We solved the profit maximization problem for a monopolist producing in a single plant (factory), but what if the firm has plants at different locations (e.g., states), each with different costs of production? For example, costs will vary if wages differ across states, even if the same technology and management practices are used everywhere.

1. Would the monopolist always produce all its output in the plant with the lowest marginal cost and shut down operations in the other? Explain briefly how this decision should be made and what should be considered.

1. If a monopolist has two plants, the total output is ? = ?₁+ ?₂, where ?₁ is the quantity produced in plant 1, located in South Carolina, and ?₂ is the quantity produced in plant 2, located in Florida. The joint profit maximization problem considering both plants is:

max JI = 1 + 12 = IR)(91,92) -TC1(91) + TR2(91,92) - TC2(92). 91,92max J = p(q1, 92) x 91 - TC1(q1)]+ [p(91, 92) x q2 - TC2(92)] 91-92 = p(91, 92) x (91 + 92) - TC1(91) - TC2(92)