Question

An industry consists of two (perfectly) firms. Firm 1 has a total cost function given by ??1(?1)=?1 +(?1)^2

while firm 2 has a total cost function given by ??2(?2)=3*?2+(1/2)*(?2)^2 .

1. (a) Let ? denote the (exogenous) price at which each firm can sell its output. Write down each firm’s profit-maximization problem and the associated first-order conditions (FOCs).

2. (b) Derive the firms’ supply functions ?∗(?) and ?∗(?) and verify that these functions are

   linearly increasing in ?.

3. (c) Derive the industry supply curve ?(?). [Hint: Draw a picture and remember the notion of horizontal summation. You should demonstrate that the industry supply curve is a piecewise function in ?]

4. Again assuming that the firms act as price takers, find the industry equilibrium when the industry demand curve is given by ??(?)=(9/2)-(1/2)p .[Hint: It may be useful to add the relevant to the graph considered in part (c)]

5. (e) Calculate the output and profit of each firm under the equilibrium characterized in part (d).

Answer 1