E1

Cargill has expanded its operations to the animal health industry and just got a patent on two different drugs, all made from natural ingredients, targeting cattle disease treatments. The patents granted the company monopoly rights in each market. Both drugs (₁ and ₂) are made in similar ways, with total cost of

(₁, ₂) = 50 + 2(₁ + ₂) + 0.5(₁ + ₂)²

It currently serves a few cattle farms in Southern states, where the inverse demand for drug ₁ is ₁(₁) = 500 ₁ and, for drug ₂, ₂(₂) = 1000 ₂, with ₁ and ₂ representing monthly quantities.

1. Set up Cargill's profit maximization problem.
2. Find the monopoly output for each drug.
3. Find the monopoly price for each drug.
4. What is Cargill's monthly profit from selling these two drugs?