Euphoria Chocolate (EC), a producer of premier chocolates, would like to set up production in Mexico to have better access to the Mexican consumers. But the firm is not very familiar with the Mexican market and considers starting a joint venture with a Mexican candy firm, Grupo Lorena (GL). Alternatively, it is considering building its own greenfield plant in Mexico. Use the following information to answer the questions below.

Inverse Mexican demand for Euphoria Chocolate products with greenfield plant: P = 48 - 2Q. Inverse Mexican Demand for Euphoria Chocolate products with joint venture: P = 48 a - 2Q, where a is a parameter greater than 1, representing the boost in demand. Constant marginal costs of 12, regardless of whether Euphoria Chocolate does a joint venture or builds a greenfield plant. Euphoria Chocolate gets 50% of the profits in a joint venture.

5. Set up Euphoria Chocolate's profit function if it produced with a greenfield plant. Evaluate the first-order conditions and calculate the optimal quantity (Q^G*).

6. Set up the joint venture's profit function. Evaluate the first-order conditions and calculate the optimal quantity in this case (Q^J*).

7. Suppose that the joint venture would mean that the parameter a takes the value of 1.25. Should Euphoria Chocolate joint venture with Grupo Lorena in this case or use a greenfield plant? Show your work.

8. Suppose that Grupo Lorena is willing to negotiate the share of profits that Euphoria Chocolate would get. What share of the profits would make Euphoria Chocolate indifferent between the joint venture or greenfield? Show calculations.