A candle store sells scented candles at $8 per box. At this price, its monthly demand is 900 boxes (assume 30 days in a month). The shop orders candles from a supplier at $5 per box, and also pays $200 in shipping fees per order to the supplier. The supplier has production capacity 30 boxes a day, and delivering each order costs him $150. The variable cost of production for the supplier is $2 per box. Assume the holding cost for both the store and the supplier is $1 per box-month.

(a) What is the store’s order quantity and annual profit (assume they are acting optimally given the demand and financial parameters they face)? How about the supplier’s profit from the relationship with this store? What share of the supply chain profit goes to the store and what to the supplier?

(b) Now suppose that the supplier and the store were co-owned. How many boxes would be produced and shipped in a batch? What would be the supply chain profits?

(c) Disregard b). What are the parameters of the two part tariff contract (fixed price per order W0 and variable price per box W1) that ensures the total profits amongst the two firms are maximized and the profit shares are the same as in (a)?

(d) Note how the optimal two-tariff contract differs from the one of the status quo. How would you describe the supplier’s current thinking?