b$.$ What is Firm One$$s best response curve?

$$

$$

$$

$$

$$

$$

c$.$ What are the Nash$-$Cournot equilibrium outputs?

$$

$$

$$

$$

$$

d$.$ What is the Nash$-$Cournot equilibrium price?

$$

$$

$$

$$

$$

e$.$ What is the firm one$$s profit in the Nash$-$Cournot equilibrium?$$

$$

$$

$$

$$

$$

$$

$$