You have the responsibility for establishing the pricing for a product to be released in three stages. A different and cheaper version of the product will be sold at the 2nd and 3rd stages. If the marginal cost of production is 50 percent lower for the second stage, and it is another 50 percent lower for the third stage, discuss the optimal pricing for the company in a case where the price elasticity of demand is twice as high for the second stage (as compared to the first stage), and the elasticity for the third stage is twice as high as it was for the second stage. Construct a numerical example and offer a conclusion about optimal pricing for the three stages. Show all your work.