The marketing team at Widgets Inc. is trying to determine the optimal price for a new product it has recently developed, code named “The Unicorn.” Management estimates that at a price of $30 per unit, it will sell 650,000 units. If it lowers the price to $27 it expects sales to increase to 875,000 units, and at a price of $24 it anticipates sales of one million units.
Because “The Unicorn” is based on entirely new technology, management expects there to be a substantial learning (i.e., production) curve. At a production volume of 650,000 units, management forecasts average costs of $15 per unit. At a production level of 875,000 units, costs will average $13 per unit; and at production volume of one million units costs should average $12 per unit.
Fixed costs will total $8 million per year, regardless of the level of production.
With this information in mind, what is the optimal price for the new product? Show your work and explain.