7. An industry has two firms producing at a constant unit cost of $10 per unit, i.e., the cost function is given by $C_1(y_1) = 10y_1$, for both firms $i = 1,2$. The inverse demand curve for the industry is $p = 110 - 0.5y$, where $y = y_1 + y_2$, is the total industry output.
a. Assume that the firms choose their output levels simultaneously. That is, we have Cournot competition. Solve for the Cournot equilibrium. That is, find $y_1^c$, $y_2^c$, $p^c$, $\pi_1^c$ and $\pi_2^c$.
b. Assume that the firm 1 is a Stackelberg leader and the Firm 2 is a Cournot follower. Solve for the Stackelberg equilibrium. That is, find $y_1^s$, $y_2^s$, $p^s$, $\pi_1^s$ and $\pi_2^s$.
d. Suppose that firm 2 finds a cheaper way to produce the same product. The new cost function of firm 2 is $C_2(y_2) = 2y_2$. Assuming that the firms choose their output levels simultaneously, solve for the new (Cournot) equilibrium.
