A Niagara Falls retailer can sell two main brands of dried cannabis products: Green and Emerald. The retailer serves three market segments: gourmet, regular, and budget. Of the 200 consumers who come into its store each day, it knows that about 40 are in the gourmet category, 80 are in the regular category, and 80 are in the budget category, but it cannot directly tell them apart. Each consumer will buy at most one pack of one brand per visit, never both brands. The retailer wants to maximize its daily gross margin: its sales revenues minus its cost of goods sold. Regarding costs, it pays its wholesaler (the Ontario Cannabis Store) $35 per pack for Green and $50 per pack for Emerald. Regarding revenues, the consumer willingness-to-pay values for each market segment and brand are as follows.

• Gourmet consumers will pay up to $70 per pack for Green and $120 per pack for Emerald.

• Regular consumers will pay up to $60 per pack for Green and $80 per pack for Emerald.

• Value consumers will pay up to $50 per pack for Green and $60 per pack for Emerald.

Your task is to advise the retailer regarding the brand(s) to offer and the price(s) to charge.

Questions

Treat this situation as a sequential-move game that you need to model, analyze, and interpret. The retailer moves first by choosing which brand(s) to sell and what price(s) to charge. Nature moves second by determining which type of consumer comes into the store. Consumers move third by deciding which brand to buy, if any. For each of questions 1 and 2, you will need to define 1 decision variable and 3 participation conditions. For each of questions 3 and 4, you will need 2 decision variables, 3 participation conditions, and 3 incentive compatibility conditions.

1. Suppose the retailer sells only the Green brand. What price should the retailer charge, who would buy the product, and what would be the total gross margin?

2. Suppose the retailer sells only the Emerald brand. What price should the retailer charge, who would buy the product, and what would be the total gross margin?

3. Suppose the retailer wants to sell Green to value consumers, but Emerald to regulars and gourmets. What prices should the retailer charge, and what would be the total gross margin?

4. Suppose the retailer wants to sell Green to value and regular consumers, but Emerald to gourmets. What prices should the retailer charge, and what would be the total gross margin?

5. Given your results for questions 1 to 4 above, what should the retailer do?