The inverse market demand curve for bean sprouts is given by P = 90 - 3Q, and the total cost function for any firm in the industry is given by T C = 3Q.

1. Assume that the bean-sprout industry is perfectly competitive. Write the profit maximization problem of a bean-sprout firm. Find the industry output and the industry price.

2. Assume that two Cournot firms operate in the market. Find the industry output and the industry price.

3. Assume that two Bertrand firms operate in the market. The two firms are identical (i.e. they have the same total cost function). Find the industry output and the industry price.

4. Explain the Bertrand paradox.