Reference no: EM132629716

The Silky Shirts Company based in Thailand makes silk women's shirts for a retailer in the U.S. It costs Silky $30 to make each shirt, it sells them to the retailer for $50 and the shirts retail for $100. The retailer estimates he can sell an average of 800 shirts with a standard deviation of 400 at this price per season (normally distributed). The retailer sells all remaining shirts for $20 at the end of the season.

a) How many shirts should the retailer order to maximize his profits?

b) If Silky had its own stores, and could make and sell (at the same retail price as above) its own shirts in its own stores instead of needing the retailer as a middleman, how many shirts would it order assuming demand remained the same as above?

c) Assume that Silky offers the retailer a revenue sharing contract where the retailer shares half the revenue on all sold shirts with Silky, and in return Silky reduces its price from $50. To what level would Silky have to reduce its price to induce the retailer to order as many units as the integrated company would order in Part b) above? (The retailer still sells the shirts for $100 during the season and discounts them to $20 at the end of the season but now gives half of all the revenue obtained to Silky.)